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  • Articles  (69)
  • Articles: DFG German National Licenses  (69)
  • Articles and Proceedings (GFZpublic)
  • Blackwell Publishers, Inc.  (69)
  • Economics  (69)
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  • Articles  (69)
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  • Articles: DFG German National Licenses  (69)
  • Articles and Proceedings (GFZpublic)
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  • 1
    Electronic Resource
    Electronic Resource
    VASIČEK BEYOND THE NORMAL (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A general Ornstein-Uhlenbeck (OU) process is obtained upon replacing the Brownian motion appearing in the defining stochastic differential equation with a general Lévy process. Certain properties of the Brownian ancestor are distribution-free and carry over to the general OU process. Explicit expressions are obtainable for expected values of a number of functionals of interest also in the general case. Special attention is paid here to gamma- and Poisson-driven OU processes. The Brownian, Poisson, and gamma versions of the OU process are compared in various respects; in particular, their aptitude to describe stochastic interest rates is discussed in view of some standard issues in financial and actuarial mathematics: prices of zero-coupon bonds, moments of present values, and probability distributions of present values of perpetuities. The problem of possible negative interest rates finds its resolution in the general setup by taking the driving Lévy process to be nondecreasing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00206.x
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  • 2
    Electronic Resource
    Electronic Resource
    ON THE STABILITY OF CONTINUOUS-TIME PORTFOLIO PROBLEMS WITH STOCHASTIC OPPORTUNITY SET (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we present some counterexamples to show that an uncritical application of the usual methods of continuous-time portfolio optimization can be misleading in the case of a stochastic opportunity set. Cases covered are problems with stochastic interest rates, stochastic volatility, and stochastic market price of risk. To classify the problems occurring with stochastic market coefficients, we further introduce two notions of stability of portfolio problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00197.x
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  • 3
    Electronic Resource
    Electronic Resource
    QUANTO LOOKBACK OPTIONS (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The lookback feature in a quanto option refers to the payoff structure where the terminal payoff of the quanto option depends on the realized extreme value of either the stock price or the exchange rate. In this paper, we study the pricing models of European and American lookback options with the quanto feature. The analytic price formulas for two types of European-style quanto lookback options are derived. The success of the analytic tractability of these quanto lookback options depends on the availability of a succinct analytic representation of the joint density function of the extreme value and terminal value of the stock price and exchange rate. We also analyze the early exercise policies and pricing behaviors of the quanto lookback options with the American feature. The early exercise boundaries of these American quanto lookback options exhibit properties that are distinctive from other two-state American option models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00199.x
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  • 4
    Electronic Resource
    Electronic Resource
    Pareto Equilibria with coherent measures of risk (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper, we provide a definition of Pareto equilibrium in terms of risk measures, and present necessary and sufficient conditions for equilibrium in a market with finitely many traders (whom we call “banks”) who trade with each other in a financial market. Each bank has a preference relation on random payoffs which is monotonic, complete, transitive, convex, and continuous; we show that this, together with the current position of the bank, leads to a family of valuation measures for the bank. We show that a market is in Pareto equilibrium if and only if there exists a (possibly signed) measure that, for each bank, agrees with a positive convex combination of all valuation measures used by that bank on securities traded by that bank.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00187.x
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  • 5
    Electronic Resource
    Electronic Resource
    Hedging and Portfolio Optimization in Financial Markets with a Large Trader (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter-dependent semimartingales, and its mathematical analysis relies on the nonlinear integration theory of such semimartingale families. The Itô–Wentzell formula is used to prove absence of arbitrage for the large investor, and, using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00179.x
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  • 6
    Electronic Resource
    Electronic Resource
    Approximation of Optimal Reinsurance and Dividend Payout Policies (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider the stochastic process of the liquid assets of an insurance company assuming that the management can control this process in two ways: first, the risk exposure can be reduced by affecting reinsurance, but this decreases the premium income; and second, a dividend has to be paid out to the shareholders. The aim is to maximize the expected discounted dividend payout until the time of bankruptcy. The classical approach is to model the liquid assets or risk reserve process of the company as a piecewise deterministic Markov process. However, within this setting the control problem is very hard. Recently several papers have modeled this problem as a controlled diffusion, presuming that the policy obtained is in some sense good for the piecewise deterministic problem as well. We will clarify this statement in our paper. More precisely, we will first show that the value function of the controlled diffusion provides an asymptotic upper bound for the value functions of the piecewise deterministic problems under diffusion scaling. Finally it will be shown that the upper bound is achieved in the limit under the optimal feedback control of the diffusion problem. This property is called asymptotic optimality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00183.x
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  • 7
    Electronic Resource
    Electronic Resource
    QUADRATIC TERM STRUCTURE MODELS FOR RISK-FREE AND DEFAULTABLE RATES (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper, quadratic term structure models (QTSMs) are analyzed and characterized in a general Markovian setting. The primary motivation for this work is to find a useful extension of the traditional QTSM, which is based on an Ornstein–Uhlenbeck (OU) state process, while maintaining the analytical tractability of the model. To accomplish this, the class of quadratic processes, consisting of those Markov state processes that yield QTSM, is introduced. The main result states that OU processes are the only conservative quadratic processes. In general, however, a quadratic potential can be added to allow QTSMs to model default risk. It is further shown that the exponent functions that are inherent in the definition of the quadratic property can be determined by a system of Riccati equations with a unique admissible parameter set. The implications of these results for modeling the term structure of risk-free and defaultable rates are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00203.x
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  • 8
    Electronic Resource
    Electronic Resource
    A FAMILY OF TERM-STRUCTURE MODELS FOR LONG-TERM RISK MANAGEMENT AND DERIVATIVE PRICING (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we propose a new family of term-structure models based on the Flesaker and Hughston (1996) positive-interest framework. The models are Markov and time homogeneous, with correlated Ornstein-Uhlenbeck processes as state variables. We provide a theoretical analysis of the one-factor model and a thorough emprical analysis of the two-factor model. This allows us to identify the key factors in the model affecting interest-rate dynamics. We conclude that the new family of models should provide a useful tool for use in long-term risk management. Suitably parameterized, they can satisfy a wide range of desirable criteria, including:〈list xml:id="l1" style="custom"〉• sustained periods of both high and low interest rates similar to the cycle lengths we have observed over the course of the 20th century in the United Kingdom and the United States• realistic probabilities of both high and low interest rates consistent with historical data and without the need for regular recalibration• a wide range of shapes of yield curves, again consistent with what we have observed in the past and including the recent Japanese yield curve.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00198.x
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  • 9
    Electronic Resource
    Electronic Resource
    A GENERAL FRAMEWORK FOR PRICING CREDIT RISK (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A framework is provided for pricing derivatives on defaultable bonds and other credit-risky contingent claims. The framework is in the spirit of reduced-form models, but extends these models to include the case that default can occur only at specific times, such as coupon payment dates. Although the framework does not provide an efficient setting for obtaining results about structural models, it is sufficiently general to include most structural models, and thereby highlights the commonality between reduced-form and structural models. Within the general framework, multiple recovery conventions for contingent claims are considered: recovery of a fraction of par, recovery of a fraction of a no-default version of the same claim, and recovery of a fraction of the pre-default value of the claim. A stochastic-integral representation for credit-risky contingent claims is provided, and the integrand for the credit exposure part of this representation is identified. In the case of intensity-based, reduced-form models, credit spread and credit-risky term structure are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.t01-1-00193.x
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  • 10
    Electronic Resource
    Electronic Resource
    On The Fundamental Theorem Of Asset Pricing: Random Constraints And Bang-Bang No-Arbitrage Criteria (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The paper generalizes and refines the Fundamental Theorem of Asset Pricing of Dalang, Morton, and Willinger (1990) in the following two respects: (a) the result is extended to a model with general portfolio constraints, and (b) versions of the no-arbitrage criterion based on the bang-bang principle in control theory are developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00189.x
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  • 11
    Electronic Resource
    Electronic Resource
    A note on completeness in large financial markets (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We study completeness in large financial markets, namely markets containing countably many assets. We investigate the relationship between asymptotic completeness in the global market and completeness in the finite submarkets, under a no-arbitrage assumption. We also suggest a way to approximate a replicating strategy in the large market by finite-dimensional portfolios. Furthermore, we find necessary and sufficient conditions for completeness to hold in a factor model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00193.x
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  • 12
    Electronic Resource
    Electronic Resource
    The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's modeling of foreign exchange markets under transaction costs. The financial market is described by a d×d matrix-valued stochastic process (Πt)Tt=0 specifying the mutual bid and ask prices between d assets. We introduce the notion of “robust no arbitrage,” which is a version of the no-arbitrage concept, robust with respect to small changes of the bid-ask spreads of (Πt)Tt=0. The main theorem states that the bid-ask process (Πt)Tt=0 satisfies the robust no-arbitrage condition iff it admits a strictly consistent pricing system. This result extends the theorems of Harrison-Pliska and Kabanov-Stricker pertaining to the case of finite Ω, as well as the theorem of Dalang, Morton, and Willinger and Kabanov, Rásonyi, and Stricker, pertaining to the case of general Ω. An example of a 5 × 5-dimensional process (Πt)2t=0 shows that, in this theorem, the robust no-arbitrage condition cannot be replaced by the so-called strict no-arbitrage condition, thus answering negatively a question raised by Kabanov, Rásonyi, and Stricker.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00180.x
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  • 13
    Electronic Resource
    Electronic Resource
    Asymptotics of the price oscillations of a European call option in a tree model (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: It is well known that the price of a European vanilla option computed in a binomial tree model converges toward the Black-Scholes price when the time step tends to zero. Moreover, it has been observed that this convergence is of order 1/n in usual models and that it is oscillatory. In this paper, we compute this oscillatory behavior using asymptotics of Laplace integrals, giving explicitly the first terms of the asymptotics. This allows us to show that there is no asymptotic expansion in the usual sense, but that the rate of convergence is indeed of order 1/n in the case of usual binomial models since the second term (in 〈inlineGraphic alt="inline image" href="urn:x-wiley:09601627:MAFI192:MAFI_192_mu1" location="equation/MAFI_192_mu1.gif"/〉) vanishes. The next term is of type C2(n)/n, with C2(n) some explicit bounded function of n that has no limit when n tends to infinity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00192.x
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  • 14
    Electronic Resource
    Electronic Resource
    Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Black's (1995) model of interest rates as options assumes that there is a shadow instantaneous interest rate that can become negative, while the nominal instantaneous interest rate is a positive part of the shadow rate due to the option to convert to currency. As a result of this currency option, all term rates are strictly positive. A similar model was independently discussed by Rogers (1995). When the shadow rate is modeled as a diffusion, we interpret the zero-coupon bond as a Laplace transform of the area functional of the underlying shadow rate diffusion (evaluated at the unit value of the transform parameter). Using the method of eigenfunction expansions, we derive analytical solutions for zero-coupon bonds and bond options under the Vasicek and shifted CIR processes for the shadow rate. This class of models can be used to model low interest rate regimes. As an illustration, we calibrate the model with the Vasicek shadow rate to the Japanese Government Bond data and show that the model provides an excellent fit to the Japanese term structure. The current implied value of the instantaneous shadow rate in Japan is negative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00181.x
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  • 15
    Electronic Resource
    Electronic Resource
    Should Stochastic Volatility Matter to the Cost-Constrained Investor? (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Significant strides have been made in the development of continuous-time portfolio optimization models since Merton (1969). Two independent advances have been the incorporation of transaction costs and time-varying volatility into the investor's optimization problem. Transaction costs generally inhibit investors from trading too often. Time-varying volatility, on the other hand, encourages trading activity, as it can result in an evolving optimal allocation of resources. We examine the two-asset portfolio optimization problem when both elements are present. We show that a transaction cost framework can be extended to include a stochastic volatility process. We then specify a transaction cost model with stochastic volatility and show that when the risk premium is linear in variance, the optimal strategy for the investor is independent of the level of volatility in the risky asset. We call this the Variance Invariance Principle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00185.x
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  • 16
    Electronic Resource
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    STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q-OPTIMAL MEASURE (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The aim of this paper is to study the minimal entropy and variance-optimal martingale measures for stochastic volatility models. In particular, for a diffusion model where the asset price and volatility are correlated, we show that the problem of determining the q-optimal measure can be reduced to finding a solution to a representation equation. The minimal entropy measure and variance-optimal measure are seen as the special cases q= 1 and q= 2 respectively. In the case where the volatility is an autonomous diffusion we give a stochastic representation for the solution of this equation. If the correlation ρ between the traded asset and the autonomous volatility satisfies ρ2 〈 1/q, and if certain smoothness and boundedness conditions on the parameters are satisfied, then the q-optimal measure exists. If ρ2≥ 1/q, then the q-optimal measure may cease to exist beyond a certain time horizon. As an example we calculate the q-optimal measure explicitly for the Heston model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00204.x
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  • 17
    Electronic Resource
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    SOME REMARKS ON ARBITRAGE AND PREFERENCES IN SECURITIES MARKET MODELS (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We introduce the notion of a market-free-lunch that depends on the preferences of all agents participating in the market. In semimartingale models of securities markets, we characterize no arbitrage (NA) and no-free-lunch-with-vanishing-risk (NFLVR) in terms of the market-free-lunch and show that the difference between NA and NFLVR consists in the selection of the class of monotone, respectively monotone and continuous, utility functions that determines the absence of the market-free-lunch. We also provide a direct proof of the equivalence between the absence of a market-free-lunch, with respect to monotone concave preferences, and the existence of an equivalent (local/sigma) martingale measure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00194.x
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  • 18
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    OPTIMAL SHOUTING POLICIES OF OPTIONS WITH STRIKE RESET RIGHT (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The reset right embedded in an option contract is the privilege given to the option holder to reset certain terms in the contract according to specified rules at the moment of shouting, where the time to shout is chosen optimally by the holder. For example, a shout option with strike reset right entitles its holder to choose the time to take ownership of an at-the-money option. This paper develops the theoretical framework of analyzing the optimal shouting policies to be adopted by the holder of an option with reset right on the strike price. It is observed that the optimal shouting policy depends on the time dependent behaviors of the expected discounted value of the at-the-money option received upon shouting. During the time period when the theta of the expected discounted value of the new option received is positive, it is never optimal for the holder to shout at any level of asset value. At those times when the theta is negative, we show that there exists a threshold value for the asset price above which the holder of a reset put option should shout optimally. For the shout floor, we obtain an analytic representation of the price function. For the reset put option, we derive the integral representation of the shouting right premium and analyze the asymptotic behaviors of the optimal shouting boundaries at time close to expiry and infinite time from expiry. We also provide numerical results for the option values and shouting boundaries using the binomial scheme and recursive integration method. Accuracy and run time efficiency of these two numerical schemes are compared.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00196.x
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  • 19
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    Fundamental Theorems of Asset Pricing for Good Deal Bounds (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We prove fundamental theorems of asset pricing for good deal bounds in incomplete markets. These theorems relate arbitrage-freedom and uniqueness of prices for over-the-counter derivatives to existence and uniqueness of a pricing kernel that is consistent with market prices and the acceptance set of good deals. They are proved using duality of convex optimization in locally convex linear topological spaces. The concepts investigated are closely related to convex and coherent risk measures, exact functionals, and coherent lower previsions in the theory of imprecise probabilities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00186.x
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  • 20
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    Valuation by Simulation of Contingent Claims with Multiple Early Exercise Opportunities (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper introduces the application of Monte Carlo simulation technology to the valuation of securities that contain many (buying or selling) rights, but for which a limited number can be exercised per period, and penalties if a minimum quantity is not exercised before maturity. These securities combine the characteristics of American options, with the additional constraint that only a few rights can be exercised per period and therefore their price depends also on the number of living rights (i.e., American-Asian-style payoffs), and forward securities. These securities give flexibility-of-delivery options and are common in energy markets (e.g., take-or-pay or swing options) and as real options (e.g., the development of a mine). First, we derive a series of properties for the price and the optimal exercise frontier of these securities. Second, we price them by simulation, extending the Ibáñez and Zapatero (2004) method to this problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00190.x
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  • 21
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    Exercise Regions And Efficient Valuation Of American Lookback Options (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper presents an efficient method to compute the values and early exercise boundaries of American fixed strike lookback options. The method reduces option valuation to a single optimal stopping problem for standard Brownian motion and an associated path-dependent functional, indexed by one parameter in the absence of dividends and by two parameters in the presence of a dividend rate. Numerical results obtained by this method show that, after a space-time transformation, the stopping boundaries are well approximated by certain piecewise linear functions with a few pieces, leading to fast and accurate approximations for American lookback option values. An explicit decomposition formula for American lookback options is derived and applied not only to the development of these approximations but also to the asymptotic analysis of the early exercise boundary near the expiration date.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00191.x
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    CHOQUET INSURANCE PRICING: A CAVEAT (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We show that, if prices in a market are Choquet expectations, the existence of one frictionless asset may force the whole market to be frictionless. Any risky asset will cause this collapse if prices depend only on the distribution with respect to a given nonatomic probability measure; the frictionless asset has to be fully revealing if such dependence is not assumed. Similar considerations apply to law-invariant coherent risk measures.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00201.x
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    Stochastic Volatility Corrections for Interest Rate Derivatives (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We study simple models of short rates such as the Vasicek or CIR models, and compute corrections that come from the presence of fast mean-reverting stochastic volatility. We show how these small corrections can affect the shape of the term structure of interest rates giving a simple and efficient calibration tool. This is used to price other derivatives such as bond options. The analysis extends the asymptotic method developed for equity derivatives in Fouque, Papanicolaou, and Sircar (2000b). The assumptions and effectiveness of the theory are tested on yield curve data.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00188.x
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    MultiFactor Valuation of Floating Range Notes (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Under a one-factor Gaussian Heath-Jarrow-Morton model, Turnbull (1995) as well as Navatte and Quittard-Pinon (1999) have provided explicit pricing solutions for range notes contracts. The present paper generalizes such closed-form solutions for the context of a multifactor Gaussian HJM framework.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00182.x
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    Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider a nonparametric method to estimate the expected shortfall—that is, the expected loss on a portfolio of financial assets knowing that the loss is larger than a given quantile. We derive the asymptotic properties of the kernel estimators of the expected shortfall and its first-order derivative with respect to portfolio allocation in the context of a stationary process satisfying strong mixing conditions. An empirical illustration is given for a portfolio of stocks. Another empirical illustration deals with data on fire insurance losses.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00184.x
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    THE SQUARED ORNSTEIN-UHLENBECK MARKET (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We study a complete market containing J assets, each asset contributing to the production of a single commodity at a rate that is a solution to the squared Ornstein-Uhlenbeck (Cox-Ingersoll-Ross) SDE. The assets are owned by K agents with CRRA utility functions, who follow feasible consumption/investment regimes so as to maximize their expected time-additive utility from consumption. We compute the equilibrium for this economy and determine the state-price density process from market clearing. Reducing to a single (representative) agent, and exploiting the relation between the squared-OU and squared-Bessel SDEs, we obtain closed-form expressions for the values of bonds, assets, and options on the total asset value. Typical model parameters are estimated by fitting bond price data, and we use these parameters to price the assets and options numerically. Implications for the total asset price itself as a diffusion are discussed. We also estimate implied volatility surfaces for options and bond yields.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00202.x
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    MONTE CARLO METHODS FOR THE VALUATION OF MULTIPLE-EXERCISE OPTIONS (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We discuss Monte Carlo methods for valuing options with multiple-exercise features in discrete time. By extending the recently developed duality ideas for American option pricing, we show how to obtain estimates on the prices of such options using Monte Carlo techniques. We prove convergence of our approach and estimate the error. The methods are applied to options in the energy and interest rate derivative markets.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00205.x
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    Dynamic Minimization of Worst Conditional Expectation of Shortfall (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In a complete financial market model, the shortfall-risk minimization problem at the terminal date is treated for the seller of a derivative security F. The worst conditional expectation of the shortfall is adopted as the measure of this risk, ensuring that the minimized risk satisfies certain desirable properties as the dynamic measure of risk, as proposed by Cvitanić and Karatzas (1999). The terminal value of the optimized portfolio is a binary functional dependent on F and the Radon-Nikodym density of the equivalent local martingale measure. In particular, it is observed that there exists a positive number x* that is less than the replicating cost xF of F, and that the strategy minimizing the expectation of the shortfall is optimal if the hedger's capital is in the range [x*, xF].
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    PRICING IN AN INCOMPLETE MARKET WITH AN AFFINE TERM STRUCTURE (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We apply the principle of equivalent utility to calculate the indifference price of the writer of a contingent claim in an incomplete market. To recognize the long-term nature of many such claims, we allow the short rate to be random in such a way that the term structure is affine. We also consider a general diffusion process for the risky stock (index) in our market. In a complete market setting, the resulting indifference price is the same as the one obtained by no-arbitrage arguments. We also show how to compute indifference prices for two types of contingent claims in an incomplete market, in the case for which the utility function is exponential. The first is a catastrophe risk bond that pays a fixed amount at a given time if a catastrophe does not occur before that time. The second is equity-indexed term life insurance which pays a death benefit that is a function of the short rate and stock price at the random time of the death of the insured. Because we assume that the occurrence of the catastrophe or the death of the insured is independent of the financial market, the markets for the catastrophe risk bond and the equity-indexed life insurance are incomplete.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00195.x
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    THE MOMENT FORMULA FOR IMPLIED VOLATILITY AT EXTREME STRIKES (2004)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 14 (2004), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Consider options on a nonnegative underlying random variable with arbitrary distribution. In the absence of arbitrage, we show that at any maturity T, the large-strike tail of the Black-Scholes implied volatility skew is bounded by the square root of 2|x|/T, where x is log-moneyness. The smallest coefficient that can replace the 2 depends only on the number of finite moments in the underlying distribution. We prove the moment formula, which expresses explicitly this model-independent relationship. We prove also the reciprocal moment formula for the small-strike tail, and we exhibit the symmetry between the formulas. The moment formula, which evaluates readily in many cases of practical interest, has applications to skew extrapolation and model calibration.
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    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.00200.x
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    Quantiles of the Euler Scheme for Diffusion Processes and Financial Applications (2003)
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    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we briefly present the results obtained in our paper (Talay and Zheng 2002a) on the convergence rate of the approximation of quantiles of the law of one component of (Xt), where (Xt) is a diffusion process, when one uses a Monte Carlo method combined with the Euler discretization scheme. We consider the case where (Xt) is uniformly hypoelliptic (in the sense of Condition (UH) below), or the inverse of the Malliavin covariance of the component under consideration satisfies the condition (M) below. We then show that Condition (M) seems widely satisfied in applied contexts. We particularly study financial applications: the computation of quantiles of models with stochastic volatility, the computation of the VaR of a portfolio, and the computation of a model risk measurement for the profit and loss of a misspecified hedging strategy.
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    Nonconvergence in the Variation of the Hedging Strategy of a European Call Option (2003)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we consider the variation of the hedging strategy of a European call option when the underlying asset follows a binomial tree. In a binomial tree model the hedging strategy of a European call option converges to a continuous process when the number of time points increases so that the price process of the underlying asset converges to a Brownian motion, the Bachelier model. However, the variation of the hedging strategy need not converge to the variation of the limit process. In fact, it is shown that the asymptotic variation of the hedging strategy may be of any order.
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    URL: http://dx.doi.org/10.1111/1467-9965.t01-1-00176
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    The Term Structure of Simple Forward Rates with Jump Risk (2003)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on “market models.” We consider very general types of jump processes, modeled through marked point processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates. We also formulate reasonably tractable subclasses of models and provide pricing formulas for some derivative securities, including interest rate caps and options on swaps. Through these formulas, we illustrate the effect of jumps on implied volatilities in interest rate derivatives.
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    URL: http://dx.doi.org/10.1111/1467-9965.00021
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    The Defaultable Lévy Term Structure: Ratings and Restructuring (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We introduce the intensity-based defaultable Lévy term structure model. It generalizes the default-free Lévy term structure model by Eberlein and Raible, and the intensity-based defaultable Heath-Jarrow-Morton approach of Bielecki and Rutkowski. Furthermore, we include the concept of multiple defaults, based on Schönbucher, within this generalization.
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    Efficient Universal Portfolios for Past-Dependent Target Classes (2003)
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    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
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    Topics: Mathematics , Economics
    Notes: We present a new universal portfolio algorithm that achieves almost the same level of wealth as could be achieved by knowing stock prices ahead of time. Specifically the algorithm tracks the best in hindsight wealth achievable within target classes of linearly parameterized portfolio sequences. The target classes considered are more general than the standard constant rebalanced portfolio class and permit portfolio sequences to exhibit a continuous form of dependence on past prices or other side information. A primary advantage of the algorithm is that it is easily computable in a polynomial number of steps by way of simple closed-form expressions. This provides an edge over other universal algorithms that require both an exponential number of computations and numerical approximation.
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    Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck type (2003)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Stochastic volatility models of the Ornstein-Uhlenbeck type possess authentic capability of capturing some stylized features of financial time series. In this work we investigate this class of models from the viewpoint of derivative asset analysis. We discuss topics related to the incompleteness of this type of markets. In particular, for structure preserving martingale measures, we derive the price of simple European-style contracts in closed form. Furthermore, the range of viable prices is determined and an empirical application is presented.
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    A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome (2003)
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    Mathematical finance 13 (2003), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper considers a portfolio problem with control on downside losses. Incorporating the worst-case portfolio outcome in the objective function, the optimal policy is equivalent to the hedging portfolio of a European option on a dynamic mutual fund that can be replicated by market primary assets. Applying the Black-Scholes formula, a closed-form solution is obtained when the utility function is HARA and asset prices follow a multivariate geometric Brownian motion. The analysis provides a useful method of converting an investment problem to an option pricing model.
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    URL: http://dx.doi.org/10.1111/1467-9965.t01-1-00177
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    Pricing Discrete European Barrier Options Using Lattice Random Walks (2003)
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    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper designs a numerical procedure to price discrete European barrier options in Black-Scholes model. The pricing problem is divided into a series of initial value problems, one for each monitoring time. Each initial value problem is solved by replacing the driving Brownian motion by a lattice random walk. Some results from the theory of Besov spaces show that the convergence rate of lattice methods for initial value problems depends on two factors, namely the smoothness of the initial value (or the value function) and the moments for the increments of the lattice random walk. This fact is used to obtain an efficient method to price discrete European barrier options. Numerical examples and comparisons with other methods are carried out to show that the proposed method yields fast and accurate results.
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    Merton's portfolio optimization problem in a Black and Scholes market with non-Gaussian stochastic volatility of Ornstein-Uhlenbeck type (2003)
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    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
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    Topics: Mathematics , Economics
    Notes: We study Merton's classical portfolio optimization problem for an investor who can trade in a risk-free bond and a stock. The goal of the investor is to allocate money so that her expected utility from terminal wealth is maximized. The special feature of the problem studied in this paper is the inclusion of stochastic volatility in the dynamics of the risky asset. The model we use is driven by a superposition of non-Gaussian Ornstein-Uhlenbeck processes and it was recently proposed and intensively investigated for real market data by Barndorff-Nielsen and Shephard (2001). Using the dynamic programming method, explicit trading strategies and expressions for the value function via Feynman-Kac formulas are derived and verified for power utilities. Some numerical examples are also presented.
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    An optimal Strategy for Hedging with Short-Term Futures Contracts (2003)
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    Topics: Mathematics , Economics
    Notes: The search for an optimal strategy to reduce the running risk in hedging a long-term supply commitment with short-dated futures contracts leads to a class of intrinsic optimization problems. We give an explicit analytic solution for this optimization problem if the market price of the commodity is based on a simple Gaussian model, thereby replacing previously used incomplete approximations to the optimal strategy.
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    Error Calculus and Path Sensitivity in Financial Models (2003)
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    ISSN: 1467-9965
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    Topics: Mathematics , Economics
    Notes: In the framework of risk management, for the study of the sensitivity of pricing and hedging in stochastic financial models to changes of parameters and to perturbations of the stock prices, we propose an error calculus that is an extension of the Malliavin calculus based on Dirichlet forms. Although useful also in physics, this error calculus is well adapted to stochastic analysis and seems to be the best practicable in finance. This tool is explained here intuitively and with some simple examples.
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    Analysis of Error with Malliavin Calculus: Application to Hedging (2003)
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The aim of this paper is to compute the quadratic error of a discrete time-hedging strategy in a complete multidimensional model. This result extends that of Gobet and Temam (2001) and Zhang (1999). More precisely, our basic assumption is that the asset prices satisfy the d-dimensional stochastic differential equation dXit=Xit(bi(Xt)dt+σi,j(Xt)dWjt). We precisely describe the risk of this strategy with respect to n, the number of rebalancing times. The rates of convergence obtained are 〈inlineGraphic alt="inline image" href="urn:x-wiley:09601627:MAFI014:MAFI_014_mu1" location="equation/MAFI_014_mu1.gif"/〉 for any options with Lipschitz payoff and 1/n1/4 for options with irregular payoff.
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    Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy Processes (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In a market driven by a Lévy martingale, we consider a claim ξ. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We discuss two types of stochastic (Malliavin) derivatives for ξ: one based on the chaos expansion in terms of iterated integrals with respect to the power jump processes and one based on the chaos expansion in terms of iterated integrals with respect to the Wiener process and the Poisson random measure components. We study the relation between these two expansions, the corresponding two derivatives, and the corresponding versions of the Clark-Haussmann-Ocone theorem.
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    Monte Carlo Evaluation of Greeks for Multidimensional Barrier and Lookback Options (2003)
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    ISSN: 1467-9965
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    Topics: Mathematics , Economics
    Notes: In this paper, we consider the problem of the numerical computation of Greeks for a multidimensional barrier and lookback style options: the payoff function depends in a rather general way on the minima and maxima of the coordinates of the d-dimensional underlying asset process. Using Malliavin calculus techniques, we derive additional weights that enable computation of the Greeks using Monte Carlo simulations. Numerical experiments confirm the efficiency of the method. This work is a multidimensional extension of previous results (see Gobet and Kohatsu-Higa 2001).
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    Malliavin's Calculus in Insider Models: Additional Utility and Free Lunches (2003)
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider simple models of financial markets with regular traders and insiders possessing some extra information hidden in a random variable that is accessible to the regular trader only at the end of the trading interval. The problems we focus on are the calculation of the additional utility of the insider and a study of his free lunch possibilities. The information drift—that is, the drift to eliminate in order to preserve the martingale property in the insider's filtration—turns out to be the crucial quantity needed to answer these questions. It is most elegantly described by the logarithmic Malliavin trace of the conditional laws of the insider information with respect to the filtration of the regular trader. Several examples are given to illustrate additional utility and free lunch possibilities. In particular, if the insider has advance knowledge of the maximal stock price process, given by a regular diffusion, arbitrage opportunities exist.
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    First-Order Schemes in the Numerical Quantization Method (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The numerical quantization method is a grid method that relies on the approximation of the solution to a nonlinear problem by piecewise constant functions. Its purpose is to compute a large number of conditional expectations along the path of the associated diffusion process. We give here an improvement of this method by describing a first-order scheme based on piecewise linear approximations. Main ingredients are correction terms in the transition probability weights. We emphasize the fact that in the case of optimal quantization, many of these correcting terms vanish. We think that this is a strong argument to use it. The problem of pricing and hedging American options is investigated and a priori estimates of the errors are proposed.
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    Stochastic Volatility for Lévy Processes (2003)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean-reverting square root process. The model for the mean-reverting time change is then generalized to include non-Gaussian models that are solutions to Ornstein-Uhlenbeck equations driven by one-sided discontinuous Lévy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general mean-corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean-corrected exponential model is not a martingale in the filtration in which it is originally defined. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered filtrations consistent with the one-dimensional marginal distributions of the level of the process at each future date.
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    Local Vega Index and Variance Reduction Methods (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this article we discuss a generalization of the Greek called vega which is used to study the stability of option prices and hedging portfolios with respect to the volatility in various models. We call this generalization the local vega index. We compute through Monte Carlo simulations this index in the cases of Asian options under the classical Black-Scholes setup. Simulation methods using Malliavin calculus and kernel density estimation are compared. Variance reduction methods are discussed.
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    An Anticipating Calculus Approach to the Utility Maximization of an Insider (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we consider a financial market with an insider that has, at time t= 0, some additional information of the whole developing of the market. We use the forward integral, which is an anticipating integral, and the techniques of the Malliavin calculus so that we can take advantage of the privileged information to maximize the expected logarithmic utility from terminal wealth.
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    Hedging Options: The Malliavin Calculus Approach versus the Δ-Hedging Approach (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: In this paper we consider a Black and Scholes economy and investigate two approaches to hedging contingent claims. We show that the general Malliavin calculus approach can generate the classical Δ-hedging formula under weaker conditions.
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    A Partially Observed Model for Micromovement of Asset Prices with Bayes Estimation via Filtering (2003)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: A general micromovement model that describes transactional price behavior is proposed. The model ties the sample characteristics of micromovement and macromovement in a consistent manner. An important feature of the model is that it can be transformed to a filtering problem with counting process observations. Consequently, the complete information of price and trading time is captured and then utilized in Bayes estimation via filtering for the parameters. The filtering equations are derived. A theorem on the convergence of conditional expectation of the model is proved. A consistent recursive algorithm is constructed via the Markov chain approximation method to compute the approximate posterior and then the Bayes estimates. A simplified model and its recursive algorithm are presented in detail. Simulations show that the computed Bayes estimates converge to their true values. The algorithm is applied to one month of intraday transaction prices for Microsoft and the Bayes estimates are obtained.
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    Efficient Computation of Hedging Portfolios for Options with Discontinuous Payoffs (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We consider the problem of computing hedging portfolios for options that may have discontinuous payoffs, in the framework of diffusion models in which the number of factors may be larger than the number of Brownian motions driving the model. Extending the work of Fournié et al. (1999), as well as Ma and Zhang (2000), using integration by parts of Malliavin calculus, we find two representations of the hedging portfolio in terms of expected values of random variables that do not involve differentiating the payoff function. Once this has been accomplished, the hedging portfolio can be computed by simple Monte Carlo. We find the theoretical bound for the error of the two methods. We also perform numerical experiments in order to compare these methods to two existing methods, and find that no method is clearly superior to others.
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    The Price-Volatility Feedback Rate: An Implementable Mathematical Indicator of Market Stability (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Geometric analysis of iterated cross-volatilities of asset prices is adopted to assess the stability of the (risk-free) measure under infinitesimal perturbations. Perturbations of asset prices evolve through time according to an ordinary linear differential equation (hedged transfer). The decay (feedback) rate is explicitly computed through a Fourier series method implemented on high frequency time series.
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    Preface (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
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    Optimal Malliavin Weighting Function for the Computation of the Greeks (2003)
    350 Main Street , Malden , MA 02148 , USA , and 108 Cowley Road , Oxford OX4 IJF , UK . : Blackwell Publishers, Inc.
    Mathematical finance 13 (2003), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper reexamines the Malliavin weighting functions introduced by Fournié et al. (1999) as a new method for efficient and fast computations of the Greeks. Reexpressing the weighting function generator in terms of its Skorohod integrand, we show that these weighting functions have to satisfy necessary and sufficient conditions expressed as conditional expectations. We then derive the weighting function with the smallest total variance. This is of particular interest as it bridges the method of Malliavin weights and the one of likelihood ratio, as introduced by Broadie and Glasserman (1996). The likelihood ratio is precisely the weighting function with the smallest total variance. We finally examine when to use the Malliavin method and when to prefer finite difference.
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    On the optimal portfolio for the exponential utility maximization: remarks to the six-author paper (2002)
    Oxford, UK : Blackwell Publishers, Inc.
    Mathematical finance 12 (2002), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This note contains ramifications of results of Delbaen et al. (2002). Assuming that the price process is locally bounded and admits an equivalent local martingale measure with finite entropy, we show, without further assumption, that in the case of exponential utility the optimal portfolio process is a martingale with respect to each local martingale measure with finite entropy. Moreover, the optimal value always can be attained on a sequence of uniformly bounded portfolios.
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    Exponential Hedging and Entropic Penalties (2002)
    Oxford, UK : Blackwell Publishers, Inc.
    Mathematical finance 12 (2002), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We solve the problem of hedging a contingent claim B by maximizing the expected exponential utility of terminal net wealth for a locally bounded semimartingale X. We prove a duality relation between this problem and a dual problem for local martingale measures Q for X where we either minimize relative entropy minus a correction term involving B or maximize the Q-price of B subject to an entropic penalty term. Our result is robust in the sense that it holds for several choices of the space of hedging strategies. Applications include a new characterization of the minimal martingale measure and risk-averse asymptotics.
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    Ranking State Environmental Outputs: Evidence from Panel Data (2000)
    Boston, USA and Oxford, UK : Blackwell Publishers, Inc.
    Growth and change 31 (2000), S. 0 
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    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper uses state-level pollution data from 1986–1997 to construct two indices that rank U.S. states according to environmental outputs. A major finding is that marginal performers in other indices, such as Wyoming, garner top spots in these ranking systems. The paper also presents findings from fixed and random effects models of panel data that imply state income levels are positively associated with environmental outputs after a threshold level of income is obtained.
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    Small Business Development and Nonmetropolitan Job Growth in Georgia (2000)
    Boston, USA and Oxford, UK : Blackwell Publishers, Inc.
    Growth and change 31 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: To assess development potential of small business, this research examines the age and size characteristics of nonmetropolitan firms and the contribution of business ‘births,’‘deaths,’ expansions, and contractions to job growth. Analysis of data derived from the federal-state unemployment insurance program in Georgia indicates that firms employing fewer than 100 workers account for 44.3 percent of private sector nonfarm employment in nonmetropolitan counties. Overall, the mix of small and large firms remained quite stable over the five year study period. The dynamics of job creation and loss differed dramatically by enterprise size and manufacturing/nonmanufacturing sector. Three segments of the business population contributed most to rural job growth: very small continuing firms, large manufacturing establishments, and non-manufacturing businesses owned by large enterprises. The paper concludes with a discussion of economic development policies that may enable rural communities to capitalize on these business demographic trends.
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    A Random Utility Model of Environmental Equity (2000)
    Boston, USA and Oxford, UK : Blackwell Publishers, Inc.
    Growth and change 31 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Past attempts to uncover evidence that economically disadvantaged groups are unjustly exposed to environmental disamenities have failed to take into account self-selection behavior of individuals or groups of individuals. For instance, when choosing a place to live, households may be trading environmental quality for other housing, neighborhood, and location characteristics they care about. Previous literature on environmental justice has investigated location choice of polluting industries, but fails to account for consumer self-selection in housing markets. This paper thus focuses on location choice of individuals based on observed housing transactions. From the results of a random utility model, a test is proposed that incorporates the no-envy concept of economic equity. The results support a finding for environmental discrimination with respect to African American households, but do not support the hypothesis that poor households in general are unfairly exposed to environmental disamenities.
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    Book Reviews (2000)
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    Growth and change 31 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Books reviewedMoazzem Hozzain, Iyanatul Islam and Reza Kibria, South Asian Economic Development:Transformation, Opportunities and Challenges,Valentine Udoh James and James S. Etim, (eds.) The Feminization of Development Processes in AfricaAura Reggiani, (ed.) Accessibility, Trade and Locational BehaviourRichard H. Olson and Thomas A. Lyson, (eds.) Under the Blade: The Conservation of Agricultural Landscapes
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    Shift-Share Analysis and Changes in Japanese Manufacturing Employment (2000)
    Boston, USA and Oxford, UK : Blackwell Publishers, Inc.
    Growth and change 31 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Shift-share analysis is used to examine the role of spatial structure on changes in regional manufacturing employment, in contrast to the traditional focus of shift-share studies on the role of industrial structure. It is argued that changes in a region's space-economy can be understood not only in terms of the economic subdivisions of the region but also in terms of the contribution of its spatial subdivisions. The latter is illustrated by means of a case study of the contribution of different types of local area to changes in regional manufacturing employment in Japan. Each region was subdivided into four types of local area based on population density. The analysis covered the period from 1981 to 1995, a time of major transformation in Japan's space-economy. The shift-share model was also used to estimate the impact of local area output and productivity on changes in regional employment. In general, the results show that there was a progressive underdevelopment of the core regions, associated with falling output and productivity. The country's peripheral regions were characterized by development, associated with rising output and productivity. Atthe local scale, however, the picture is far more complex. Types of local area contributed to regional employment change in very different ways, with respect to both time, region, and output/productivity. The contribution of local spatial structure to the regional space-economy of Japan is fundamentally fragmented and uneven.
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    Labor Market Dynamics During a Period of Structural Change: California inEarly 1990s (2000)
    Boston, USA and Oxford, UK : Blackwell Publishers, Inc.
    Growth and change 31 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper contributes to the literature on labor market dynamics in four ways. First, unlike most of the existing literature, it uses the Survey of Income and Program Participation (SIPP). This panel survey, with a 32-month window of observation, allows a more precise measure of employment flows than other data sources. It was found that one out of three workers experiences a job transition during the observation period. Second, it focuses on the state of California during an economic cycle. According to these estimates, the net decline in employment represents just 2.6 percent of all job rotations (separations offset by accessions), and gross job flows were as important during the downturn as they were during the economic expansion. Third, it estimates gross flows by sector, and finds significant variation in gross flows relative to employment across sectors of economic activity. Fourth, it examines the coexistence of cyclical and structural changes of California in the early 1990s. The results suggest a labor market link between structural changes and economic cycles.
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    The Interaction of Economic Reforms, Socio-economic Structure and Agriculture in Mexico (2000)
    Boston, USA and Oxford, UK : Blackwell Publishers, Inc.
    Growth and change 31 (2000), S. 0 
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    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: National policydecisions in developing countries contribute to the increasing integration of agriculture into national and world economies. The spatial consequences of national policies, however, vary across regions and agricultural systems. Employing and adapting a methodology first proposed by King (1970), this study explores the relationship between national policy, agriculture, and population characteristics at the regional level in Mexico during the presidency of Carlos Salinas de Gortari (1988–94). Statistical analyses corroborate the hypothesis that the impact of policy reforms on the agricultural sector in Mexico is mediated by the characteristics of the population. Results suggest that government credit for agriculture and federal funding of rural development during the Salinas de Gortari administration were mediated by factors associatedwith the level of urbanization. The provision of commercial credit at the regional level, however, does not appear to depend on population characteristics. Disparities in the impact of national policies are attributed to a historical urban bias, the differential ability of more highly urbanized states to attract government funding, manage and implement programs, and the existence of highly profitable, commercial agriculture in more developed states.
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    Equilibrium with Default and Endogenous Collateral[The author] (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers, Inc.
    Mathematical finance 10 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: We study a two-period general equilibrium model with incomplete asset markets and default. We make collateral endogenous by allowing each seller of assets to fix the level of collateral. Sellers are required to provide collateral whose first-period value, per unit of asset, exceeds the asset price by an arbitrarily small amount. Moreover, borrowers are also required to be fully covered by the purchase, in the first period, of state-by-state default insurance. These insurance contracts are offered by lenders. The insurance cost or revenue is a linear charge and plays the role of a spread penalizing borrowers who will incur in default and benefiting lenders who will suffer default. Under these assumptions, equilibrium always exists.
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    Approximating Large Diversified Portfolios[The author] (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers, Inc.
    Mathematical finance 10 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper considers a financial market with asset price dynamics modeled by a system of lognormal stochastic differential equations. A one-dimensional stochastic differential equation for the approximate evolution of a large diversified portfolio formed by these assets is derived. This identifies the asymptotic dynamics of the portfolio as being a lognormal diffusion. Consequentially an efficient way for computing probabilities, derivative prices, and other quantities for the portfolio are obtained. Additionally, the asymptotic strong and weak orders of convergence with respect to the number of assets in the portfolio are determined.
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    On the Rate of Convergence of Discrete-Time Contingent Claims[We are gra] (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers, Inc.
    Mathematical finance 10 (2000), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper characterizes the rate of convergence of discrete-time multinomial option prices. We show that the rate of convergence depends on the smoothness of option payoff functions, and is much lower than commonly believed because option payoff functions are often of all-or-nothing type and are not continuously differentiable. To improve the accuracy, we propose two simple methods, an adjustment of the discrete-time solution prior to maturity and smoothing of the payoff function, which yield solutions that converge to their continuous-time limit at the maximum possible rate enjoyed by smooth payoff functions. We also propose an intuitive approach that systematically derives multinomial models by matching the moments of a normal distribution. A highly accurate trinomial model also is provided for interest rate derivatives. Numerical examples are carried out to show that the proposed methods yield fast and accurate results.
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    The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets[I am very ] (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers, Inc.
    Mathematical finance 10 (2000), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: Let χ be a family of stochastic processes on a given filtered probability space (Ω, F, (Ft)t∈T, P) with T⊆R+. Under the assumption that the set Me of equivalent martingale measures for χ is not empty, we give sufficient conditions for the existence of a unique equivalent martingale measure that minimizes the relative entropy, with respect to P, in the class of martingale measures. We then provide the characterization of the density of the minimal entropy martingale measure, which suggests the equivalence between the maximization of expected exponential utility and the minimization of the relative entropy.
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    Endogenous Random Asset Prices in Overlapping Generations Economies[This resea] (2000)
    Oxford, UK and Boston, USA : Blackwell Publishers, Inc.
    Mathematical finance 10 (2000), S. 0 
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    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper derives a general explicit sequential asset price process for an economy with overlapping generations of consumers. They maximize expected utility with respect to subjective transition probabilities given by Markov kernels. The process is determined primarily by the interaction of exogenous random dividends and the characteristics of consumers, given by arbitrary preferences and expectations, yielding an explicit random dynamical system with expectations feedback. The paper studies asset prices and equity premia for a parametrized class of examples with CARA utilities and exponential distributions. It provides a complete analysis of the role of risk aversion and of subjective as well as rational beliefs.
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