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  • Articles  (65,229)
  • 2000-2004  (65,229)
  • Mathematics  (65,229)
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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
    Electronic Resource
    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 
    Details
    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
    Electronic Resource
    Cumulative Index (2004)
    Oxford [u.a.] : Blackwell Publishing
    Mathematical finance 14 (2004), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.0960-1627.2004.20040906.x
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  • 18
    Electronic Resource
    Electronic Resource
    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 
    Details
    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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  • 19
    Electronic Resource
    Electronic Resource
    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 
    Details
    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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  • 20
    Electronic Resource
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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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  • 21
    Electronic Resource
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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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  • 22
    Electronic Resource
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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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    TEACHING STATISTICS 
EDITORIAL (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    What Are the Chances? (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A lottery coincidence provides the background for discussing the assessment of probabilities and the definition of events.
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    Effect of Prior Information on String Length Estimates (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes an activity through which students collect data and explore ways to display them through graphs and charts. It also motivates various summary measures for location, spread and shape. Finally, it gives an introduction to concepts of validity, reliability and unbiasedness.
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    Line-Fitting with Outliers (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article illustrates a method for fitting straight lines to data that is resistant to outliers and might therefore sometimes be preferred to the customary least squares procedure.
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    Chernoff Faces in Microsoft Excel (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes how Chernoff faces can be drawn in Microsoft Excel.
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    Great Expectations? (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article introduces the concept of a prediction interval in a gambling context.
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    The Most Compact Subdomain of a Continuous Probability Distribution (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes the most compact 100c% interval for a probability density for 0 〈 c 〈 1. An unbiased, distribution-free estimator when c = 0.5 is presented.
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    A Lower Bound for the Most Deviant Z Score (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article demonstrates that the lower bound for the most deviant Z score and the upper bound for the sample standard deviation are attained simultaneously.
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    A Further Coin Tossing Experiment (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
    Teaching statistics 26 (2004), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: In this note, a coin tossing experiment which leads to three discrete distributions is discussed.
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    Investigating Probabilistic Intuitions (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
    Teaching statistics 26 (2004), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article explores the intuitions of secondary education majors regarding probability. This is accomplished by administering a two-question instrument to 113 participants. Their responses to these questions, and more importantly the explanations they provide for these answers, are analysed. The conclusions drawn may be informative to teachers of probability and statistics as they attempt to remediate common probabilistic misconceptions and devise more effective teaching strategies.
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    STATISTICAL DIVERSIONS (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    TEACHING STATISTICS 
Index to Volume 26 (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    IASE matters (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    Notes for Contributors to TEACHING STATISTICS (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
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    COMPETITION REPORT (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    NEWS & NOTES (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
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    LOOK AHEAD (2004)
    Oxford, UK : Blackwell Publishing, Ltd.
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    Notes for Contributors to 
TEACHING STATISTICS (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    EDITORIAL (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    An Upper Bound on the Value of the Standard Deviation (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article derives a simple upper bound for the sample standard deviation that could be useful in guarding against gross errors of calculation.
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    About the Cover (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The cover's statistics and beading are discussed.
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    Presentation of Type I and Type II Error Rates to Non-statisticians (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes a simple computer program which graphically demonstrates both Type I and Type II statistical errors.
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    A Useful Example when Teaching Hypothesis Testing (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes an example which is useful when teaching hypothesis testing in order to highlight the interrelationships that exist among the level of significance, the sample size and the statistical power of a test. The example also allows students to see how what they learn in the classroom directly affects the content of some of the commercials that they watch on television.
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    Charts in Excel – A Series Matter (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: The Chart Wizard in Microsoft Excel is supposed to make chart drawing so easy that a child can do it, yet many intelligent adults fail to use it successfully. This article suggests some simple principles that resolve many of the difficulties.
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    Of Poohsticks and p-Values: Hypothesis Testing in the Hundred Acre Wood (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: A walk through Milne's Enchanted Forest leads to an unexpected encounter with hypothesis testing.
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    NEWS & NOTES (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    A VBA-based Simulation for Teaching Simple Linear Regression (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: In spite of the name, simple linear regression presents a number of conceptual difficulties, particularly for introductory students. This article describes a simulation tool that provides a hands-on method for illuminating the relationship between parameters and sample statistics.
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    LOOK AHEAD (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    THE C. OSWALD GEORGE PRIZE (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    STATISTICAL DIVERSIONS (2004)
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    Classical versus Bayesian Inference: A Classroom Illustration (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article describes an illustration of Bayesian inference that has proved popular with students.
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    IASE matters (2004)
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    EDITORIAL (2004)
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    Resampling with Excel (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Standard Microsoft Excel functions and the Excel Data Table facility are used in randomization applications using resampling with and without replacement.
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    STATISTICAL DIVERSIONS (2004)
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    Turning Points in Random Permutations (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Topics: Mathematics
    Notes: The mean and variance of the number of turning points in random permutations are evaluated. These results are applied to a test of randomness of fluctuations.
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    Useful Data for Teaching Statistics from Hockey World Cup Matches (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Notes: This article presents some data from a major sports event that can be used in common statistical analyses.
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    BOOK REVIEW (2004)
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    Sensitivity of the χ2 Goodness-of-Fit Test to the Choice of Classes (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
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    Notes: The χ2 goodness-of-fit test is often one of the first tests of hypotheses encountered by students. When some of the expected frequencies are small, classes need to be combined. A real-life example is given that illustrates a surprising sensitivity of the results of the test to the way in which such combinations are chosen.
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    In All Probability, Probability is not All (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    Notes: The national lottery is often portrayed as a game of pure chance with no room for strategy. This misperception seems to stem from the application of probability instead of expectancy considerations, and can be utilized to introduce the statistical concept of expectation.
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    IASE matters (2004)
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    LETTER TO THE EDITOR (2004)
    Oxford, UK : Blackwell Publishing Ltd
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    LETTER TO THE EDITOR (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    Water Quality Statistics (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: Water quality experiments, especially the use of macroinvertebrates as indicators of water quality, offer an ideal context for connecting statistics and science. In the STAR program for secondary students and teachers, water quality experiments were also used as a context for teaching statistics. In this article, we trace one activity that uses virtual streams and repeated sampling to develop the notion of a hypothesis test for one proportion.
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    The Generalized Mean (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article defines the generalized mean and shows how it relates to such statistics as the arithmetic, geometric and harmonic means.
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    Odds That Don’t Multiply Up (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
    Notes: This article discusses the calculation of odds for combined events.
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    News & Notes (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    LOOK AHEAD (2004)
    Oxford, UK : Blackwell Publishing Ltd
    Teaching statistics 26 (2004), S. 0 
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    ISSN: 1467-9639
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics
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    Switching Regimes in the Term Structure of Interest Rates during U.S. Post-War: A Case for the Lucas Proof Equilibrium? (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 1, art5 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Farmer (1991) suggests that in a model in which there are multiple rational expectations (RE) equilibria agents may find it useful to coordinate their expectations in a unique RE equilibrium which is immune to the Lucas Critique. In this paper, we evaluate Lucas proof (LP) equilibrium performance in the context of the term structure of interest rates model by using post-war US data. Estimation results show that LP equilibrium exhibits some important features of the data that are not reproduced by the fundamental equilibrium. For instance, the short rate behaves as a random walk in a regime characterized by low conditional volatility, whereas the term spread Granger-causes changes in the short-rate in periods characterized by high conditional volatility.
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    Extensions of the Forward Search to Time Series (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art2 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper extends the forward search technique to the analysis of structural time series data. It provides a series of powerful new forward plots that use information from the whole sample to display the effect of each observation on a wide variety of aspects of the fitted model and shows how the forward search, free from masking and swamping problems, can detect the main underlying features of the series under study (masked multiple outliers, level shifts or transitory changes). The effectiveness of the suggested approach is shown through the analysis of real and simulated data.
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    GARCH-type Models with Generalized Secant Hyperbolic Innovations (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art7 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: GARCH-type models have been analyzed assuming various nongaussian distributions of errors. In general, the asymmetric generalized Student-t random variable seems to be the distribution which better captures the nonnormality features of financial data. However, a drawback of this distribution is represented by the technical dificulties due to the evaluation of moments, especially in the case of fractional degrees of freedom. In this paper we propose to model high frequency time series returns using GARCH-type models with a generalized secant hyperbolic (GSH) distribution. The main advantage of the GSH distribution over the Student-t distribution is that all the moments are finite for each value of the shape parameter. The distribution is symmetric with respect to the mean, but we show that it is still possible to obtain the density in a closed form introducing a skewness parameter according to the method proposed by Fernandez and Steel. We use a Monte Carlo experiment to validate this distribution in the context of GARCH models with maximum likelihood estimates of parameters. Finally, we show an application to log returns of a stock index.
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    Experimental Design for Time-Dependent Models with Correlated Observations (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art13 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We describe an algorithm for the construction of optimum experimental designs for the parameters in a regression model when the errors have a correlation structure. Our example is drawn from chemical kinetics, so that the model is nonlinear. Our algorithm has been implemented to be used when the model consists of a set of differential equations for which only numerical solutions ar available. However, the algorithm can also be used for standard regression models when the errors are correlated. The paper concludes with some discussion of outstanding issues in optimum design with correlated errors.
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    Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art4 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Several methods have been proposed for identifying clusters of extreme values leading to estimators of the extremal index; the latter represents,in the limit, the mean-size of each cluster of thresholds exceedances. The detection of clusters of extremes is relevant for the class of processes commonly used in financial econometrics, such as GARCH processes. The paper illustrates a novel approach to the above identification that exploits additional knowledge of the trajectory of the process around extreme events, and compares it to traditional approaches, using simulation from a GARCH process. We assess the relative performance of estimators in terms of bias, mean square error and distributional properties.
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    The ARAR Error Model for Univariate Time Series and Distributed Lag (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 1, art2 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We show that the use of prior information derived from former empirical findings and/or subject matter theory regarding the lag structure of the observable variables together with an AR process for the error terms can produce univariate and single equation models that are intuitively appealing, simple to implement and work well in practice.
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    Inferring the Forward Looking Equity Risk Premium from Derivative Prices (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 1, art3 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper considers the measurement of the equity risk premium in financial markets from a new perspective that picks up on a suggestion from Merton (1980) to use implied volatility of options on a market portfolio as a direct 'ex-ante' estimate for market variance, and hence the risk premium. Here the time variation of the unobserved risk premium is modelled by a system of stochastic differential equations connected by arbitrage arguments between the spot equity market, the index futures and options on index futures. We motivate and analyse a mean-reverting form for the dynamics of the risk premium. Since the risk premium is not directly observable, information about its time varying conditional distribution is extracted using an unobserved component state space formulation of the system and Kalman filtering methodology. In order to cater for the time variation of volatility we use the option implied volatility in the dynamic equations for the index and its derivatives. This quantity is in a sense treated as a signal that impounds the market's 'ex-ante', forward looking, view on the equity risk premium. The results using monthly U.S. market data over the period January 1995 to June 2003 are presented and the model fit is found to be statistically significant using a number of measures. Comparisons with ex-post returns indicate that such historical measures may be understating the market risk premium.
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    Nonlinear Monetary Policy Rules: Some New Evidence for the U.S. (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 3, art2 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper derives optimal monetary policy rules in setups where certainty equivalence does not hold because either central bank preferences are not quadratic, and/or the aggregate supply relation is nonlinear. Analytical results show that these features lead to sign and size asymmetries, and nonlinearities in the policy rule. Reduced-form estimates indicate that US monetary policy can be characterized by a nonlinear policy rule after 1983, but not before 1979. This finding is consistent with the view that the Fed's inflation preferences during the Volcker-Greenspan regime differ considerably from the ones during the Burns-Miller regime.
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    An Investigation of Current Account Solvency in Latin America Using Non Linear Nonstationarity Tests (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 1, art4 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Using a new methodology that allows nonlinearities, we find frequent support for external debt sustainability in a number of Latin American countries. Our findings reverse the results for several countries, obtained with traditional unit-root tests and present a richer framework for evaluating the external solvency of an economy. Our results also provide some justification for the assumption the international current accounts are based on.
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    A Nonparametric Dimension Test of the Term Structure (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 3, art6 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In an economy with multiple sources of risk, the short-term interest rate does not capture all the information that determines the conditional distribution of bond yields. This is also true for path-dependent term structure models. In either case, the current short rate level is not a sufficient statistic for the conditional density of future short rates. This paper studies the empirical relevance of both issues from a time-series nonparametric perspective. The analysis is formulated as a test for the dependence of the short rate drift and diffusion on variables other than the short rate, and exploits Ait-Sahalia, Bickel, and Stocker (2001) dimension reduction method. The paper explores the finite sample performance of the method and applies the test to US interest rate data. Results reject a single-factor Markovian model, although conclusions are sensitive to the choice of additional conditioning variables.
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    Combining Forecasts with Nonparametric Kernel Regressions (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 4, art2 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We introduce a flexible nonparametric technique that can be used to select weights in a forecast-combining regression. We perform a Monte Carlo study that evaluates the performance of the proposed technique along with other linear and nonlinear forecast-combining procedures. The simulation results show that when forecast errors are correlated across models, the nonparametric weighting scheme dominates. As a general rule, our simulation results suggest that the practice of combining forecasts, no matter the technique employed in selecting the combination weights, can yield lower forecast errors on average. An application to inflation forecasting is also presented to demonstrate the use of all forecast-combining techniques.
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    A New Test of the Martingale Difference Hypothesis (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 4, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In this paper we propose a new class of tests for the martingale difference hypothesis based on the moment conditions derived by Bierens (1982). In contrast with the existing consistent tests, the proposed test has a standard limiting distribution and is easy to implement. Comparing with many commonly used autocorrelation- and spectrum-based tests, it has better power against a larger class of alternatives that may be serially correlated or uncorrelated. Moreover, this test does not rely on the assumption of conditional homoskedasticity and requires a weaker moment condition. Our simulations confirm that the proposed test is powerful against various linear and nonlinear alternatives and is quite robust to the failure of higher-order moments. Our empirical study on exchange rate returns also shows that the conclusion resulted from the proposed test is different from that of the conventional tests.
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    Linearizations and Equilibrium Correction Models (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 4, art5 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Linear dynamic equilibrium correction mechanisms are shown to follow from the discretisation of continuous processes with steady-state solutions.
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    Introduction (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
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    MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art6 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In this paper we present a stochastic volatility model assuming that the return shock has a Skew-GED distribution. This allows a parsimonious yet flexible treatment of asymmetry and heavy tails in the conditional distribution of returns. The Skew-GED distribution nests both the GED, the Skew-normal and the normal densities as special cases so that specification tests are easily performed. Inference is conducted under a Bayesian framework using Markov Chain MonteCarlo methods for computing the posterior distributions of the parameters. More precisely, our Gibbs-MH updating scheme makes use of the Delayed Rejection Metropolis-Hastings methodology as proposed by Tierney and Mira (1999), and of Adaptive-Rejection Metropolis sampling. We apply this methodology to a data set of daily and weekly exchange rates. Our results suggest that daily returns are mostly symmetric with fat-tailed distributions while weekly returns exhibit both significant asymmetry and fat tails.
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    Assessing Chaos in Time Series: Statistical Aspects and Perspectives (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art11 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Chaos theory offers to time series analysis new perspectives as well as concepts and ideas that have a through contribution to statistics. On the other hand, statistical methodology has shown to play a crucial role for the comprehension of nonlinear and chaotic phenomena. One peculiar feature of chaotic systems is sensitivity to initial conditions, which is responsible of the unpredictability we experience in such phenomena. One of the most popular quantity that measures this property is the maximum Lyapunov characteristic exponent (MLCE). In this paper we discuss from a statistical perspective the problems arising in estimating both the MLCE and its generalizations in time series, issues that have recently deserved attention in the community of time series analysts. We also present a method based on resampling in order to assign confidence interval to the estimates of the MLCE. It is shown that in addition to answering the question of the presence of chaos, these methods give relevant contributions to the characterization of many other aspects of nonlinear time series.
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    Mixture Processes for Financial Intradaily Durations (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art8 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The instantaneous volatility of the price process is analyzed through the intraday financial durations between price changes. Previous research has traditionally dealt with parametric models without reaching a satisfactory level of adequacy. In this study, it is shown that by using a mixture of two exponential distributions a highly satisfactory fit can be obtained. The presence on financial markets of traders with different information sets makes reasonable the mixture assumption.
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    Working Time and Employment Under Uncertainty (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 3, art5 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The standard literature on working time has modelled the decisions of firms in a deterministic framework in which firms can choose between employment and overtime (given mandated standard hours). Contrary to this approach, we consider the impact of uncertainty and real options on the decision of working time and examine the determinants of employment and hours in a stochastic framework. A number of simulation exercises to illustrate the workings of the model are also undertaken.
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    Household Income Dynamics in Two Transition Economies (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 3, art4 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We test for the existence of poverty traps and distribution-dependent growth using a nonlinear dynamic panel data model of household incomes allowing for endogenous attrition. Our estimates for Hungary and Russia in the 1990s reveal significant nonlinearity in the dynamics, consistent with the claim that income inequality attenuates growth in mean income. However, we do not find evidence of a threshold effect at low incomes, as postulated by models of dynamic poverty traps. Our results indicate that households generally bounce back from transient shocks, though we find that the adjustment process is slower for households who are poorer in steady state.
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    An Integer-Valued Time Series Model for Hotels that Accounts for Constrained Capacity (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 4, art6 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Many service industry firms strive hard to fill free capacity in order to cover their costs for a fixed capital stock. This paper presents a time series model where the capacity constraint is an integral part. The integer-valued autoregressive model builds on a simple idea of how daily time series arise for hotels and other similar establishments. Measures that follow naturally from the time series model are the occupancy probability and the duration of stay for the visitor. Empirically, we study the effects of price changes and a large festival, on these measures.
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    Private Information and High-Frequency Stochastic Volatility (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 1, art1 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: We study the effect of privately informed traders on measured high frequency price changes and trades in asset markets. We use a standard market microstructure framework where exogenous news is captured by signals that informed agents receive. We show that the entry and exit of informed traders following the arrival of news accounts for high-frequency serial correlation in squared price changes (stochastic volatility) and trades. Because the bid-ask spread of the market specialist tends to shrink as individuals trade and reveal their information, the model also accounts for the empirical observation that high-frequency serial correlation is more pronounced in trades than in squared price changes. A calibration test of the model shows that the features of the market microstructure, without serially correlated news, accounts qualitatively for the serial correlation in the data, but predicts less persistence than is present in the data.
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    Relationship between Local and Global Nonparametric Estimators Measures of Fitting and Smoothing (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art17 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Following Henderson (1916) who developed a smoothing measure as a function of the weight system of a linear filter, Dagum and Luati (2002a) proposed a set oflocal statistical measures of bias, variance and mean square error which are intrinsic to the smoother and, thus, independent of the data to which they will be applied on.Theoretical measures of local fitting (LMSE) and smoothing (S) are calculated on the basis of the weight systems of the following nonparametric function estimators,Loess of degree 1 and 2, the cubic smoothing spline, the Gaussian kernel, and the 13-term Henderson filter.Our aim is to evaluate the extent to which these local or weight-based measures of fitting and smoothing can be used to obtain a priori general information on theglobal (data-based) goodness of fit and smoothness when such filters are applied to real time series. A priori knowledge of a smoother fit and smoothness performanceswhen applied to real data is relevant, among others, for current economic analysis, the main interest of which is the detection of true turning points.For each function estimator, we calculate global measures of fitting (MSE) and smoothing (Q) using two large samples of real and simulated series characterizedby different degrees of variability.The results show that the theoretical (weight-based) local smoothing measures are always in agreement with the global empirical ones. Similarly, the local (weight-based) mean square error, analyzed in terms of bias and variance composition, provides sound a priori information on the global goodness of fit given by the symmetric filters of each nonparametric estimator. For the asymmetric filters, the above analysis must be done taking into consideration also the impact of phase shifts whichcan be inferred from the smoothing measures.
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    Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art9 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: State space models provide a useful stochastic description for dynamic phenomena, based on unobserved or latent variables. When the model rests on linear and Gaussian assumptions there exists a well-known iterative procedure, called the Kalman filter, which gives analytic updating recursion for the filtering, the prediction and the smoothing distributions. However, this is rare and a state space model does not usually admit such a filter. For this reason, instead of looking for analytic solutions, a number of papers aim to define alternative procedures, giving numerical or approximate solutions. This paper concerns a particular class of models based on the assumption that the mixed process, obtained by alternating states and observations, is a Markov process. The main features of this class of models, proposed for stochastic volatility description by Barndorff-Nielsen (1997), are emphasized. In this framework, some new non-linear Gaussian state space models, computationally tractable and of potential interest for applications, may be defined.
    Type of Medium: Electronic Resource
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    On the Stationarity of First-order Nonlinear Time Series Models: Some Developments (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art12 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In the present paper we consider the general class of first-order nonlinear models. The main contributions concern primerly a generalization of the conditions for geometric ergodicity presented in Ferrante et al. (2003). The obtained result is then applied to two classes of first-order nonlinear models not previously addressed. Secondly we apply to general firstorder nonlinear models some recently developed conditions for the existence of the invariant measure of a Markov process. For this class of nonlinear models we also prove that the usual drift-condition for geometric ergodicity for Markov chains still holds even in the presence of an alternative assumption than T-continuity.
    Type of Medium: Electronic Resource
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    Analyzing Financial Time Series through Robust Estimators (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art3 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In this paper we suggest an extension of the forward search methodology to GARCH models which are often used for forecasting stock market volatility. It is frequently found that estimated residuals from GARCH models have excess kurtosis, even when one allows for conditional t-distributed errors. Some papers have appeared on outlier detection in GARCH models but the proposed methods are iterative and may suffer from masking effects. The forward search is a method for determining the effect of outliers on fitted parameters and for detecting also masked outliers. In the case of GARCH models outliers are strictly related to extreme observations which are responsible for the well-known volatility clustering of financial returns. It is possible, through the forward search, to visualize the effect on estimated parameters of patches of extremal observations.
    Type of Medium: Electronic Resource
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    Neural Tests for Conditional Heteroskedasticity in ARCH-M Models (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 3, art3 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper deals with tests for detecting conditional heteroskedasticity in ARCH-M models usingthree kinds of methods:neural networks techniques, bootstrap methods and both combined.As regards the ARCH models, Péguin-Feissolle (2000) developed tests based on the modellingtechniques with neural network.However, as regards the ARCH-M models, a nuisance parameter is not identified and the tests arenot applicable.To solve this problem, we propose to adapt these neural tests to Davies procedure (1987) leadingto new tests.The performance of these latter tests are compared with those of Bera and Ra test (1995).However, Bera and Ra test has not really satisfactory performance and suffer from serious sizedistortion.Our neural test will have the same problem.To solve this second problem, without loss of power, we apply parametric and nonparametricbootstrap methods on the underlying test statistics.Lastly, to examine the size and the power properties of the tests in small samples, Monte Carlosimulations are carried out with various standard and non-standard models for conditionalheteroskedasticity as to illustrate a variety of situations.In addition, the graphical presentation of Davidson and MacKinnon (1998a) is used to show the"true" power of the tests and not only the (nominal) power, as it is often the case, that canbe meaningless.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/snde/vol8/iss3/art3
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    Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art14 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: Practical aspects of likelihood-based inference and forecasting of series with long memory are considered, based on the arfima(p; d; q) model with deterministic regressors. Sampling characteristics of approximate and exact first-order asymptotic methods are compared. The analysis is extended using modified profile likelihood analysis, which is a higher-order asymptotic method suggested by Cox and Reid (1987). The relevance of the differences between the methods is investigated for models and forecasts of monthly core consumer price inflation in the US and quarterly overall consumer price inflation in the UK.
    Type of Medium: Electronic Resource
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    Nonlinear Intraday Dynamics in Eurostoxx50 Index Markets (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 4, art3 
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    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: This paper analyses the nonlinear dynamic behaviour of intraday returns in the Eurostoxx50 cash and futures index which, given their relatively recent appearance, have not yet been analysed. We find that both return series show nonlinear individual dynamics that cannot exclusively be explained by the presence of conditional heteroskedasticity. Our findings also indicate nonlinear dynamic relationships between both market prices. The adjustment process to mispricing errors is nonlinear and shows periods of explosive behaviour. Finally, we distinguish between linear and nonlinear Granger causality and establish that the information flow is bi-directional both in the linear as well as in the nonlinear sphere.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/snde/vol8/iss4/art3
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    A Stochastic Version of Zeeman's Market Model (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 4, art4 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: In a heterogenous agents framework, we study a randomized version of Zeeman's market model with fundamental and momentum traders. Using methods from random dynamical systems theory, we examine convergence properties of invariant measures which correspond to market equilibria. It turns out that due to a stochastic stabilisation effect the market stays stable up to some critical value of speculative activity. If this threshold is surpassed, sudden trend reversals are possible without being induced by some exogenous shock.
    Type of Medium: Electronic Resource
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    Seasonal Specific Structural Time Series (2004)
    Cambridge, Mass. : Berkeley Electronic Press (now: De Gruyter)
    Studies in nonlinear dynamics and econometrics 8.2004, 2, art16 
    Details
    ISSN: 1081-1826
    Source: Berkeley Electronic Press Academic Journals
    Topics: Mathematics , Economics
    Notes: The paper introduces the class of seasonal specific structural time series models, according to which each season follows specific dynamics, but is also tied to the others by a common random effect. Seasonal specific models are dynamic variance components models that account for some kind of periodic behaviour, such as periodic heteroscedasticity, and are also tailored to deal with situations such that one or a group of seasons behave differently. Trends and non periodic features can still be extracted and their nature is discussed. Multivariate extensions entertain the case when cointegration pertains only to groups of seasons. It is finally shown that a circular correlation pattern for the idiosyncratic disturbances yields a periodic component that is isomorphic to a trigonometric seasonal com- ponent.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/snde/vol8/iss2/art16
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