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  • 1
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    Smoothing complements and randomized score functions (1992)
    Springer
    Details
    Publication Date: 1992-12-01
    Print ISSN: 0254-5330
    Electronic ISSN: 1572-9338
    Topics: Mathematics , Economics
    Published by Springer
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  • 2
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    Contagion in Financial Networks (2016)
    American Economic Association
    Details
    Publication Date: 2016-09-01
    Description: The recent financial crisis has prompted much new research on the interconnectedness of the modern financial system and the extent to which it contributes to systemic fragility. Network connections diversify firms' risk exposures, but they also create channels through which shocks can spread by contagion. We review the extensive literature on this issue, with the focus on how network structure interacts with other key variables such as leverage, size, common exposures, and short-term funding. We discuss various metrics that have been proposed for evaluating the susceptibility of the system to contagion and suggest directions for future research. (JEL D85, E44, G01, G21, G22, G23, G28)
    Print ISSN: 0022-0515
    Electronic ISSN: 1547-1101
    Topics: Economics
    Published by American Economic Association
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  • 3
    Electronic Resource
    Electronic Resource
    [ohne Titel] (2002)
    Oxford, UK : Blackwell Publishers, Inc.,
    Mathematical finance 12 (2002), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit a quadratic approximation to the portfolio loss, such as the delta-gamma approximation. In the first method, we derive the characteristic function of the quadratic approximation and then use numerical transform inversion to approximate the portfolio loss distribution. Because the quadratic approximation may not always yield accurate VAR estimates, we also develop a low variance Monte Carlo method. This method uses the quadratic approximation to guide the selection of an effective importance sampling distribution that samples risk factors so that large losses occur more often. Variance is further reduced by combining the importance sampling with stratified sampling. Numerical results on a variety of test portfolios indicate that large variance reductions are typically obtained. Both methods developed in this paper overcome difficulties associated with VAR calculation with heavy-tailed risk factors. The Monte Carlo method also extends to the problem of estimating the conditional excess, sometimes known as the conditional VAR.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00141
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  • 4
    Electronic Resource
    Electronic Resource
    Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options (1999)
    Oxford, UK and Boston, USA : Blackwell Publishers Inc.
    Mathematical finance 9 (1999), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: This paper develops a variance reduction technique for Monte Carlo simulations of path-dependent options driven by high-dimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to be optimal in an asymptotic sense. The drift selected has an interpretation as the path of the underlying state variables which maximizes the product of probability and payoff—the most important path. The directions used for stratified sampling are optimal for a quadratic approximation to the integrand or payoff function. Indeed, under differentiability assumptions our importance sampling method eliminates variability due to the linear part of the payoff function, and stratification eliminates much of the variability due to the quadratic part of the payoff. The two parts of the method are linked because the asymptotically optimal drift vector frequently provides a particularly effective direction for stratification. We illustrate the use of the method with path-dependent options, a stochastic volatility model, and interest rate derivatives. The method reveals novel features of the structure of their payoffs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00065
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  • 5
    Electronic Resource
    Electronic Resource
    A Continuity Correction for Discrete Barrier Options (1997)
    Boston, USA and Oxford, UK : Blackwell Publishers Inc
    Mathematical finance 7 (1997), S. 0 
    Details
    ISSN: 1467-9965
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Mathematics , Economics
    Notes: The payoff of a barrier option depends on whether or not a specified asset price, index, or rate reaches a specified level during the life of the option. Most models for pricing barrier options assume continuous monitoring of the barrier; under this assumption, the option can often be priced in closed form. Many (if not most) real contracts with barrier provisions specify discrete monitoring instants; there are essentially no formulas for pricing these options, and even numerical pricing is difficult. We show, however, that discrete barrier options can be priced with remarkable accuracy using continuous barrier formulas by applying a simple continuity correction to the barrier. The correction shifts the barrier away from the underlying by a factor of exp(bet sig sqrt dt), where bet approx 0.5826, sig is the underlying volatility, and dt is the time between monitoring instants. The correction is justified both theoretically and experimentally.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00035
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  • 6
    Electronic Resource
    Electronic Resource
    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 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1467-9965.00021
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  • 7
    Electronic Resource
    Electronic Resource
    Connecting discrete and continuous path-dependent options (1999)
    Springer
    Finance and stochastics 3 (1999), S. 55-82 
    Details
    ISSN: 1432-1122
    Keywords: Key words: Barrier options, lookback options, continuity corrections, trinomial trees JEL classification: G13, C63, G12 Mathematics Subject Classification (1991): 90A09, 60J15, 65N06
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts. We also develop discrete-time discrete-state lattice methods for determining accurate prices of discrete and continuous path-dependent options. In several cases, the lattice methods use correction terms based on the connection between discrete- and continuous-time prices which dramatically improve convergence to the accurate price.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s007800050052
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  • 8
    Electronic Resource
    Electronic Resource
    Arbitrage-free discretization of lognormal forward Libor and swap rate models (2000)
    Springer
    Finance and stochastics 4 (2000), S. 35-68 
    Details
    ISSN: 1432-1122
    Keywords: Key words:Interest rate models, Monte Carlo simulation, market models ; JEL Classification: G14, E43 ; Mathematics Subject Classification (1991): 60G42, 60G44, 60G15, 60J60, 65C05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. An important recent development in the pricing of interest rate derivatives is the emergence of models that incorporate lognormal volatilities for forward Libor or forward swap rates while keeping interest rates stable. These market models\/ have three attractive features: they preclude arbitrage among bonds, they keep rates positive, and, most distinctively, they price caps or swaptions according to Black's formula, thus allowing automatic calibration to market data. But these features of continuous-time formulations are easily lost when the models are discretized for simulation. We introduce methods for discretizing these models giving particular attention to precluding arbitrage among bonds and to keeping interest rates positive even after discretization. These methods transform the Libor or swap rates to positive martingales, discretize the martingales, and then recover the Libor and swap rates from these discretized variables, rather than discretizing the rates themselves. Choosing the martingales proportional to differences of ratios of bond prices to numeraire prices turns out to be particularly convenient and effective. We can choose the discretization to price one caplet of arbitrary maturity without discretization error. We numerically investigate the accuracy of other caplet and swaption prices as a gauge of how closely a model calibrated to implied volatilities reproduces market prices. Numerical results indicate that several of the methods proposed here often outperform more standard discretizations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s007800050002
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  • 9
    Electronic Resource
    Electronic Resource
    Smoothing complements and randomized score functions (1992)
    Springer
    Annals of operations research 39 (1992), S. 41-67 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper establishes connections between two derivative estimation techniques:infinitesimal perturbation analysis (IPA) and thelikelihood ratio orscore function method. We introduce a systematic way of expanding the domain of the former to include that of the latter, and show that many likelihood ratio derivative estimators are IPA estimators obtained in a consistent manner through a special construction. Our extension of IPA is based onmultiplicative smoothing. A function with discontinuities is multiplied by asmoothing complement, a continuous function that takes the value zero at a jump of the first function. The product of these functions is continuous and provides an indirect derivative estimator after an appropriate normalization. We show that, in substantial generality, the derivative of a smoothing complement is a randomized score function: its conditional expectation is a derivative of a likelihood ratio. If no conditional expectation is applied, derivative estimates based on multiplicative smoothing have higher variance than corresponding estimates based on likelihood ratios.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02060935
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  • 10
    Electronic Resource
    Electronic Resource
    Stationary waiting time derivatives (1992)
    Springer
    Queueing systems 12 (1992), S. 369-389 
    Details
    ISSN: 1572-9443
    Keywords: Perturbation analysis ; stability ; stochastic difference equations ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We investigate the stability of waiting-time derivatives when inputs to a queueing system-service times and interarrival times-depend on a parameter. We give conditions under which the sequence of waiting-time derivatives admits a stationary distribution, and under which the derivatives converge to the stationary regime from all initial conditions. Further hypotheses ensure that the expectation of a stationary waiting-time derivative is, in fact, the derivative of the expected stationary waiting time. This validates the use of simulation-based infinitesimal perturbation analysis estimates with a variety of queueing processes. We examine waiting-time sequences satisfying recursive equations. Our basic assumption is that the input and its derivatives are stationary and ergodic. Under monotonicity conditions, the method of Loynes establishes the convergence of the derivatives. Even without such conditions, the derivatives obey a linear difference equation with random coefficients, and we exploit this fact to find stability conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01158809
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