Value at Risk For Derivatives

Lina El‐Jahel · William Robert Maurice Perraudin · Peter Sellin

44 citations0/0 files storedThe Journal of Derivatives

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Risk and Portfolio Optimization

Abstract

Value at Risk (VaR) techniques are di cult to apply when portfolios contain signi cant exposures to `non-linear ' derivative claims such as options. This paper analyses the biases introduced by standard delta and delta-gamma VaR methods for options. These methods employ local approximations and adopt very strong assumptions about the Gaussianity of returns on derivatives. Making extensive use of characteristic functions, we develop a new method based on multivariate square root processes which avoids the assumption of Gaussian returns. JEL Nos.: G11, G21, L51.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1973Theory of Rational Option Pricing 1987The Pricing of Options on Assets with Stochastic Volatilities 1996Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options 1991Stock Price Distributions with Stochastic Volatility: An Analytic Approach 1998Evaluating Density Forecasts with Applications to Financial Risk Management 1997An Overview of Value at Risk 1987The Pricing of Options on Assets with Stochastic Volatilities

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2001Bayesian Risk Measures for Derivatives via Random Esscher Transform 2007A PDE approach for risk measures for derivatives with regime switching 2004A new Fourier transform algorithm for value-at-risk 1999A comparison of analytical VaR methodologies for portfolios that include options 2010Value at Risk

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