Value at Risk For Derivatives

Abstract

Value at Risk is close to becoming the method of choice for assessing risk exposures faced by financial firms. The assets and liabilities in the firm's risk portfolio are mapped onto a smaller set of standard factors, whose variances and correlation's are given (estimated) The returns variance for the entire position is computed and the desired cutoff value for the lower tail of the portfolio's returns distribution, under the typical assumption of joint lognormality, gives an estimate of the Value at Risk. But this procedure runs into large problems when derivatives with non-linear payoffs are included in the portfolio, an it also can be very difficult to implement with non-Gaussian returns. El Jahel, Perraudin, and Sellin present a new technique that greatly extends the range of assets and returns distribution that can be handled conveniently in a VaR calculation. For example, their framework easily accommodates non-linear payoffs, fat-tailed returns distributions, and stochastic volatility. It begins by computing the characteristic function for the whole portfolio, which is used to determine the first four moments of the returns distribution. Finally, an approximating distribution selected from a general family of distributions is fitted to these moments, and becomes the distribution used for VaR calculations. As the article shows, the results are distinctly more accurate than standard approaches.