VALUE-AT-RISK COMPUTATIONS IN STOCHASTIC VOLATILITY MODELS USING SECOND-ORDER WEAK APPROXIMATION SCHEMES

Eva Lütkebohmert and Lydienne Matchie ()
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Lydienne Matchie: Department of Financial Mathematics, Faculty of Economics and Behavioral Sciences, University of Freiburg, Platz der Alten Synagoge, 79098 Freiburg, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 01, 1-26

Abstract: We explore the class of second-order weak approximation schemes (cubature methods) for the numerical simulation of joint default probabilities in credit portfolios where the firm's asset value processes are assumed to follow the multivariate Heston stochastic volatility model. Correlation between firms' asset processes is reflected by the dependence on a common set of underlying risk factors. In particular, we consider the Ninomiya–Victoir algorithm and we study the application of this method for the computation of value-at-risk and expected shortfall. Numerical simulations for these quantities for some exogenous portfolios demonstrate the numerical efficiency of the method.

Keywords: Cubature methods; stochastic volatility; structural credit risk models; weak approximation schemes (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0219024914500046

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