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Quantiles of the Euler Scheme for Diffusion Processes and Financial Applications

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  • Denis Talay
  • Ziyu Zheng

Abstract

In this paper we briefly present the results obtained in our paper (Talay and Zheng 2002a) on the convergence rate of the approximation of quantiles of the law of one component of (Xt), where (Xt) is a diffusion process, when one uses a Monte Carlo method combined with the Euler discretization scheme. We consider the case where (Xt) is uniformly hypoelliptic (in the sense of Condition (UH) below), or the inverse of the Malliavin covariance of the component under consideration satisfies the condition (M) below. We then show that Condition (M) seems widely satisfied in applied contexts. We particularly study financial applications: the computation of quantiles of models with stochastic volatility, the computation of the VaR of a portfolio, and the computation of a model risk measurement for the profit and loss of a misspecified hedging strategy.

Suggested Citation

  • Denis Talay & Ziyu Zheng, 2003. "Quantiles of the Euler Scheme for Diffusion Processes and Financial Applications," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 187-199, January.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:1:p:187-199
    DOI: 10.1111/1467-9965.00013
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    References listed on IDEAS

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    1. Talay, Denis & Zheng, Ziyu, 2004. "Approximation of quantiles of components of diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 23-46, January.
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    Cited by:

    1. Laurent Denis & Begoña Fernández & Ana Meda, 2009. "Estimation Of Value At Risk And Ruin Probability For Diffusion Processes With Jumps," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 281-302, April.
    2. Talay, Denis & Zheng, Ziyu, 2004. "Approximation of quantiles of components of diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 23-46, January.
    3. Balder, Sven & Brandl, Michael & Mahayni, Antje, 2009. "Effectiveness of CPPI strategies under discrete-time trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 204-220, January.

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