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Stochastic Taylor Expansions and Saddlepoint Approximations for Risk Management
Company: ETH Zurich
Year Of Publication: 2001
Month Of Publication: November
Pages: 155
Download Count: 804
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Comment Num: 0
Language: EN
Who Can Read: Free
Date: 5-2-2005
Publisher: Administrator
The present work can be divided into two parts. The first part starts with anoverview over different approaches to risk management and risk measures.Then we review and partly extend saddlepoint approximations and stochasticTaylor expansions. Saddlepoint approximations, a relatively old statisticaltechnique, give in some cases important alternatives to Fourier inversion andmay lead especially for the problem of quantile calculation to fast and oftenaccurate answers. Stochastic Taylor expansions are stochastic analoguesof the well-known Taylor expansion of deterministic analysis and are mainlyused for simulation purposes. We review the basic facts of stochastic Taylorexpansions for diffusion processes and develop an analogue for multivariatePoisson processes. These two expansions are then linked together.In the second part of the thesis we examine the applicability of theseapproximations to questions relevant within risk management. We examinethe performance of stochastic Taylor expansions and/or saddlepoint approximationsin contrast to some existing approximations. The applicability isexamined for three specific types of model, covering a large part of continuoustime models used in finance. We start with the standard Black-Scholesmodel. Although this model is a special case of the second type, we devote tothis model a separate chapter because of its importance for practice. We thenmove to general diffusion models which capture the important sub-classes ofstochastic volatility models and models for bond prices. As a last type we examineLevy type models which are currently in vogue as models for the priceevolution of some financial asset.
Studer, Michael Sign in to follow this author
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