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Erschienen in:
2018 | OriginalPaper | Buchkapitel
1. Cumulant Generating Functions and Steepest Descent Method
verfasst von : Yue Kuen Kwok, Wendong Zheng
Erschienen in: Saddlepoint Approximation Methods in Financial Engineering
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Abstract
The density functions of most stochastic processes that model the stochastic evolution of the underlying state variables in financial engineering models do not admit closed form analytic representation while their generalized Fourier transform and Laplace transform may have closed form formulas. The pricing of derivatives and computation of risk measures in general involve the evaluation of Fourier or Laplace type integrals. First, we discuss the fundamental properties related to the characteristic functions and cumulant generating functions of random variables.