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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This vertical strip always contains the imaginary axis since \(\kappa _X(0)=0\).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 The Author(s)
About this chapter
Cite this chapter
Kwok, Y.K., Zheng, W. (2018). Cumulant Generating Functions and Steepest Descent Method. In: Saddlepoint Approximation Methods in Financial Engineering. SpringerBriefs in Quantitative Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-74101-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-74101-7_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-74100-0
Online ISBN: 978-3-319-74101-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)