Saddlepoint Approximation Methods in Financial Engineering
Authors: Yue Kuen Kwok, Wendong Zheng

About the authors
Yue Kuen Kwok, Department of MathematicsHong Kong University of Science and Technology, Hong Kong, China
Wendong Zheng, Department of MathematicsHong Kong University of Science and Technology, Hong Kong, China

About this book
This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.
The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results.
Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quantitative analysts in financial institutions who strive for effective valuation of prices of exotic financial derivatives and risk positions of portfolios of risky instruments.

Table of contents

• Cumulant Generating Functions and Steepest Descent Method
• Saddlepoint Approximations to Density Functions, Tail Probabilities and Tail Expectations
• Extended Saddlepoint Approximation Methods
• Saddlepoint Approximation Formulas for Pricing Options
• Saddlepoint Approximation for Credit Portfolios
  

Series: SpringerBriefs in Quantitative Finance
Length: 128 pages
Copyright: 2018
Language: English
Publisher: Springer, Cham
ISBN: 978-3-319-74101-7