Title（问题）：Inverting Analytic Characteristic Functions and Simulating Lévy Processes

Speaker（报告人）：Liming Feng, Associate Professor

The University of Illinois at Urbana-Champaign

Time（时间）：2011年12月29日（周四）下昼2:00-3:00

Place（所在）：伟易博新楼217课堂

Abstract（摘要）：Analytic characteristic functions arise in many applications in statistics, engineering, and computational finance. We explore the analyticity of such characteristic functions and propose simple but highly accurate inversion schemes. The schemes have the following advantages: (1) they are very easy to implement; one does not need to rely on packages that are only available commercially; (2) despite the simplicity, they are highly accurate, with exponentially decaying errors; (3) they admit explicit error estimates that only depend on the given characteristic function; (4) they are robust in handling extreme inputs; (5) multiple values of the desired quantity can be computed simultaneously using the fast Fourier transform. As an example, we consider the pricing of European vanilla options with extreme strike prices. Our schemes produce nearly exact option prices, while some commonly used methods lead to large pricing errors or even negative option prices. We further consider Monte Carlo simulation of Lévy processes with analytic characteristic functions and derive explicit bounds for the estimation bias of the inverse transform method. These bounds allow us to determine the grid where probabilities are computed and stored for any given bias tolerance level.

About the speaker（关于报告人）：Liming Feng is an assistant professor at the University of Illinois at Urbana-Champaign. He obtained his B.S. in Mathematics from Beijing Normal University, M.S. in Mathematics from Northwestern University, and Ph.D. in Industrial Engineering and Management Sciences from Northwestern University. His main research interests are in applied probability, stochastic modeling, and financial engineering. He is currently interested in developing high performance computational methods for solving financial problems. He helped build the Master of Science in Financial Engineering program at the University of Illinois and is involved in all aspects of the program.

https://netfiles.uiuc.edu/fenglm/www/