Efficient Computation of Option Prices
Dr. Fred J. Hickernell
Department of Applied Mathematics
Illinois Institute of Technology
Stuart Building 223
Monday, November 21st, 2011
11:00AM - 12:00PM
Abstract: In finance the fair price of a put or call option is the expected value of the discounted payoff. This payoff depends on the future stock price path. Although it cannot be known in advance, different possible scenarios can be simulated and their average computed. Efficient computation of the option price involves several factors. This talk highlights how choosing the stock price paths carefully can significantly speed computation. We will demonstrate these efficient computational methods with some option pricing examples and briefly summarize the theoretical basis for these efficiency gains.
Bio: Fred Hickernell was born in Okinawa, and grew up in Phoenix, Arizona. He enjoyed mathematics and science in elementary and high school, so he majored in both mathematics and physics at Pomona College. Two enjoyable summers of research as an undergraduate whetted Fred's appetite for graduate study. He obtained his PhD in (applied) mathematics from Massachussets Institute of Technology in 1981. Fred has been a faculty member at the University of Southern California (1981-1985) and Hong Kong Baptist University (1985-2005). Since 2005, he has been serving as Department Chair and Professor of Applied Mathematics at Illinois Institute of Technology in Chicago. Fred's early research investigated nonlinear waves and instability in fluids. For the nearly 20 years, he has studied efficient quasi-Monte Carlo algorithms for high dimensional integration, function approximation using splines based on kernels, also called meshfree methods or kriging, and experimental design. This research draws on ideas from both computational mathematics and statistics. It has applications in option pricing and analysis of computer experiments. Fred's research has been funded by the National Science Foundation, the Department of Energy, and the Hong Kong Research Grants Council and has resulted in more than 100 publications. Fred serves on the editorial boards of several journals, including Journal of Complexity, Mathematics of Computation, and SIAM Journal on Numerical Analysis. Fred married his college sweetheart, Elaine Chu, more than thirty years ago, and they have two children. Fred and his family are members of Wheaton Chinese Alliance Church. The Hickernells enjoy music, tennis, and good Chinese food.