The Department of Finance and Risk Engineering welcomes Weilong Fu, Ph.D. Candidate, Department of Industrial Engineering and Operations Research at Columbia University, to the BQE Lecture Series.
Fast Pricing of American Options Under Variance Gamma
We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure-jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it a time-changed Brownian motion. In the case of the Black-Merton-Scholes model, there are fast approximation methods for pricing American options, but they cannot be utilized for the variance gamma model. We develop a new fast and accurate approximation method inspired by the quadratic approximation to get rid of the time steps required in finite difference methods and simulation methods, while reducing the error by making use of a machine learning technique on pre-calculated quantities. We compare the performance of our method with those of the existing methods and show that this method is efficient and accurate for practical use.
Weilong is a fourth-year PhD candidate at Columbia University in the Department of Industrial Engineering and Operations Research. Before that, he received his bachelor's degree in Statistics from Peking University. Weilong's research interest is focused on computational and quantitative finance.