Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Using a geometric expansion of the transition density function of a possibly time-inhomogeneous two-dimensional diffusion, we obtain a two-term asymptotic expansion for the call price near expiry for a general stochastic volatility models. This in turn yields a three-term approximation of the implied volatility. For the SABR model, the underlying geometry is hyperbolic and relevant calculations can be made explicit and our results generalize earlier works by Hagan, Kumar Lesniewski, Woodward, and Henry-Labordere. This research is a joint work with G. Ben Arous, Peter Laurence, Cheng Ouyang, and Tai-Ho Wang.

Speaker: Elton Hsu, Northwestern University

Slides: (TBA)