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

Implied volatility from local volatility: A path integral approach

Tuesday, November 15, 2011 at 11:30am - 12:30pm

Speaker: Tai-Ho Wang, Baruch College

Starting from an argument given in Gatheral, Hsu, Laurence, Ouyang,and Wang (GHLOW, 2011), we derive an exact Brownian bridge representation for the transition density in a local volatility model, which then leads to an exact expression for the transition density in terms of a path integral. In the time homogeneous case, we recover the heat kernel expansion by Taylor-expanding around the most-likely-path. Repeating the same procedure in the time inhomogeneous case leads to a new more accurate and natural approximation to the transition density which differs from the heat kernel expansion as developed in GHLOW, 2011. We show that by suitably approximating the path integral representation, we recover the results previously obtained in GHLOW, 2011 and Gatheral and Wang (2011). Finally, we obtain an improved most-likely-path approximation for implied volatility in terms of local volatility with explicit skew and curvature corrections.

Speaker: Tai-Ho Wang, Baruch College

Location   Hill 705