Brownian Moton, Short Time Heat Kernel Asymptotion Differential Geometry, and Implied Volatility Expansion in Local and Stochastic Volatility Models
主 题: Brownian Moton, Short Time Heat Kernel Asymptotion Differential Geometry, and Implied Volatility Expansion in Local and Stochastic Volatility Models
报告人: Prof. Elton P Hsu (Northwestern University)
时 间: 2010-04-30 14:00-15:00
地 点: 理科一号楼1114(数学所活动)
In local and stochastic volatility models, the call price near expiry can investigated through the study of the short-time behavior of the transition density function of the underlying diffusion process. In stochastic volatility models, the diffusion process determines a Riemannian geometry in the stock-volatilityspace. The most relevant case is the so-called SABR model, whose geometryis that of hyperbolic space of constant curvature. We illustrate this point of view by investigating the asymptotic expansion of the implied volatility near expiry (joint work with Jim Gatheral, Peter Laurence, Ouyang Cheng, and Tai-Ho Wang).
