Tuesday, September 22, 2009
10:30 AM in REC 307
Cheng Ouyang
Golomb Assistant Professor of Mathematics, Purdue University

Near expiry asymptotics of the implied volatility in local volatility models and stochastic volatility models

Abstract

Using the heat kernel expansion technique, we give the first term in the asymptotics of European call option prices with respect to the time to the expiry T. We use this formula to calculate both the leading value of the implied volatility σI and the first order deviation of σI from its leading value. Some geometric interpretations will be discussed for these two terms. In particular, the leading value of the implied volatility could be interpreted as the Riemannian distance under the metric determined by the equation satisfied by the stock price S.

A quick survey of the background of the problem including some back-ground knowledge in mathematical finance will be given at the beginning of the talk.