Ruoting Gong : Small-time asymptotics and expansions of option prices under Lévy-based models

Posted by Cheng Ouyang , part of the Statistics and Data Science Seminar.

At

Oct. 1, 2014, 4 p.m.

In

SEO 636

Abstract

The small-time asymptotic behavior of option prices and implied volatilities for jump-diffusion models has received much attention in recent years. In this presentation, we study the time-to-maturity asymptotics of call option prices under a variety of models with Lévy jumps. In the out-of-the-money (OTM) and in-the-money (ITM) case, we consider a general stochastic volatility model with independent Lévy jumps for the log-return process of the underlying stock price. In this setting, small-time expansions, of arbitrary polynomial order, in time-t, are obtained for both OTM and ITM call option prices. In the at-the-money (ATM) case, a novel second-order approximation of the call option price is obtained for a large class of exponential "tempered-stable-like" Lévy models with or without Brownian component. As a consequence, small-time expansions of the corresponding Black-Scholes implied volatilities are also addressed in both cases. This is the joint work with J. E. Figueroa-López and C. Houdré.