On the Short-Time Behavior of the Implied Volatility for Jump-Diffusion Models With Stochastic Volatility
22 Pages Posted: 24 Jul 2007
Date Written: June 2006
In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.
Keywords: Black-Scholes formula, derivative operator, Itô's formula for the Skorohod integral, jump-diffusion stochastic volatility model
JEL Classification: G12, G13
Suggested Citation: Suggested Citation