A Hull and White Formula for a General Stochastic Volatility Jump-Diffusion Model with Applications to the Study of the Short-Time Behavior of the Implied Volatility

[摘要] We obtain a Hull and White type formula for ageneral jump-diffusion stochastic volatility model, where theinvolved stochastic volatility process is correlated not only withthe Brownian motion driving the asset price but also with theasset price jumps. Towards this end, we establish an anticipative Itô's formula, using Malliavin calculus techniques for Lévy processes on the canonical space. As an application, we show that the dependence of the volatility process on the asset price jumps has no effect on the short-time behavior of theat-the-money implied volatility skew.

[学科分类] 应用数学