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
15 Pages Posted: 24 Apr 2008
Date Written: January 4, 2008
In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).
Keywords: Hull and White formula, Malliavin calculus, Ito's formula for the Skorohod integral, jumpdiffusion stochastic volatility models
JEL Classification: G12, G13
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