This paper derives an analytic expression for the distribution of the average volatility ds in the stochastic volatility model of Hull and White. This result answers a longstanding question, posed by Hull and White (Journal of Finance 42, 1987), whether such an analytic form exists. Our findings...

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the...

We consider a stochastic volatility model with Lévy jumps for a log-return process Z=(Zt)t≥0 of the form Z=U+X, where U=(Ut)t≥0 is a classical stochastic volatility process and X=(Xt)t≥0 is an independent Lévy process with absolutely continuous Lévy measure ν. Small-time expansions, of...