Malliavin Differentiability of a Class of Feller-Diffusions with Relevance in Finance

Abstract

In this paper we discuss the Malliavin differentiability of a particular class of Feller diffusions which we call $\delta$-diffusions. This class is given by \begin{equation*} d\nu_t=\kappa(\theta-\nu_t))dt \eta \nu_t^{\delta}d\mathbb W_t^2, \delta\in[\frac{1}{2},1] \end{equation*} and appears to be of relevance in Finance, in particular for interest and foreign-exchange models, as well as in the context of stochastic volatility models. We extend the result obtained in Alos and Ewald (2008) for $\delta=\frac{1}{2}$ and proof Malliavin differentiability for all $\delta \in [\frac{1}{2},1]$.