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

13 Pages Posted: 26 Jun 2009 Last revised: 12 Jan 2011

See all articles by Christian-Oliver Ewald

## Christian-Oliver Ewald

University of Glasgow; Høgskole i Innlandet

## Yajun Xiao

University of Freiburg - Department of Economics

## Yang Zou

University of Kaiserslautern - Department of Mathematics

## Tak-Kuen Siu

Macquarie University, Macquarie Business School

Date Written: June 25, 2009

### 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 $\delta \in [\frac{1}{2},1]$.

Keywords: Malliavin calculus, Feller diffusions, Greeks, Option pricing

JEL Classification: G13, C61, C63

Suggested Citation

Ewald, Christian-Oliver and Xiao, Yajun and Zou, Yang and Siu, Tak-Kuen, Malliavin Differentiability of a Class of Feller-Diffusions with Relevance in Finance (June 25, 2009). Available at SSRN: https://ssrn.com/abstract=1425855 or http://dx.doi.org/10.2139/ssrn.1425855