Malliavin Calculus applied to finance

Malliavin Calculus applied to Finance

In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where close formulas are not available, and we also open the view for including more ex...

Malliavin Calculus in Finance

This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index.

Applications of Malliavin calculus to Monte Carlo methods in finance

This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the integration-by-parts formula, which lies at the core of the theory of variational stochastic calculus, as developed in the Malliavin calculus. The Greeks formulae, both with respect to initial conditions and for smooth perturbations of...

Malliavin Greeks without Malliavin Calculus

We derive and analyze Monte Carlo estimators of price sensitivities (“Greeks”) for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is t...

An Introduction to Malliavin Calculus