Advertisement

Elements of Malliavin calculus

  • Andrea Pascucci
Part of the Bocconi & Springer Series book series (BS)

Abstract

This chapter offers a brief introduction to Malliavin calculus and its applications to mathematical finance, in particular the computation of the Greeks by the Monte Carlo method. As we have seen in Section 12.4.2, the simplest way to compute sensitivities by the Monte Carlo method consists in approximating the derivatives by incremental ratios obtained by simulating the payoffs corresponding to close values of the underlying asset. If the payoff function is not regular (for example, in the case of a digital option with strike K and payoff function 1[K,+∞[) this technique is not efficient since the incremental ratio has typically a very large variance. In Section 12.4.2 we have seen that the problem can be solved by integrating by parts and differentiating the density function of the underlying asset, provided it is sufficiently regular: if the underlying asset follows a geometric Brownian motion, this is possible since the explicit expression of the density is known.

Keywords

Brownian Motion Duality Relation Geometric Brownian Motion Underlying Asset Asian Option 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Italia 2011

Authors and Affiliations

  • Andrea Pascucci
    • 1
  1. 1.Department of MathematicsUniversity of BolognaBologna

Personalised recommendations