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...

In this article, we develop a Malliavin calculus associated to a timecontinuous Markov chain with finite state space. We apply it to get a criterion of density for solutions of SDE involving the Markov chain and also to compute greeks. keywords: Dirichlet form; Integration by parts formula; Malliavin calculus; Markov chain; computation of greeks. Mathematics subject classification: 60H07; 60J10...

We translate into the language of semi-group theory Bismut’s Calculus on boundary processes Bismut 1983 , Lèandre 1989 which gives regularity result on the heat kernel associated with fractional powers of degenerated Laplacian. We translate into the language of semi-group theory the marriage of Bismut 1983 between the Malliavin Calculus of Bismut type on the underlying diffusion process and the...

Abstract. We present a method to apply the Malliavin calculus to calculate sensitivities for exponential Levy models built from the Variance Gamma and Normal Inverse Gaussian processes. We also present new sensitivities for these processes. The calculation of the sensitivities is based on a finite dimensional Malliavin calculus and we compare the results with finite difference calculations. Thi...

This article establishes existence and uniqueness of solutions to two classes of stochastic systems with finite memory subject to anticipating initial conditions which are sufficiently smooth in the Malliavin sense. The two classes are semilinear stochastic functional differential equations (sfdes) and fully nonlinear sfdes with a sublinear drift term. For the semilinear case, we use Malliavin ...