Computation of Greeks for Barrier and Lookback Options Using Malliavin Calculus

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...

Discrete Barrier and Lookback Options

Discrete barrier and lookback options are among the most popular path-dependent options in markets. However, due to the discrete monitoring policy almost no analytical solutions are available for them. We shall focus on the following methods for discrete barrier and lookback option prices: (1) Broadie–Yamamoto method based on fast Gaussian transforms. (2) Feng–Linetsky method based on Hilbert t...

Stephan Sturm Calculation of the Greeks by Malliavin Calculus

Efficient simulation of Greeks of multiasset European and Asian style options by Malliavin calculus and quasi-Monte Carlo methods

Keywords: Multiasset options Option sensitivities or Greeks Malliavin calculus Monte Carlo and quasi-Monte Carlo methods a b s t r a c t This paper discusses simulation of sensitivities or Greeks of multiasset European and Asian style options by Malliavin calculus combined with Monte Carlo and quasi-Monte Carlo methods. By using the Malliavin calculus, we are able to express Greeks of both Euro...

An Algorithm for the Pricing of Path-Dependent American Options using Malliavin Calculus

We propose a recursive scheme to calculate backward the values of conditional expectations of functions of path values of Brownian motion. This schemes is based on the Clark-Ocone formula in discrete time. We construct an algorithm based our scheme to effectively calculate the price of American options on securities with path-dependent payoffs. Our algorithm remedies the decrease of performance...