Computations of Greeks in a market with jumps via the Malliavin calculus
type: Item
instance of: scholarly article
title: Computations of Greeks in a market with jumps via the Malliavin calculus
zbMATH Open document ID: 1098.91050
author: Youssef El-Khatib
author: Nicolas Privault
published in: Finance and Stochastics
publication date: 2004-11-24T00:00:00Z
review text: The authors deal with Asian options in a market model with jumps, and present formulas for the computation of Greeks using a particular version of the Malliavin calculus on a Poisson space. The family of jump processes includes sums of independent Poisson processes with arbitrary jump sizes. A version of the operator is used that has the derivation property and its adjoint coincides with the Poisson stochastic integral, which provides a natural way to make explicit computation of weights. The integration by parts formula is presented which is the main tool for computing Greeks using a random variable called a weight. They consider the Delta of a binary Asian option and the Gamma of a standard Asian option with numerical simulations. These simulations show that the Malliavin approach applied to Asian options in the case of a market driven by a Poisson process is more efficient than the finite difference method.
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 2118694
zbMATH Keywords: Greeks
zbMATH Keywords: market with jumps
zbMATH Keywords: Asian options
zbMATH Keywords: Poisson process
zbMATH Keywords: Malliavin calculus
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s00780-003-0111-6
OpenAlex ID: W2064599895
DOI: 10.1007/S00780-003-0111-6
Recommended article: Computation of Greeks using Malliavin's calculus in jump type market models
Recommended article: Computation of Greeks in jump-diffusion models using discrete Malliavin calculus
Recommended article: Calculations of greeks for jump diffusion processes
Recommended article: Q3195634
Recommended article: Computation of Greeks using the discrete Malliavin calculus and binomial tree
Recommended article: Computation of option Greeks under hybrid stochastic volatility models via Malliavin calculus
Recommended article: Malliavin Monte Carlo Greeks for jump diffusions
Recommended article: Computation of Greeks for barrier and look-back options using Malliavin calculus
Recommended article: Malliavin Calculus for Pure Jump Processes and Applications to Finance
Recommended article: Q3996311
description: scientific article; zbMATH DE number 2118694