A Simple Discretization Scheme for Nonnegative Diffusion Processes, with Applications to Option Pricing

27 Pages Posted: 8 Jun 2010 Last revised: 16 Nov 2010

See all articles by Chantal Labbé

Chantal Labbé

HEC Montreal

Bruno Remillard

Department of Decision Sciences, HEC Montreal

Jean-Francois Renaud

University of Quebec at Montreal (UQAM)

Date Written: November 14, 2010

Abstract

A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically from finance, especially for path-dependent option pricing. The scheme is simple: one only needs to find a nonnegative distribution whose mean and variance satisfy a simple condition to apply it. Then, for virtually any (path-dependent) payoff, Monte Carlo option prices obtained from this scheme will converge to the theoretical price. Examples of models and diffusion processes for which the scheme applies are provided.

Keywords: Euler discretization schemes, nonnegativity preservation, diffusion processes, Markov chains, martingale problem, convergence in distribution, interest rate models, stochastic volatility models, path-dependent options

JEL Classification: C00, G13

Suggested Citation

Labbé, Chantal and Remillard, Bruno and Renaud, Jean-Francois, A Simple Discretization Scheme for Nonnegative Diffusion Processes, with Applications to Option Pricing (November 14, 2010). Available at SSRN: https://ssrn.com/abstract=1619989 or http://dx.doi.org/10.2139/ssrn.1619989

Chantal Labbé

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada

Bruno Remillard

Department of Decision Sciences, HEC Montreal ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada
514-340-6794 (Phone)

Jean-Francois Renaud (Contact Author)

University of Quebec at Montreal (UQAM) ( email )

PB 8888 Station DownTown
Succursale Centre Ville
Montreal, Quebec H3C3P8
Canada

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