A simple discretization scheme for nonnegative diffusion processes, with applications to option pricing

TL;DR

This paper introduces a straightforward discretization method for nonnegative diffusion processes, ensuring convergence for Monte Carlo option pricing, with applications mainly in finance and path-dependent options.

Contribution

It presents a novel, simple discretization scheme for nonnegative diffusions with proven convergence, applicable to a wide range of models in option pricing.

Findings

Scheme guarantees convergence of Monte Carlo prices to theoretical values.

Applicable to various models and diffusion processes.

Simplifies the discretization process for nonnegative diffusions.

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.