Error Estimates for Multinomial Approximations of American Options in Merton's Model

TL;DR

This paper provides new error estimates for multinomial approximations of American options within a multidimensional jump-diffusion Merton's model, extending previous results to more complex models and path-dependent payoffs.

Contribution

It introduces the first error estimates for multinomial approximations of American options in a jump-diffusion setting, using strong approximation theorems.

Findings

Error estimates for multinomial approximations in Merton's model.

Extension to path-dependent payoffs in Black--Scholes model.

Improved estimates for multinomial approximations in Black--Scholes model.

Abstract

We derive error estimates for multinomial approximations of American options in a multidimensional jump--diffusion Merton's model. We assume that the payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates for such type of approximations were not obtained before. Our main tool is the strong approximations theorems for i.i.d. random vectors which were obtained [14]. For the multidimensional Black--Scholes model our results can be extended also to a general path dependent payoffs which satisfy Lipschitz type conditions. For the case of multinomial approximations of American options for the Black--Scholes model our estimates are a significant improvement of those which were obtained in [8] (for game options in a more general setup)