Error estimates for discrete approximations of game options with multivariate diffusion asset prices

TL;DR

This paper develops error estimates for discrete approximations of multivariate diffusion processes and applies these to compute fair prices of game options with path-dependent payoffs in multi-asset markets.

Contribution

It introduces new error bounds for strong approximations of multivariate diffusions and uses them to estimate game option prices via discrete-time Dynkin's games.

Findings

Provides effective error estimates for diffusion approximations.

Enables accurate computation of game option prices.

Applicable to multi-asset markets with path-dependent payoffs.

Abstract

We obtain error estimates for strong approximations of a diffusion with a diffusion matrix $\sigma$ and a drift b by the discrete time process defined recursively X_N((n+1)/N) = X_N(n/N)+N^{1/2}\sigma(X_N(n/N))\xi(n+1)+N^{-1}b(XN(n/N)); where \xi(n); n\geq 1 are i.i.d. random vectors, and apply this in order to approximate the fair price of a game option with a diffusion asset price evolution by values of Dynkin's games with payoffs based on the above discrete time processes. This provides an effective tool for computations of fair prices of game options with path dependent payoffs in a multi asset market with diffusion evolution.