Shortfall Risk Approximations for American Options in the multidimensional Black--Scholes Model

TL;DR

This paper demonstrates that shortfall risks for American options in multinomial approximations of the multidimensional Black--Scholes model converge to the true risks in the continuous model, extending previous work to multiple assets using weak convergence.

Contribution

It introduces a convergence result for shortfall risks in a multi-asset setting using multinomial approximations and weak convergence methods.

Findings

Shortfall risks in multinomial models converge to continuous model risks.

Extension of convergence results to multidimensional Black--Scholes models.

Use of weak convergence approach for multi-asset American options.

Abstract

We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we consider the multi assets case for which we use the weak convergence approach.