A unified approach to determining the early exercise boundary position at expiry for American style of general class of derivatives

TL;DR

This paper introduces an analytic method to determine the early exercise boundary at expiry for American-style derivatives, validated against known results and numerical methods, enhancing pricing accuracy.

Contribution

It presents a novel analytic formula for the early exercise boundary at expiry applicable to various American derivatives, improving upon existing numerical approaches.

Findings

Analytic formula matches known boundary values.

Method applies to vanilla, Asian, and lookback options.

Results agree with PSOR numerical method.

Abstract

In this paper, we present a new method for calculating the limit of early exercise boundary at expiry. We price American style of general derivative using a formula expressed as a sum of the value of European style of derivative and so called American premium. We use the latter expression to calculate an analytic formula for limit of early exercise boundary at expiry. Method applied on American style plain vanilla, Asian and lookback options yields identical results with already known values. Results for selected American style of derivative strategies are compared with limits calculated by the PSOR method.