The early exercise premium representation for American options on multiply assets

TL;DR

This paper derives a general early exercise premium formula for American options on multiple assets with convex payoffs, using advanced stochastic analysis techniques.

Contribution

It introduces a unified early exercise premium representation applicable to a wide class of multi-asset American options with convex payoffs.

Findings

Provides a general formula for early exercise premium in multi-asset American options.

Connects optimal stopping, obstacle problems, and reflected BSDEs in valuation.

Applicable to various options like index, spread, max, min, and power-product options.

Abstract

In the paper we consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follow the classical multidimensional Black and Scholes model. We provide a general early exercise premium representation formula for options with payoff functions which are convex or satisfy mild regularity assumptions. Examples include index options, spread options, call on max options, put on min options, multiply strike options and power-product options. In the proof of the formula we exploit close connections between the optimal stopping problems associated with valuation of American options, obstacle problems and reflected backward stochastic differential equations.