The valuation of American options in a multidimensional exponential Levy model

TL;DR

This paper develops a mathematical framework for valuing American options on dividend-paying assets modeled by multidimensional exponential Levy processes, linking PDEs, variational inequalities, and stochastic equations.

Contribution

It introduces regularity results for the value function and derives an early exercise premium formula for a broad class of payoffs in this complex setting.

Findings

Established regularity of the value function.

Derived early exercise premium formula.

Linked PDEs, variational inequalities, and stochastic equations.

Abstract

We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial integro-differential variational inequalities and reflected backward stochastic differential equations. In particular, we prove regularity results for the value function and obtain the early exercise premium formula for broad class of payoff functions.