American Passport options in an exponential L\'evy model

TL;DR

This paper develops a mathematical framework for valuing American passport options driven by Le9vy processes, deriving the pricing equation and proving key properties of the solution.

Contribution

It introduces a novel approach to pricing exotic options with Le9vy process underlying, establishing the viscosity solution and uniqueness of the valuation.

Findings

Derived the pricing equation using dynamic programming

Proved the viscosity solution property of the option value

Established the comparison principle ensuring uniqueness

Abstract

In this paper we examine the problem of valuing an exotic derivative known as the American passport option where the underlying is driven by a L\'evy process. The passport option is a call option on a trading account. We derive the pricing equation, using the dynamic programming principle, and prove that the option value is a viscosity solution of variational inequality. We also establish the comparison principle, which yields uniqueness and the convexity of the viscosity solution.