Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type

TL;DR

This paper develops a mathematical framework using viscosity solutions to accurately price American options within a stochastic volatility model of Ornstein-Uhlenbeck type, addressing complexities in derivative valuation.

Contribution

It introduces a novel characterization of American option values as unique viscosity solutions to an integral-PDE in a specific stochastic volatility setting.

Findings

Viscosity solutions uniquely characterize American option prices.

The model accommodates stochastic volatility of Ornstein-Uhlenbeck type.

The approach handles Lipschitz continuous payoff functions.

Abstract

In this paper, we study the valuation of American type derivatives in the stochastic volatility model of Barndorff-Nielsen and Shephard (2001). We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condition.