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

2008/12/12 by Alexandre F. Roch, Roch, Alexandre F.
Economics, Econometrics and Finance · Mathematics · #35D05 #60H30 #91B28 #Analysis of PDEs (math.AP) #Computational Finance (q-fin.CP) #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Stochastic processes and financial applications #math.AP #msc:35D05 #msc:60H30 #msc:91B28 #q-fin.CP

paper · pdf · doi:10.48550/arxiv.0812.2444

arxiv created 2008/12/12 · openalex publication_date 2008/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Properties of the American price function in the Heston-type models
• Option prices in stochastic volatility models
• The Stochastic Balance Equation for the American Option Value Function and its Gradient
• Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view
• Valuation equations for stochastic volatility models