The Black-Scholes equation in stochastic volatility models

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:368

Article

Ekstrom, Erik¹  Tysk, Johan¹ 

[1] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden

关键词: Parabolic equations;    Feynman-Kac theorems;    Option pricing;    Stochastic volatility;    Boundary conditions;   

DOI  :  10.1016/j.jmaa.2010.04.014

来源: Elsevier

【 摘 要 】

We study the Black-Scholes equation in stochastic volatility models. In particular, we show that the option price is the unique classical solution to a parabolic differential equation with a certain boundary behaviour for vanishing values of the volatility. If the boundary is attainable, then this boundary behaviour serves as a boundary condition and guarantees uniqueness in appropriate function spaces. On the other hand, if the boundary is non-attainable, then the boundary behaviour is not needed to guarantee uniqueness, but is nevertheless very useful for instance from a numerical perspective. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free