The Black-Scholes equation in stochastic volatility models
2010 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 368, no 2, 498-507 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2010. Vol. 368, no 2, 498-507 p.
Parabolic equations, Feynman-Kac theorems, Option pricing, Stochastic volatility, Boundary conditions
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-137205DOI: 10.1016/j.jmaa.2010.04.014ISI: 000277395900011OAI: oai:DiVA.org:uu-137205DiVA: diva2:377883