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The Black-Scholes equation in stochastic volatility models
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
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
Abstract [en]

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.
Keyword [en]
Parabolic equations, Feynman-Kac theorems, Option pricing, Stochastic volatility, Boundary conditions
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-137205DOI: 10.1016/j.jmaa.2010.04.014ISI: 000277395900011OAI: oai:DiVA.org:uu-137205DiVA: diva2:377883
Available from: 2010-12-15 Created: 2010-12-15 Last updated: 2017-12-11

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Ekström, Erik

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