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  • In this paper we provide an extensive classification of one and two dimensional diffusion processes which admit an exact solution to the Kolmogorov (and hence Black-Scholes) equation (in terms of hypergeometric functions). By identifying the one-dimensional solvable processes with the class of {\it integrable superpotentials} introduced recently in supersymmetric quantum mechanics, we obtain new analytical solutions. In particular, by applying {\it supersymmetric transformations} on a known solvable diffusion process (such as the Natanzon process for which the solution is given by a hypergeometric function), we obtain a hierarchy of new solutions. These solutions are given by a sum of hypergeometric functions, generalizing the results obtained in the paper "Black-Scholes Goes Hypergeometric" \cite{alb}. For two-dimensional processes, more precisely stochastic volatility models, the classification is achieved for a specific class called gauge-free models including the Heston model, the $3/2$-model and the geometric Brownian model. We then present a new exact stochastic volatility model belonging to this class. (xsd:string)
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?:dateModified
  • 2007 (xsd:gyear)
?:datePublished
  • 2007 (xsd:gyear)
?:doi
  • 10.1080/14697680601103045 ()
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  • en (xsd:string)
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  • 5 (xsd:string)
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  • Solvable Local and Stochastic Volatility Models: Supersymmetric Methods in Option Pricing (xsd:string)
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  • Zeitschriftenartikel (xsd:string)
  • journal_article (en)
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  • GESIS-SSOAR (xsd:string)
  • In: Quantitative Finance, 7, 2007, 5, 525-535 (xsd:string)
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?:urn
  • urn:nbn:de:0168-ssoar-220959 ()
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  • 7 (xsd:string)