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Solvable Local and Stochastic Volatility Models: Supersymmetric Methods in Option Pricing
[Zeitschriftenartikel]
Abstract 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 ... mehr
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.... weniger
Klassifikation
Wirtschaftsstatistik, Ökonometrie, Wirtschaftsinformatik
Allgemeines, spezielle Theorien und "Schulen", Methoden, Entwicklung und Geschichte der Wirtschaftswissenschaften
Methode
Theorieanwendung
Freie Schlagwörter
Applied Mathematical Finance; Econophysics; Black-Scholes Model; Stochastic Volatility; Calibration of Stochastic Volatility; Volatility Modelling
Sprache Dokument
Englisch
Publikationsjahr
2007
Seitenangabe
S. 525-535
Zeitschriftentitel
Quantitative Finance, 7 (2007) 5
DOI
https://doi.org/10.1080/14697680601103045
Status
Postprint; begutachtet (peer reviewed)
Lizenz
PEER Licence Agreement (applicable only to documents from PEER project)