Solvable Local and Stochastic Volatility Models: Supersymmetric Methods in Option Pricing

Journal article | Zeitschriftenartikel

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.

Angaben zum Objekt

• Umfang: Seite(n): 525-535
• Sprache: Englisch
• Anmerkungen: Status: Postprint; begutachtet (peer reviewed)

Verweise und Beziehungen

• Erschienen in: Quantitative Finance, 7(5)

Klassifikation und Themen

• Thema: Wirtschaft ; Wirtschaftsstatistik, Ökonometrie, Wirtschaftsinformatik ; Allgemeines, spezielle Theorien und Schulen, Methoden, Entwicklung und Geschichte der Wirtschaftswissenschaften ; Theorieanwendung

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Henry-Labordere, Pierre
• Ereignis: Veröffentlichung
• (wo): Vereinigtes Königreich
• (wann): 2007

Weitere Informationen

• DOI: https://doi.org/10.1080/14697680601103045
• URN: urn:nbn:de:0168-ssoar-220959
• Rechteinformation: GESIS - Leibniz-Institut für Sozialwissenschaften. Bibliothek Köln
• Letzte Aktualisierung: 21.06.2024, 16:26 MESZ