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

Pierre Henry-Labordere
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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 integrable superpotentials introduced recently in supersymmetric quantum mechanics, we obtain new analytical solutions. 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.

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Pierre Henry-Labordere. 2005-11-01. Solvable Local and Stochastic Volatility Models: Supersymmetric Methods in Option Pricing. https://arxiv.org/abs/cond-mat/0511028

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