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Exactly Solvable Diffusion Equations and Pricing Models Based on Exceptional Hermite Polynomials

Date

2023-07-31

Authors

Menchions, Yvonne

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Abstract

In 1973, Black-Scholes and Merton developed a partial differential equation that models the price evolution of a European call option, now referred to as the Black-Scholes equation. Because of its importance in options pricing, there has been a lot of research put into developing solvable derivative models. Through a gauge transformation, the classical Black-Scholes equation can be transformed into a Schrodinger equation. From there, we apply supersymmetric methods to construct a family of orthogonal solutions in terms of exceptional Hermite polynomials. We use these techniques to generalize the classical Black-Scholes equation and obtain solvable derivative models.

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Keywords

exceptional hermite polynomials

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