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arXiv · 1912.06533

Solution of option pricing equations using orthogonal polynomial expansion

Falko Baustian·Kateřina Filipová·Jan Pospíšil
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Abstract

In this paper we study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial diferential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare obtained solutions to existing semi-closed pricing formulas. Special attention is paid to the solution of Heston model at the boundary with vanishing volatility.

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Falko Baustian, Kateřina Filipová, Jan Pospíšil. 2019-12-13. Solution of option pricing equations using orthogonal polynomial expansion. https://doi.org/10.21136/am.2021.0361-19

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