Solution of option pricing equations using orthogonal polynomial expansion

Falko Baustian, Kate\v{r}ina Filipov\'a and Jan Posp\'i\v{s}il

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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.

Date: 2019-12, Revised 2020-06
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Published in Applications of Mathematics, Volume 66 (4), pp. 553-582, 2021

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1912.06533

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