Geodesic
Solution of option pricing equations using orthogonal polynomial expansion
Applications of Mathematics, Tome 66 (2021) no. 4, pp. 553-582

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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 differential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare the obtained solutions to existing semi-closed pricing formulas. Special attention is paid to the solution of the Heston model at the boundary with vanishing volatility.
DOI : 10.21136/AM.2021.0361-19
Classification : 33C45, 65M60, 91G20, 91G60
Keywords: orthogonal polynomial expansion; Hermite polynomial; Laguerre polynomial; Heston model; option pricing 
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Baustian, Falko; Filipová, Kateřina; Pospíšil, Jan. Solution of option pricing equations using orthogonal polynomial expansion. Applications of Mathematics, Tome 66 (2021) no. 4, pp. 553-582. doi: 10.21136/AM.2021.0361-19

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