Solution of option pricing equations using orthogonal polynomial expansion
Pricing of Securities
2021-11-17 v3 Computational Engineering, Finance, and Science
Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1912.06533,
title = {Solution of option pricing equations using orthogonal polynomial expansion},
author = {Falko Baustian and Kateřina Filipová and Jan Pospíšil},
journal= {arXiv preprint arXiv:1912.06533},
year = {2021}
}