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Solution of option pricing equations using orthogonal polynomial expansion

Author

Listed:
  • Falko Baustian
  • Katev{r}ina Filipov'a
  • Jan Posp'iv{s}il

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.

Suggested Citation

  • Falko Baustian & Katev{r}ina Filipov'a & Jan Posp'iv{s}il, 2019. "Solution of option pricing equations using orthogonal polynomial expansion," Papers 1912.06533, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:1912.06533
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    References listed on IDEAS

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