Solution of option pricing equations using orthogonal polynomial expansion

Falko Baustian; Kateřina Filipová; Jan Pospíšil

Applications of Mathematics (2021)

  • Volume: 66, Issue: 4, page 553-582
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Baustian, Falko, Filipová, Kateřina, and Pospíšil, Jan. "Solution of option pricing equations using orthogonal polynomial expansion." Applications of Mathematics 66.4 (2021): 553-582. <http://eudml.org/doc/298093>.

@article{Baustian2021,
abstract = {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.},
author = {Baustian, Falko, Filipová, Kateřina, Pospíšil, Jan},
journal = {Applications of Mathematics},
keywords = {orthogonal polynomial expansion; Hermite polynomial; Laguerre polynomial; Heston model; option pricing},
language = {eng},
number = {4},
pages = {553-582},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solution of option pricing equations using orthogonal polynomial expansion},
url = {http://eudml.org/doc/298093},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Baustian, Falko
AU - Filipová, Kateřina
AU - Pospíšil, Jan
TI - Solution of option pricing equations using orthogonal polynomial expansion
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 4
SP - 553
EP - 582
AB - 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.
LA - eng
KW - orthogonal polynomial expansion; Hermite polynomial; Laguerre polynomial; Heston model; option pricing
UR - http://eudml.org/doc/298093
ER -

References

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