Option Pricing with Orthogonal Polynomial Expansions

Mathematical Finance, Forthcoming

Swiss Finance Institute Research Paper No. 17-41

40 Pages Posted: 29 Nov 2017 Last revised: 9 Jun 2019

See all articles by Damien Ackerer

Damien Ackerer

Swissquote Bank

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Date Written: May 20, 2019

Abstract

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the nested affine case. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.

Keywords: Greeks, Option Pricing, Orthogonal Polynomials, Parameter Sensitivity, Polynomial Diffusion Models, Stochastic Volatility

JEL Classification: C32, G12, G13

Suggested Citation

Ackerer, Damien and Filipovic, Damir, Option Pricing with Orthogonal Polynomial Expansions (May 20, 2019). Mathematical Finance, Forthcoming; Swiss Finance Institute Research Paper No. 17-41. Available at SSRN: https://ssrn.com/abstract=3076519 or http://dx.doi.org/10.2139/ssrn.3076519

Damien Ackerer (Contact Author)

Swissquote Bank ( email )

Ch. de la Crétaux 33
Gland, Vaud 1196
Switzerland

Damir Filipovic

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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