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Closed Form Option Pricing Under Generalized Hermite Expansions

42 Pages Posted: 5 Nov 2013 Last revised: 8 Jan 2018

Gabriel G. Drimus

Institute of Banking and Finance, University of Zürich

Walter Farkas

University of Zurich, Swiss Finance Institute (SFI) at Department of Banking and Finance; ETH Zürich - Department of Mathematics; Swiss Finance Institute

Ciprian Necula

University of Zurich - Department of Banking and Finance; Bucharest University of Economic Studies, Department of Money and Banking

Anastasiia Sokko

University of Zurich, Department of Banking and Finance; Swiss Finance Institute

Date Written: January 7, 2018

Abstract

In this article we generalize the classical Edgeworth series expansion, the Gram- Charlier Type A expansion and the Gauss-Hermite expansion used in the option pricing literature. We obtain a closed-form pricing formula for European options by employing the generalized Hermite expansion for the risk-neutral density. The main advantage of the generalized expansion is that it can be applied to heavy-tailed return distributions, a case for which the standard Edgeworth expansions are not suitable. The expansion coefficients can be inferred directly from market option prices. We calibrate the model to European options on the S&P 500 index, and the results indicate that the option price data can be explained well by a risk-neutral density, whose tails are heavier than of normal distribution, but are not fat.

Keywords: European options, generalized Hermite series expansion, calibration

JEL Classification: C63, G13

Suggested Citation

Drimus, Gabriel G. and Farkas, Walter and Necula, Ciprian and Sokko, Anastasiia, Closed Form Option Pricing Under Generalized Hermite Expansions (January 7, 2018). Available at SSRN: https://ssrn.com/abstract=2349868 or http://dx.doi.org/10.2139/ssrn.2349868

Gabriel G. Drimus

Institute of Banking and Finance, University of Zürich ( email )

Plattenstrasse 14
Zürich, CH-8032
Switzerland

Walter Farkas

University of Zurich, Swiss Finance Institute (SFI) at Department of Banking and Finance ( email )

Plattenstrasse 14
CH-8032 Zurich, Zurich 8032
Switzerland
+41-44-634 3953 (Phone)
+41-44-634 4345 (Fax)

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

Swiss Finance Institute

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

Ciprian Necula (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

Bucharest University of Economic Studies, Department of Money and Banking ( email )

6, Romana Square, District 1
Bucharest, 010374
Romania

HOME PAGE: http://www.dofin.ase.ro/cipnec

Anastasiia Sokko

University of Zurich, Department of Banking and Finance ( email )

Schönberggasse 1
Zurich
Switzerland

Swiss Finance Institute ( email )

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

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