A General Closed Form Option Pricing Formula

41 Pages Posted: 2 Feb 2013 Last revised: 13 Jun 2018

See all articles by Ciprian Necula

Ciprian Necula

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

Gabriel G. Drimus

Institute of Banking and Finance, University of Zürich

Walter Farkas

University of Zurich - Department of Banking and Finance; Swiss Finance Institute; ETH Zurich

Date Written: October 30, 2017

Abstract

A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram-Charlier series expansion, known as the Gauss-Hermite expansion. This expansion converges for fat-tailed distributions commonly encountered in the study of financial returns. The expansion coefficients can be calibrated from observed option prices and can also be computed, for example, in models with the probability density function or the characteristic function known in closed form. We investigate the properties of the new option pricing model by calibrating it to both real-world and simulated option prices and find that the resulting implied volatility curves provide an accurate approximation for a wide range of strike prices. Based on an extensive empirical study, we conclude that the new approximation method outperforms other methods both in-sample and out-of-sample.

Keywords: European options, expansion-based approximation of risk-neutral density, Gauss-Hermite series expansion, calibration

JEL Classification: C63, G13

Suggested Citation

Necula, Ciprian and Drimus, Gabriel G. and Farkas, Walter, A General Closed Form Option Pricing Formula (October 30, 2017). Review of Derivatives Research, Forthcoming; Swiss Finance Institute Research Paper No. 15-53. Available at SSRN: https://ssrn.com/abstract=2210359 or http://dx.doi.org/10.2139/ssrn.2210359

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

Gabriel G. Drimus

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

Plattenstrasse 14
Zürich, CH-8032
Switzerland

Walter Farkas

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

Schönberggasse 1
Zürich, 8001
Switzerland
+41-44-634 3953 (Phone)
+41-44-634 4345 (Fax)

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

ETH Zurich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

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