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A General Closed Form Option Pricing Formula


Necula, Ciprian; Drimus, Gabriel G; Farkas, W (2015). A General Closed Form Option Pricing Formula. SSRN 2210359, University of Zurich.

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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:2015
Deposited On:26 Nov 2015 11:00
Last Modified:16 Aug 2017 14:48
Series Name:SSRN
Free access at:Official URL. An embargo period may apply.
Official URL:http://ssrn.com/abstract=2210359
Other Identification Number:merlin-id:12582, 2210359

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