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A general closed form option pricing formula


Necula, Ciprian; Drimus, Gabriel; Farkas, Walter (2019). A general closed form option pricing formula. Review of Derivatives Research, 22:1-40.

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:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Social Sciences & Humanities > Finance
Social Sciences & Humanities > Economics, Econometrics and Finance (miscellaneous)
Language:English
Date:15 April 2019
Deposited On:07 Jan 2020 14:37
Last Modified:19 Mar 2021 14:44
Publisher:Springer
ISSN:1380-6645
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s11147-018-9144-z
Related URLs:https://www.zora.uzh.ch/id/eprint/115035/
Other Identification Number:merlin-id:18286

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