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A General Closed Form Option Pricing Formula

Ciprian Necula, Gabriel G. Drimus and Walter Farkas
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Gabriel G. Drimus: Institute of Banking and Finance
Walter Farkas: University of Zurich, Ecole Polytechnique Fédérale de Lausanne, Swiss Finance Institute, and ETH Zürich

No 15-53, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
Date: 2015-02, Revised 2016-03
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