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A General Closed Form Option Pricing Formula

Author

Listed:
  • Ciprian Necula

    (University of Zurich and Bucharest University of Economic Studies)

  • Gabriel G. Drimus

    (Institute of Banking and Finance)

  • Walter Farkas

    (University of Zurich, Ecole Polytechnique Fédérale de Lausanne, Swiss Finance Institute, and ETH Zürich)

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.

Suggested Citation

  • Ciprian Necula & Gabriel G. Drimus & Walter Farkas, 2015. "A General Closed Form Option Pricing Formula," Swiss Finance Institute Research Paper Series 15-53, Swiss Finance Institute, revised Mar 2016.
    • Handle: RePEc:chf:rpseri:rp1553
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    File URL: http://ssrn.com/abstract=2210359
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    References listed on IDEAS

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    Citations

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    Cited by:

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    2. Gangadhar Nayak & Subhranshu Sekhar Tripathy & Agbotiname Lucky Imoize & Chun-Ta Li, 2024. "Application of Extended Normal Distribution in Option Price Sensitivities," Mathematics, MDPI, vol. 12(15), pages 1-18, July.
    3. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
    4. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    5. Laurent Devineau & Pierre-Edouard Arrouy & Paul Bonnefoy & Alexandre Boumezoued, 2017. "Fast calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion," Working Papers hal-01521491, HAL.
    6. Inés Jiménez & Andrés Mora-Valencia & Javier Perote, 2022. "Dynamic selection of Gram–Charlier expansions with risk targets: an application to cryptocurrencies," Risk Management, Palgrave Macmillan, vol. 24(1), pages 81-99, March.
    7. Zhang, Yuanyuan & Zhang, Qian & Wang, Zerong & Wang, Qi, 2024. "Option valuation via nonaffine dynamics with realized volatility," Journal of Empirical Finance, Elsevier, vol. 77(C).
    8. Julien Hok & Tat Lung Chan, 2016. "Option pricing with Legendre polynomials," Papers 1610.03086, arXiv.org, revised Mar 2017.

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    More about this item

    Keywords

    European options; expansion-based approximation of risk-neutral density; Gauss-Hermite series expansion; calibration;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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