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Testing option pricing with the Edgeworth expansion

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  • Balieiro Filho, Ruy Gabriel
  • Rosenfeld, Rogerio

Abstract

There is a well-developed framework, the Black–Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is flawed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black–Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more efficient hedging strategies of these instruments.

Suggested Citation

  • Balieiro Filho, Ruy Gabriel & Rosenfeld, Rogerio, 2004. "Testing option pricing with the Edgeworth expansion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 484-490.
    • Handle: RePEc:eee:phsmap:v:344:y:2004:i:3:p:484-490
    DOI: 10.1016/j.physa.2004.06.018
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    Citations

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    Cited by:

    1. André Catalão & Rogério Rosenfeld, 2020. "Analytical Path-Integral Pricing Of Deterministic Moving-Barrier Options Under Non-Gaussian Distributions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-52, February.
    2. Del Brio, Esther B. & Mora-Valencia, Andrés & Perote, Javier, 2014. "Semi-nonparametric VaR forecasts for hedge funds during the recent crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 330-343.
    3. Andre Catalao & Rogerio Rosenfeld, 2018. "Analytical Path-Integral Pricing of Moving-Barrier Options under non-Gaussian Distributions," Papers 1804.07852, arXiv.org.
    4. 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.
    5. Gaston Milanesi & Gabriela Pesce & Emilio El Alabi, 2015. "Strategic Asset Valuation: A Model Including Asymmetry and Kurtosis in Its Distribution in Continuous Time," Academic Journal of Economic Studies, Faculty of Finance, Banking and Accountancy Bucharest,"Dimitrie Cantemir" Christian University Bucharest, vol. 1(1), pages 91-104, March.
    6. Ramos, Antônio M.T. & Carvalho, J.A. & Vasconcelos, G.L., 2016. "Exponential model for option prices: Application to the Brazilian market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 161-168.
    7. Milanesi, Gastón, 2021. "Modelo de valoración con opciones reales, rejillas trinomial, volatilidad cambiante, sesgo y función isoelástica de utilidad || Valuation model with real options, trinomial lattice, changing volatilit," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 32(1), pages 257-273, December.
    8. Felipe Isaza Cuervo & Sergio Botero Boterob, 2014. "Aplicación de las opciones reales en la toma de decisiones en los mercados de electricidad," Estudios Gerenciales, Universidad Icesi, November.

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    Keywords

    Option pricing; Non-gaussian distribution;

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