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Bayesian Analysis of the Black-Scholes Option Price

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  • Darsinos, T.
  • Satchell, S.E.

Abstract

This paper investigates the statistical properties of the Black-Scholes option price under a Bayesian approach. We incorporate randomness, both in the price process and in volatility, to derive the prior and posterior densities of a European call option. Expressions for the density of the option price conditional on the sample estimates of volatility and on the asset price respectively, are also derived. Numerical results are presented to compare how the dispersion of the option price changes in the transition from prior to posterior information, where information may be price or sample variance or both.

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  • Darsinos, T. & Satchell, S.E., 2001. "Bayesian Analysis of the Black-Scholes Option Price," Cambridge Working Papers in Economics 0102, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0102
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    Cited by:

    1. Darsinos, T. & Satchell, S.E., 2002. "The Implied Distribution for Stocks of Companies with Warrants and/or Executive Stock Options," Cambridge Working Papers in Economics 0217, Faculty of Economics, University of Cambridge.
    2. Shu Wing Ho & Alan Lee & Alastair Marsden, 2011. "Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models," JRFM, MDPI, vol. 4(1), pages 1-23, December.
    3. Henryk Gzyl & Enrique ter Horst & Samuel W. Malone, 2008. "Bayesian parameter inference for models of the Black and Scholes type," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 507-524, November.
    4. Cangrejo Esquivel, Álvaro Javier & Tovar Cuevas, José Rafael & García, Isabel Cristina & Manotas Duque, Diego Fernando, 2022. "Estimación clásica y bayesiana de la volatilidad en el modelo de Black-Scholes [Classical and Bayesian estimation of volatility in the Black-Scholes model]," 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. 34(1), pages 237-262, December .
    5. Hanno Gottschalk & Elpida Nizami & Marius Schubert, 2016. "Option Pricing in Markets with Unknown Stochastic Dynamics," Papers 1602.04848, arXiv.org, revised Jan 2017.
    6. Darsinos, T. & Satchell, S.E., 2001. "Bayesian Forecasting of Options Prices: A Natural Framework for Pooling Historical and Implied Volatiltiy Information," Cambridge Working Papers in Economics 0116, Faculty of Economics, University of Cambridge.

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