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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.

Suggested Citation

  • 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. Hanno Gottschalk & Elpida Nizami & Marius Schubert, 2016. "Option Pricing in Markets with Unknown Stochastic Dynamics," Papers 1602.04848, arXiv.org, revised Jan 2017.
    2. 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.
    3. 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.
    4. 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," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 4(1), pages 1-23, December.

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