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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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Bibliographic Info

Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0102.

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Length: 37
Date of creation: Jan 2001
Date of revision:
Handle: RePEc:cam:camdae:0102

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Citations

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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, Faculty of Economics, University of Cambridge 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," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 4(1), pages 74-96, December.
  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, Faculty of Economics, University of Cambridge 0116, Faculty of Economics, University of Cambridge.

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