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Bayesian Analysis of the Black-Scholes Option Price

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Darsinos, T.
Satchell, S.E.

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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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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
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Handle: RePEc:cam:camdae:0102

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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  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. [Downloadable!]
  2. 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. [Downloadable!]
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