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Bayesian parameter inference for models of the Black and Scholes type

✍ Scribed by Henryk Gzyl; Enrique ter Horst; Samuel W. Malone

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
166 KB
Volume
24
Category
Article
ISSN
1524-1904

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✦ Synopsis

Abstract

In this paper, we describe a general method for constructing the posterior distribution of the mean and volatility of the return of an asset satisfying d__S__=S__d__X for some simple models of X. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as well as the likelihood function implied by the observed price history for the underlying. As an application of our framework, we compute the value at risk (VaR) and conditional VaR (CVaR) measures for the changes in the price of an option implied by the posterior distribution of the volatility of the underlying. The implied VaR and CVaR are more conservative than their classical counterpart, since it takes into account the estimation risk that arises due to parameter uncertainty. Copyright Β© 2008 John Wiley & Sons, Ltd.

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