In this paper Bayesian inference and the Stochastic Volatility models are used in European option pricing. We show how can compute option prices from Bayesian inference viewpoint, using the Stochastic volatility models for the dynamics of the volatility of the underlying asset. The basic for direct option pricing is the distribution of the payoff function, induced by the predictive density of future observables. We consider also another approach to option pricing, where the predictive distribution of the Black-Sholes and Hull-White formulas are used. In our empirical illustration we consider the hypothetical European call options on WIG index with different maturity: 30, 60, 90 working days. The results presented in this paper are obtained by Monte Carlo Markov chain. The Metropolis-Hastings algorithm and the acceptance-rejection sampling are used within the Gibbs sampler.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.