This paper shows how one can compute option prices from a Bayesian inference view point, using a GARCH model for the dynamics of the the volatility of the underlying asset. The proposed evaluation of an option is the predictive expectation of its payoff function. The predictive distribution of this function provides a natural metric, provided it is neutralised with respect to the risk, for gauging the predictive option price or other option evaluations. The proposed method is compared to the Black and Scholes evaluation, in which a marginal mean volatility is plugged, but which does not provide a natural metric. The methods are illustrated using symmetric, asymmetric and smooth transition GARCH models with data on a stock index in Brussels.

This paper explains how the Gibbs sampler can be used to perform Bayesian inference on GARCH models. Although the Gibbs sampler is usually based on the analyti-cal knowledge of the full conditional posterior densities, such knowledge is not available in regression models with GARCH errors. We show that the Gibbs sampler can be combined with a unidimensional deterministic integration rule applied to each coordinate of the poste-rior density. The full conditional densities are evaluated and inverted numerically to obtain random draws of the joint posterior. The method is shown to be feasible and competitive compared with importance sampling and the Metropolis-Hastings algorithm. It is applied to estimate an asymmetric Student-GARCH model for the return on a stock exchange index, and to compute predictive option prices on the index. We prove, moreover, that a flat prior on the degrees of freedom parameter leads to an improper posterior density.

This paper examines the determinants of equilibrium wage and unemployment rates in Belgium within the framework of a quantity rationing, right-to-manage model with decentralised wage setting. Empirical results are obtained by first using the Johansen maximum-likelihood procedure for the analysis of cointegration among the variables of interest. The information from this stage is then used to estimate a three-equation econometric model explaining the wage-share, the unemployment rate and the capital gap. The slowdown in world trade is depicted as the most important factor explaining the rise in unemployment in Belgium, with dampening effects due to wage control policies imposed in the eighties. Because we obtain only two cointegrating relations, for three endogenous variables, our results are compatible with the hypothesis of path dependency and multiple equilibria.

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