Bayesian Forecasting of the Discounted Payoff of Options on WIG20 Index in Discrete-Time SV Models

In this paper the bivariate stochastic volatility models (with stochastic volatility and stochastic interest rate) and the univariate fat-tailed and correlated stochastic volatility model (with stochastic volatility and constant interest rate) are used in the Bayesian forecasting of the payoff of European call options. The basic instrument is the WIG20 index. The predictive distribution of the discounted payoff is induced by the predictive distribution of the growth rate of the WIG20 index and the WIBOR1m interest rate. The Bayesian inference about the volatilities and the predictive distribution of the discounted payoff function is based on the joint posterior distribution of the latent variables, the parameters, and the predictive distribution of future observations, which we simulate via Markov chain Monte Carlo methods (the Metropolis-Hastings algorithm is used within the Gibbs sampler). The results show that allowing interest rate to be stochastic does not significantly improve forecasting performance of the discounted payoff. The predictive distributions of the discounted payoff are characterised by huge dispersion and thick tails, thus uncertainty about the future value of the payoff was ex-ante very big.