The main goal of this article was to present an application of GARCH (Generalised Auto Regressive Conditionally Heteroscedastic) and CSV (Correlated Stochastic Volatility) processes in modelling the volatility of the daily returns of PLN/USD exchange rate and pricing the European call option for this exchange rate. The authors offer the Bayesian interpretation of commonly used methods of volatility assessment as well as predictive consequences of different volatility models. They also consider Bayesian estimation of the delta coefficient for the European call option. From the Bayesian point of view posterior distribution of delta enables to predict the cost of so called delta-neutral hedging strategy. They show the predictive distributions of the cost of this strategy as well as the cost of its managing.