  We present an adaptive approach for valuing the European call option on
assets with stochastic volatility. The essential feature of the method is a
reduction of uncertainty in latent volatility due to a Bayesian learning
procedure. Starting from a discrete-time stochastic volatility model, we derive
a recurrence equation for the variance of the innovation term in latent
volatility equation. This equation describes a reduction of uncertainty in
volatility which is crucial for option pricing. To implement the idea of
adaptive control, we use the risk-minimization procedure involving random
volatility with uncertainty. By using stochastic dynamic programming and a
Bayesian approach, we derive a recurrence equation for the risk inherent in
writing the option. This equation allows us to find the fair price of the
European call option. We illustrate numerically that the adaptive procedure
leads to a decrease in option price.
