Market with markov jump volatility IV: price of risk monitoring algorithm given high frequency observation flows of assets prices

The fourth part of the series presents a suboptimal algorithm of the market price of risk monitoring given the observations of the underlying and derivative asset prices. As in the previous papers, the market model contains the stochastic volatility described by a hidden Markov jump process. This market has no arbitrage; so, the market price of risk is a function of the Markov process state. The key feature of the investigated market lies in the structure of the available observations. They represent the underlying and derivative prices registered at random instants. The underlying prices are observed accurately, while the derivative prices are corrupted by a random noise. The distribution of the interarrival times between the observable prices and the observation noises depends on the estimated process. The essential feature of the obtained observations is their high arrival intensity compared with the hidden process transition rate. This property allows one to use the central limit theorem for generalized regenerative processes for the filter design. The influence of the estimation performance depending on the observation complexes is illustrated with a numerical example.