Market with Markov jump volatility III: Price of risk monitoring algorithm given discrete-time observations of asset prices

The third part of the series is devoted to the online estimation of the market price of risk. The market model includes a deposit, underlying, and derivative assets. The model of the underlying asset prices contains stochastic volatility represented by a arkov jump process (MJP). There is no arbitrage in the considered market; so, the market price of risk is a function of the MJP's current value. So, the MJP monitoring problem transforms into the MJP state filtering one. The statistical data are available at discrete moments and contain the direct observations of the underlying assets and indirect observations of the derivative ones. The paper presents the solution to the optimal filtering problem and the corresponding algorithm of its numerical realization. The paper also contains a numerical example demonstrating the performance of the MJP state estimates in dependence on the type and structure of the available observations.