Monte Carlo derivative pricing with partial information in a class of doubly stochastic Poisson processes with marks
To model intraday stock price movements we propose a class of marked doubly stochastic Poisson processes, whose intensity process can be interpreted in terms of the effect of information release on market activity. Assuming a partial information setting in which market agents are restricted to observe only the price process, a filtering algorithm is applied to compute, by Monte Carlo approximation, contingent claim prices, when the dynamics of the price process is given under a martingale measure. In particular, conditions for the existence of the minimal martingale measure Q are derived, and properties of the model under Q are studied.
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