Monte Carlo Derivative Pricing With Partial Info In Marked DSPP.pdf

In a class of doubly stochastic Poisson processes with marks, the intensity process can be interpreted as the effect of information release on market activity. Assuming a partial information setting where market agents can only observe the price process, a filtering algorithm is applied to compute contingent claim prices by Monte Carlo approximation. The dynamics of the price process is given under a martingale measure Q, and conditions for the existence of the minimal martingale measure Q are derived. Properties of the model under Q are studied, including the reversible jump Markov chain Monte Carlo method for approximating the filtering distribution. The model is applied to ultra-high frequency data, and the results show that the proposed framework is rich enough to model many features of UHF data, including deterministic seasonalities and the behavior of less liquid assets. The class of doubly stochastic Poisson processes with marks is mathematically tractable, and a trajectory of the price process in any bounded time interval is characterized by a finite number of marks. The model can be used to compute optimal hedging strategies and to price contingent claims in a partial information setting. The authors thank Gino Favero for useful suggestions. The proposed framework is a contribution to the literature on financial modeling, and it provides a new approach to modeling intraday stock price movements and contingent claim pricing.