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Option Pricing with a General Marked Point Process

THEMA, Université de Cergy-Pontoise, 33 boulevard du Port, Cergy, France
prigent{at}u-cergy.fr

This paper examines the impact of a random number of price changes on the options valuation. The model introduces the structure of the general marked point processes (MPP). This kind of model allows us to take account of more general distributions of interarrival times than usual jump-diffusion models. In particular, stock price variations can be correlated with the times of transactions. Thus, the investors can decide to trade according to the history of market values and the sizes of price variations can also depend on the past times of transactions. By using the special decomposition of predictable processes, with respect to a marked point process, the determination of all risk-neutral probabilities is detailed. Derivative prices are calculated in this context with different basic examples.

Key Words: Option pricing; marked point process; predictable processes
History: Received: April 26, 1999; revision received: October 22, 1999;revision received: April 3, 2000;