Information and option pricings

How can one relate stock fluctuations and information-based human activities? We present a model of an incomplete market by adjoining the Black-Scholes exponential Brownian motion model for stock fluctuations with a hidden Markov process, which represents the state of information in the investors’ community. The drift and volatility parameters take different values depending on the state of this hidden Markov process. Standard option pricing procedure under this model becomes problematic. Yet, with an additional economic assumption, we provide an explicit closed-form formula for the arbitrage-free price of the European call option. Our model can be discretized via a Skorohod imbedding technique. We conclude with an example of a simulation of IBM stock, which shows that, not surprisingly, information does affect the market. AMS classification: 60J65; 60J10; Tel: (914) 945 2348; Fax: (914) 945 3434; E-mail: [email protected].