Heterogeneous information arrival and option pricing

Abstract

We model the arrival of heterogeneous information in a financial market as a doubly stochastic Poisson process (DSPP). A DSPP is a member of the family of Poisson processes in which the mean value of the process itself is governed by a stochastic mechanism. We explore the implications for pricing stock, index and foreign currency options of the assumption that the underlying security evolves as a mixed diffusion DSPP. We derive an intertemporal CAPM and demonstrate that accounting for heterogeneous information arrival may minimize the ubiquitous pricing bias — ‘smile effect’ — of standard option pricing models. We propose a conceptually simple but numerically intensive maximum likelihood estimator of the parameters of a DSPP. A simulation study verifies the adequacy of the asymptotic approximations in finite samples.