On the Pricing of Options in Incomplete Markets

In this paper we reconsider the pricing of options in incomplete continuous time markets.We first discuss option pricing with idiosyncratic stochastic volatility.This leads, of course, to an averaged Black-Scholes price formula.Our proof of this result uses a new formalization of idiosyncraticy which encapsulates other definitions in the literature.Our method of proof is subsequently generalized to other forms of incompleteness and systematic (i.e. non-idiosyncratic) information.Generally this leads to an option pricing formula which can be expressed as the average of a complete markets formula.