Title:

Pricing under random information flow and the theory of information pricing

This thesis presents a mathematical formulation of informational inhomogeneity in financial markets, with emphasis on its impact on asset volatility, the notion of information extraction, and the role of information providers. We begin with a brief review of the BHM framework, which models the market filtration by an information process consisting of a signal and a noise term, such that the signaltonoise ratio is determined by the information flow rate. Motivated by the observations that valuable information is rarely circulated homogeneously across financial markets, and that the information flow rate is typically random, we introduce, in the first part of the thesis, an extension of the BHM approach that leads to the simplest class of stochastic volatility models. In this extended framework we derive closed form expressions: for (a) asset price processes; (b) pricing formulae for options; and (c) option deltas. We show that the model can be calibrated to fit volatility surfaces reasonably well, and that it can be used effectively to model information manipulation. In the second part we introduce a framework for the valuation of information. In particular, a new formulation of the utilityindifference argument is introduced and used as a basis for pricing. We regard information as a quantity that converts a prior distributions into a posterior distributions. The amount of information can thus be quantified by relative entropy. The key to our theory is to equate the maximised a posterior utility with the a posterior expectation of the utility of the a priori optimal strategy. This formulation leads to one price for a given quantity of upside, and another for a given quantity of downside information. Various intuitive, as well as counterintuitive implications (for example, price of information is not necessarily an increasing function of the volume of information) of our theory are discussed in detail.
