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An Information-Based Framework for Asset Pricing: X-Factor Theory and its Applications

by Andrea Macrina of King's College London

October 24, 2006

Abstract: This thesis presents a new framework for asset pricing based on modelling the information available to market participants. Each asset is characterised by the cash flows it generates. Each cash flow is expressed as a function of one or more independent random variables called market factors or "X-factors". Each X-factor is associated with a "market information process", the values of which become available to market participants. In addition to true information about the X-factor, the information process contains an independent "noise" term modelled here by a Brownian bridge. The information process thus gives partial information about the X-factor, and the value of the market factor is only revealed at the termination of the process. The market filtration is assumed to be generated by the information processes associated with the X-factors. The price of an asset is given by the risk-neutral expectation of the sum of the discounted cash flows, conditional on the information available from the filtration. The thesis develops the theory in some detail, with a variety of applications to credit risk management, share prices, interest rates, and inflation. A number of new exactly solvable models are obtained for the price processes of various types of assets and derivative securities; and a novel mechanism is proposed to account for the dynamics of stochastic volatility and correlation. If the cash flows associated with two or more assets share one or more X-factors in common, then the associated price processes are dynamically correlated in the sense that they share one or more Brownian drivers in common. A discrete-time version of the information-based framework is also developed, and is used to construct a new class of models for the real and nominal interest rate term structures, and the dynamics of the associated price index.

Keywords: Credit-risky discount bond, defaultable coupon bond, Credit Default Swap, Baskets of defaultable bonds, correlation, partial information, X-factor, asset pricing.

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