Dynamic models for credit spreads and credit correlations

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Sophisticated mathematical modelling has now been enshrined in the Basel II Accord on Capital Measurement and Capital Standards as a strategic element of paramount importance in the regulatory environment of the global finance industry. Perhaps the most exciting open research topic in this area is the credit risk problem, a basic form of which is to model the dynamics of the corporate bond market, in particular the causes of defaults, jointly with the now understood dynamics of stock and fixed income markets. Mathematically, it means to develop a no-arbitrage (NA) framework which nests the pricing of equities, government bonds, and the default risky bonds of publicly listed corporations, which then implies a consistent methodology for pricing and hedging all associated derivative securities, including important products such as credit default swaps and collateralized debt obligations (CDOs). An accurate credit framework would lead to more reliable financial trading and risk management systems, helping to stabilize the world's markets from inevitable future default shocks as dramatic as those of Enron, WorldCom and the like. My proposal is to develop useful and accurate realizations of the multifirm Affine Markov Chain (AMC) framework introduced in 2005 by Hurd and Kuznetsov, and to establish AMC as a leading mathematical framework for credit risk. Realization of a useful AMC model requires completion of three tasks: to connect its components with the market drivers of default intensity; to derive pricing formulas for market traded credit products; to develop calibration techniques to fit these formulas to market data. Techniques developed along the way, for instance the saddlepoint method for CDOs, and the method of stochastic time change, will also be applied to extend existing credit methods. Beyond its potential impact on trading and risk management for banks, investment funds and insurance companies, my proposal will have an additional impact on HQP: my research associates, as they leave PhiMAC (the Financial Mathematics Lab at McMaster), will be in high demand for key careers both in the finance industry and academia, both in Canada and worldwide.