Credit risk in derivative products

Martin, Marcel (1997) Credit risk in derivative products. Doctoral thesis, University of London: London Business School.

Abstract

After two decades of rapid growth in terms of volume and sophistication, there is growing recognition among both academics and practitioners that the development of transfer mechanisms for market risk has reached a mature stage. Investors have available to them an unprecedented instrumentarium of financial instruments allowing them to implement complicated exposure profiles with respect to interest rate, equity, foreign exchange and commodity risk. By contrast, development of similar mechanisms for credit risk has only recently achieved significant attention. While the growing involvement of regulatory institutions in this area attests to the urgency of the task, there is no consensus as to how credit risk should best be modeled, priced and managed. The objective of this thesis is to make a contribution to the debate on how to best model, price and manage credit risk. After a brief review of the literature, I proceed to outline a framework for the pricing of credit contingent claims. Given the decision to characterize credit risk in terms of a probability of default and a set of payoffs conditional on default having occurred, I provide for both elements to be subject to uncertainty. The concept of a forward probability of default is introduced, capturing the idea of default probabilities varying randomly over time and facilitating incorporation of a correlation structure between credit risk and market risk. In contrast, conventional approaches, by subsuming uncertainty into one credit risk component, limit the scope of a given model to address comprehensively the pricing and risk management issues associated with credit risk and fail to capture interaction with other risks. Development of a pricing methodology as well as articulation of the relationship between credit risk and market risk require that the components of credit risk be embedded in a market structure in which credit risky and credit risk free instruments are being traded. I propose an arbitrage free securities market in which treasury, Libor and credit risky corporate bonds are traded. Specification of a correlation structure between credit risk and market risk requires the presence of the treasury instrument, assumed to be subject to market risk only. Inclusion of the Libor instrument is motivated in terms of the need to specify spread elements unrelated to credit risk. The corporate instrument incorporates credit risk. Restrictions on the distribution of recovery rates necessary to malce use of the no arbitrage paradigm are identified. Equivalent martingale measure densities associated with the use of alternative numeraire assets are derived and securities under these measures are characterized. Using the developed methodology, a number of pricing results for contracts on credit risk variables are provided. A second application provides analysis of quantification and management of credit risk in conventional contracts. Model specification to a level of sophistication unwarranted by the requirements of a particular application will result in a waste of resources. Whether there is merit in making allowance for uncertainty in credit risk or sacrificing tractability in return for incorporating a correlation structure between credit risk and market risk is ultimately an empirical question. Using US data on corporate bonds issued by financial institutions I examine the impact of credit risk specification on the valuation of securities subject to credit risk. Relative to the particular metric I impose, a model incorporating credit risk uncertainty and correlation with market risk dominates the same model with the correlation parameter constrained to be zero, and both models dominate a naive model which stipulates that credit risk is not subject to uncertainty. Consequently, the empirical results validate the relevance of my modelling choices.