A topic of fundamental importance in today's finance industry is the integration of market risk (the risk due to changing asset values in the market) and credit risk (the bank's exposure to default by its counterparties). In current practice, these risks are treated in very different ways, but there is general agreement that risk management would be vastly improved if credit risk could be quantified using some model-based approach similar to those already in universal use for evaluating market risk. These lectures will provide an introduction to this area, survey the current status of default risk modelling and make some suggestions for further developments.

The topics to be covered are as follows:

• Default: what the problem is and where the data comes from.
• Two approaches to default modelling

  1. The ``structural" approach
  2. The ``reduced form" approach

• Models for the distribution of hazard rates and their calibration
• Products: Default and total return swaps
• Modelling stochastic hazard rates
• Numerical implementation using trinomial trees
• More products: Convertible bonds and collateralized bond obligations (CBOs)
• Default correlation: a new approach using ``infection" models