Credit Risk - A Survey

This paper presents a review of the developments in the area of credit risk. Starting in 1974, Merton developed a pricing method for a bond facing default risk, which was mainly settled in the framework of Black and Scholes (1973). Certain attempts have been made to relax the assumptions, giving rise to a class of models called structural models. A second class, called hazard rate models, was first addressed in Pye (1974) and more recently reached attention with the works of, e.g., Lando (1994). There are extensions in different directions, e.g., models which incorporate ratings, models for a portfolio of bonds or market models. The so called commercial models are readily implemented models which are widely accepted in practice. Finally we describe certain credit derivatives. 1. Structural Models The first class of models tries to measure the credit risk of a corporate bond by relating the firm value of the issuing company to its liabilities. If the firm value at maturity T is below a certain level, the company is not able to pay back the full amount of money, so that a default event occurs. 1.1. Merton (1974). In his landmark paper Merton (1974) applied the framework of Black and Scholes (1973) to the pricing of a corporate bond. A corporate bond promises the repayment F at maturity T . Since the issuing company might not be able to pay the full amount of money back, the payoff is subject to default risk. Let Vt denote the firm’s value at time t. If, at time T , the firm’s value VT is below F , the company is not able to make the promised repayment so that a default event occurs. In Merton’s model it is assumed that there are no bankruptcy costs and that the bond holder receives the remaining VT , thus facing a financial loss. If we consider the payoff of the corporate bond in this model, we see that it is equal to F in the case of no default (VT ≥ F ) and VT otherwise, i.e., 1{VT >F}F + 1{VT≤F}VT = F − (F − VT ). 1991 Mathematics Subject Classification. 2000 AMS Classification. Primary: 60-02, 91B28, 91B26, Secondary: 60H30, 60J75.