Chapter 4 Structural Models of Credit Risk

Chapter 4 Structural Models of Credit Risk Broadly speaking, credit risk concerns the possibility of financial losses due to changes in the credit quality of market participants. The most radical change in credit quality is a default event. Operationally, for medium to large cap firms, default is normally triggered by a failure of the firm to meet its debt servicing obligations, which usually quickly leads to bankruptcy proceedings, such as Chapter 11 in the U.S. Thus default is considered a rare and singular event after which the firm ceases to operate as a viable concern, and which results in large financial losses to some security holders. With some flexible thinking, this view of credit risk also extends to sovereign bonds

issued by countries with a non-negligible risk of default, such as those of developing countries. Under structural models, a default event is deemed to occur for a firm when its assets reach a sufficiently low level compared to its liabilities. These models require strong assumptions on the dynamics of the firm’s asset, its debt and how its capital is structured. The main advantage of structural models is that they provide an intuitive picture, as well as an endogenous explanation for default. We will discuss other advantages and some of their disadvantages in what follows. 4.1 The Merton Model (1974) The Merton model takes an overly simple debt structure, and assumes that the total value A t of a firm’s assets follows a geometric Brownian motion under the physical measure dA t = µA t dt+ σA t dW t ,A 0 > 0, (4.1) where µ is the mean rate of return on the assets and σ is the asset volatility. We also need further assumptions: there are no bankruptcy charges, meaning the liquidation value equals the firm value; the debt and equity are frictionless tradeable assets. Large and medium cap firms are funded by shares (“equity”) and bonds (“debt”). The Merton model assumes that debt consists of a single outstanding bond with face value K and maturity T. At maturity, if the total value of the assets is greater than the debt, the latter is paid in full and the remainder is distributed among shareholders. However, if 41 42 CHAPTER 4. STRUCTURAL MODELS OF CREDIT RISK A T
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