Merton Credit Risk

Structural Models of Credit Risk and the Merton (1974) model

The Black-Scholes-Merton edifice has shaped the way many analysts view the world particularly when measuring credit risk. The KMV-Merton model is very conspicuous application in credit markets and investment circles of ideas from option theory. Merton (1974) observed that the equity of a firm was effectively a call option on the underlying assets of a firm with the strike price equivalent to the firm’s debt. Kealhofer, McQuown, and Vasicek (KMV) developed this insight further in a commercial setting. Their approach was so successful in fact that in 2002, Moody’s the credit rating agency, acquired (KMV).

Normally, valuation in the Black Scholes world is simply the inputting of 6 parameters values into same. The Merton-KMV model however recognized that the underlying value of assets and volatility are not directly observable. These can only be inferred. Their methodology is explained in the playlist below. Once baselines parameters are inferred, the probability of default can be determined from the normal cumulative density function. Merton-KMV is a stylized structural model that requires a number of assumptions. The value of the firm's assets adheres to geometric Browninan motion and that each firm has issued just one zero-coupon bond.

For a deeper appraisal Suresh Sundaresan provides a good overview of the Merton (1974) model. Loeffler and Posch also provide a excellent implementation in Excel VBA in their textbook which I strongly recommend. In brief, we can say credit risk relates to the possibility of financial costs due to changes in the credit quality of market participants, counterparties and debtors. The most extreme credit quality event is default. Thereafter, we look to see how many cent in the dollar can be recovered. In practice, for larger market cap enterprises, default is normally precipitated by a failure of the firm to honor its debt servicing obligations, which usually quickly deteriorates to bankruptcy proceedings in the U.S , e.g. Chapter 11. There also a few more Chapters that could be relevant here. Thus default is considered a singularly important event after which the firm ceases to operate as a viable concern. (Not excluding here the possibility of bail-outs and bail-ins). Large financial losses generally ensue with substantial costs falling on security holders. (Often, a condition of bailing-out first entails burning the bondholders). Structural model proposed by Merton (1974), defines the default as occurring when the assets, A of a firm reach a sufficiently low level compared to its liabilities, L.

Thus, an option structure would seem quite logical. Under this model, the value of stock equity is modeled as a call option on the value of the whole company assets. Equity (the call) is presented as max(A - L, 0). In a Black_Scholes_Merton world the equity market value is a function of the volatility of the market value of the company assets. Equity may be configured or modeled as a call option on the firm. The Principle of limited liability ensures shareholders losses are bounded by the amount they invested only. They would elect not to repay the firm's debt where the value of the firm's Assets are inferior to the value of the outstanding debt, L. When the value of Assets exceed debt value, the shareholders would elect to repay – i.e. keep the option alive.