What information about a counterparty's default probability is determined by their stock price? The answer may be that there is quite a bit, as first recognized by Robert Merton in a 1974 paper, "On the Pricing of Corporate Debt."
Merton's idea is that an equity is little more than being long a call option on the firm's total asset value, with a strike price equal to the firm's total liabilities. Like any long call option, an equity can never have less than a zero value, but can have a value greater than the intrinsic value of the option, which is the difference of the underlying (in this case, the firm's asset value) and the strike (the firm's liabilities). There are obvious differences between equity viewed as an option and ordinary options. For instance, equity has no maturity date and the value of the underlying, the asset value of the firm, is unobserved. However, as an option, it should be amenable to the same sort of option pricing models that have become common on trading desks.
Make the very mild assumption that the equity markets are information rich, and that any firm's credit state is noticed by the market and reflected in the equity price. The equity price then becomes a crystal ball into the credit state of the firm, if only that information could be unraveled from the observed equity price. It turns out there is a way to decode this credit information, albeit in a roundabout way.
In reality a firm's default is a complicated process, but at its core, it comes about when the assets become equal to or, even worse, less than the value of the firm's liabilities. When this happens, the firm's net valuation becomes negative and default is inevitable. There are just two pieces of information that determine this simple model of default, the total value of the liabilities of a firm, and the total value of the assets of the firm. The liabilities of a firm are actually fairly accessible, provided you are willing to do some calculations, in terms of publicly available interest expense figures and debentures. The firm's asset values, however, are not observable, directly.
What is observable is the firm's equity price. Assuming the market is fairly valuing the equity, and assuming we have deduced the total value of the liabilities of the firm, we have the kernel of the information we need to infer the value of the assets of the firm. We have the option price, given by the total value of equity, we have the strike price, given by the total value of the liabilities, and we can make reasonable estimates of the other option pricing parameters. In particular, the volatility of the (unobserved) total asset value can reasonably be approximated by the equity's volatility. In short, we have the answer to an option pricing problem, and we need to use that to find out the remaining input, the total firm asset value.
Once we take out the total asset value, we need some way to compare it to the option strike, the total value of the liabilities. It turns out that this is provided by the option pricing model which assumed a distribution for the underlying parameterized by the volatility we provided. This provides a normalized measure of how far our inference of the total asset value is from the default boundary, demarcated by the total value of liabilities. This normalized measure to the default boundary, in conjunction with the distribution of the asset value, should give us information about the credit state and default probability of the firm.
In actuality, the various simplifying assumptions we have made along the way in this analysis will probably not make these direct probabilities of default very reliable. But all is not lost; the normalized measure of asset value to the default boundary may still have rich informational content and serve very well as the basis of a credit scoring or rating system. By incorporating equity prices, a scoring system based on this methodology has the added benefit that it will probably be a leading indicator of developing credit problems instead of a lagging indicator.
This week's Learning Curve was written byJeffrey McIverofInfinity, a Sungard Company.