Credit and the Fair Valuing of Loans
As we have reminded ourselves in the previous chapter, our prime focus is debt and therefore credit. We have seen how, when we discount a future cash flow, we are essentially using credit considerations implicit in interest-rate instruments. Here, we are going to consider credit explicitly. We are going to define what we mean by credit and what underlyings are used to capture it. Of all the possible ways to model credit we shall introduce a simple risk-neutral framework to assess survival probabilities. These will be used to value a loan, which, as we have said, is the fundamental tool of development banking.
3.1 CREDIT AS AN ASSET CLASS
Of all the asset classes, credit is arguably the most unusual. Whereas in other fields we deal with tangible objects—in equity, through shares, with the ownership of a company; in commodities with the ownership of something very real; in FX with the relative worth of money in different currencies—when it comes to credit we deal with something more elusive, we deal with the possibility of someone defaulting on a debt obligation. In this sense, if the interest rate is the asset class of borrowing, credit can be considered a by-product of it.
As pointed out by Schönbucher  in a great introduction to the topic, the most important characteristics of credit events (a term for default) is that they are rare, they can happen unexpectedly, and they do so with a magnitude unknown beforehand. Although we ...