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.
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 Schonbucher  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 might not be familiar with the details of a bankruptcy, we can easily imagine it to be a process likely to be drawn out over a lengthy period of time and, despite the legal framework in place, not necessarily very clear.
Since credit risk is the risk linked to payment default, in order for it to exist there needs to first be the promise of a payment: if there is no promise of payment there is no question of credit risk. The second question, not an easy one, is what constitutes default: is it the default on one payment, any payment, all payments? There are of course laws and agreements in place but, because of the rare and unexpected nature of the event itself, they might not be absolutely clear on all possible scenarios. A great difference applies to the credit risk presented by corporate and sovereign entities: the former needs to abide by binding bankruptcy laws easily enforceable within a country or a treaty, the latter have on the surface looser restrictions, which are made in practice tighter by the markets (if they want to borrow again in the future). We will see how these differences apply in particular when it comes to development institutions, and we will see how the special form sovereign credit risk takes in the eyes of a development institution influences the way trades are priced.
Throughout this chapter and in even more detail when we will analyze the activity of a treasury desk, we will notice how credit is pervasive. The financial world is made of payments and promises of payment, to each one of them a credit risk is attached without exception. Credit touches upon the notion of trust and honoring of a promise. Although there is a framework to deal with the situation, when this is broken, there is still the sense that a credit event takes us into a region very close to the outer limits of what we consider civil society. Although in the everyday life of a practitioner this is something very far from his main concerns, when credit events occur, or we are very close to them, we experience a sense of unease and fear. This is probably one of the reasons, after all the technical ones, why a credit crisis such as the Great Recession is far more scarring than a crisis of another type (such as the tech bubble).
Credit, as we said above, is somehow a less tangible asset class than others. Within this asset class people have nonetheless managed to build a solid framework around the probability of default and create market instruments useful to protect us against it. Let us introduce what the underlying instruments of credit are and identify the derivatives used to hedge them.