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3.1.1 The Underlyings

Although we will describe both of them in far greater detail later, let us introduce here, for the sake of understanding the basics of credit modeling, loans and bonds as the fundamental underlyings of credit.

A loan is a contract where a borrower repays an amount N over time. This usually involves repaying the principal itself and paying a (fixed or floating) interest with a certain frequency. The most common type of loan is the amortizing loan in which, at the same time the borrower pays the interest, he also repays a portion of the principal. As a consequence, the subsequent interest payment will be on the remaining principal. More precisely, the cash flow structure of a loan is given by


where Li is a LIBOR-like floating rate but it could as easily be a fixed-coupon C. The spread s is a value driven by the credit risk associated with the borrower. We have seen in Chapter 2 that while financial institutions lend to each other at LIBOR, the spread s is whatever financial institutions would charge a subsequent borrower[1] on top of that LIBOR. Note that here, as opposed to when we were dealing with curve construction in Chapter 2, we are not discussing, yet, the present value of a loan; we are simply describing its cash flow structure.

Loans are far from standardized instruments; there can be many variations (as anyone who has applied for a mortgage can attest) on the type of repayment profile, on grace periods, different spreads on top of the floating rate, and so on. However, Equation 3.1 represents a good general description. An interesting point to be made about loans is that, in general, they tend to be held as assets by the lender and they are not traded in some secondary market. An exception to this is the activity known as loan syndication by which the lender passes on the whole, or part, of the loan to other market participants for a profit. The activity, however, is fairly complicated and definitively over the counter and cannot be compared to the secondary market of, say, vanilla equity options.

A bond can be seen as either the opposite of a loan (whereas a loan is a lending instrument, a bond is a borrowing instrument) or as the securitized version of a loan. An entity wishing to raise capital without relinquishing control of itself (which would happen by issuing shares) can do so by issuing a bond. From the start, this is not anymore a contract between two parties (as in the case of a loan), but immediately an exchange-traded instrument sold through an auction. The investor (which can be seen as a faceless lender) buys a bond and receives the promise of repayment of capital at the end and, in most cases, the promise of regular payments in between.

The bond can be subsequently and easily passed onto secondary investors, and these transactions, for the most liquid bonds, are as liquid as any equity stock. Because of the secondary activity requiring simplicity, particularly when it comes to knowing what amount is redeemable at the end, a bond is almost never amortizing. The simplest and most general form of the cash flow structure of a bond could written as

where, again, N is the nominal amount and fi is a function that can be a fixed coupon, a floating rate, or some more complicated function. An even simpler version is the case of zero coupon bond (similar to the discount bonds met in Section 2.2.1) in which the bond is made simply of the promise to repay the principal at the end.

A final point needs to be made when it comes to the payment of the principal before maturity, effectively putting an end to the transaction. This action is usually defined as prepaying when it comes to loans and call- ing/putting when it comes to bonds. A borrower would prepay a loan, an issuer would call the bond, and an investor would put the bond. Being that a loan is, in general, a transaction between two specific parties, it is almost impossible for the lender not to accept the principal should the borrower wish to prepay. This means that even if it is not explicitly stated (although it is almost always in the details of an agreement), a loan always has an embedded option of prepayment. Option is intended here in the financial sense of the word: the option holder has the possibility to make a decision based on some market information (e.g., finding a lower rate somewhere else), and the upside from this market information can be either zero or positive in a precise manner. As always, when there is an option there is some value for the option holder, which is why in the case of mortgages there is a charge for repaying the amount before maturity.[2] We shall see in Section 3.3 that on this aspect the case of development institutions is very different from the


norm. When it comes to bonds, because of their securitized nature and active secondary market trading, there can be an option of prepaying on the part of the issuer (calling the note), or on the part of the investor (putting the note), but this option has to be stated explicitly and cannot be assumed.

We have shown the fundamental underlyings of credit. As we have stressed, with every promise of payment there is a credit risk associated with it. We are now going to discuss the main derivative instrument used to hedge against this risk.

  • [1] This subsequent borrower could be either an entity that is not a financial institution and therefore would have a borrowing level different from LIBOR or another financial institution which, since we have defined the LIBOR as an average, would have a borrowing level away from the mean.
  • [2] The charge can be explicitly expressed as a fee or included in a higher rate.
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