Default risk and innovations in the design of interest rate swaps - includes appendix - Security Design Special Issue

Financial Management (Financial Management Association), Summer, 1993 by Keith C. Brown, Donald J. Smith

III. Swap Design Innovations: Forward Rate Swaps

A. Departures from the Plain Vanilla Swap Structure

The inherent structure of a plain vanilla interest rate swap, whereby a single fixed rate applies to all settlement dates, is itself a source of default risk. This is because in virtually all yield curve environments, there will be actual default risk exposure associated with a given contract even if interest rate movements are nonstochastic. In other words, if the future path for the floating-rate index were fully deterministic, a firm would typically incur a financial loss if its swap counterparty defaulted. The exceptional circumstance when this might not occur is an extended period of constant interest rates and a totally flat yield curve. That rarity aside, default risk arises because interest rates are stochastic, a reality exacerbated by the setting of a uniform fixed rate for the lifetime of the swap.

Consider again the fixed rate ([F.sub.0, N]) on a new N-period swap set on date 0. For both counterparties to the swap, the sequence of expected future payments and receipts is determined by the sign of [F.sub.0, N] - E([I.sub.t-1]). However, assuming risk-neutral participants, the swap market will be in equilibrium only if the present value of the fixed flows set by [F.sub.0, N] equal the present value of the expected variable flows set according to [I.sub.t]. This, in turn, means that the swap has an initial economic value of zero to each counterparty if the following condition holds:

[Mathematical Expression Omitted]

Note from Equation (5) that the initial exchange at the end of the first period is based on the known, current level of the floating- rate index ([I.sub.0]) while subsequent exchanges are only known to the level of their expected values.

Suppose that the overall market environment is one of expected rising short-term rates, reflected by an upward-sloping yield curve. This means that as the single swap fixed rate, [F.sub.0, N], will be a complex average of the yields expected to prevail during the N-period life of the agreement. Consequently, for the fixed- payer (fixed-receiver) on the swap, there is likely to be some future date t* after (before) which the firm expects to be receiving cash settlement payments and before (after) which it expects to be making payments. To the fixed-payer, the default risk exposure is then "back-loaded" in that it would be more concerned about its counterparty defaulting in the later years of the agreement when receipts are anticipated. For the fixed-receiver, on the other hand, the default risk would be front-loaded because it expects to be receiving settlement payments early and to be paying later. These conclusions, of course, implicitly rely on the expectations theory of the yield curve and the parties to the swap having subjective expectations aligned with the overall market.

A departure from the structure of a plain vanilla swap to address this front-loading and back-loading problem would be to set a time-varying fixed rate on the swap. That is, the fixed rate would be prespecified for all future settlement periods at inception but it would differ for each period so as to minimize expected settlement payments and receipts, thereby minimizing the expected default risk. For example, suppose that the uniform fixed rate is replaced in Equation (5) with the set of implied forward rates known at date O, based on the swap yield curve for maturities ranging from one to N periods.