The Default Risk of Swaps

We characterize the exchange of financial claims from risky swaps. These transfers are among three groups: shareholders, debtholders, and the swap counterparty. From this analysis we derive equilibrium swap rates and relate them to debt market spreads. We then show that equilibrium swaps in perfect markets transfer wealth from shareholders to debtholders. In a simplified case, we obtain closed-form solutions for the value of the default risk in the swap. For interest-rate swaps, we obtain numerical solutions for the equilibrium swap rate, including default risk. We compare these with equilibrium debt market default risk spreads. SWAPS HAVE BEEN ONE of the most explosive and important innovations in international capital markets in the last 10 years. In its simplest form, a swap consists of an agreement hetween two entities (called counterparties) to exchange in the future two streams of cash flows. In a currency swap, these streams of cash flows consist of a stream of interest and principal payments in one cvtrrency exchanged for a stream, of interest and principal payments of the same maturity in another currency. In an interest rate swap they consist of streams of interest payments of one type (fixed or floating) exchanged for streams of interest payments of the other type in the same currency. The two types of swap are shown in Appendix 1.̂ The economic importance of swap transactions is the fact that they can he comhined with deht issues to change the nature of the liahility for the borrower. The sum of a hond issue and a currency swap gives a net liability stream which is equivalent to transforming the bond liability into a different currency. A floating rate note combined with an interest rate swap results in a liability equivalent to fixed rate debt. Two issues have dominated the academic literature on swaps. The first concerns the reasons for their use. Arbitrage of imperfections in capital markets was the original cause of their appearance (Price and Henderson (1984)). Turnbull (1987) shows that lowering borrowing costs by a synthetic transaction involving a swap is not possible in a complete, integrated capital market. Subsequent authors (Wall and Pringle (1988); Arak, Estrella, Groodman, and Silver (1988); Smith, Smithson, and Wakeman (1987)) observe *Cooper is Associate Professor of Finance at the London Business School. Mello is Assistant Professor of Finance at MIT. We are grateful to participants at workshops at Bristol University, Cambridge University, HEC, London Business School, LSE, MIT, and Warwick University for comments. We are especially grateful to Dick Brealey, Bernard Dumas, Michael Selby, Rene Stulz, and two anonymous referees for suggestions. 'For an excellent summary of swaps see Wall and Pringle (1988).