Decomposing the Term Structure of Swap Rates in Light of the Financial Crisis

Abstract

Interest rate swaps are one of the most important financial instruments in the world. The BIS reports that the notional amount of these contracts outstanding as of June 2009 was $342 trillion, with a gross market value of $13.9 trillion. Not only are these contracts important hedging instruments, but the term structure of swap rates has become a benchmark in its own right in that it is often used as reference curve in derivative models. Clearly, understanding the determinants of the term structure of swap rates is important. Under specific assumptions regarding the nature of default and counterparty credit risk, Duffie and Singleton (1997) show that the swap and the LIBOR curve are the same. However, as the swap market has matured, ISDA introduced standards of credit enhancement, the most important being posting of collateral and frequent marking to market. Due to these enhancements, the swap curve now deviates enormously from the LIBOR curve. Recent studies of swap spreads take the absence of counter party credit risk for granted and focus on the credit risk inherent in the LIBOR itself, or more precisely in the refreshed LIBOR index published by the British Bankers Association, together with flight to quality discounts, sovereign risk premia associated with governments, and costly posting of collateral. Studies along these lines are well summarized by Johannes and Sundaresan (2006) and Feldhuetter and Lando (2008), and the references therein. The financial crisis has disrupted historical relationships between FRAs, swaps and their standard spot LIBOR replications. Further, large basis spreads have appeared for exchanging floating payments with different tenors that traditional models cannot explain. The impact of establishing the appropriate discounting factors for the simplest of collateralized derivatives is now profound. For example, our analysis shows that pricing one-year swaps using appropriate LIBOR or Treasury rates results, in each case, in persistent errors, the magnitude of which, subsequent to the financial crisis, is often as large as 100 basis points. Many of the existing studies on swaps cannot explain this phenomenon. Our paper contributes to the literature by carefully investigating the determinants of swap rates along the maturity spectrum. We accomplish this by jointly modeling not only the term structure of Treasury, LIBOR and swap rates, but also the Overnight Indexed Swap (OIS) curve. Using information from the OIS market is key to our analysis, since in contrast to LIBOR and Treasury rates, OIS rates are viewed as being a closer indicator of true riskless rates among private counterparties that transact in collateralized markets. All data are obtained from Bloomberg, Datastream and the FRED database at the St. Louis Fed. A preliminary analysis shows that the term structure of swap rates is indeed sensitive to the term structure of LIBOR-OIS spreads, the term structure of OIS-Treasury spreads and the term structure obtained from prices of bonds of AA rated financial firms, with the degree of dependence varying systematically with maturity. Our goal is to develop arbitrage-free models of swap and OIS rates that reflect these empirical features. Our study also examines how the relative importance of each swap rate component has changed since the crisis. The results will cast insight into the appropriate discount rates to use when pricing collateralized interest rate sensitive derivatives, and will directly contribute to the ongoing debate on how best to regulate over-the-counter contracts.