An Analytic Solution for Interest Rate Swap Spreads

Abstract

This paper argues that liquidity differences between government securities and short–term Eurodollar borrowings account for interest rate swap spreads. It then models the convenience of liquidity as a linear function of two mean–reverting state variables and values it. The interest rate swap spread for a swap of particular maturity is the annuitized equivalent of this value. It has a closed form solution: a simple integral. Special cases examined include the Vasicek and Cox–Ingersoll–Ross one–factor term structure models. Numerical values for the parameters in both special cases illustrate that many realistic ‘swap spread term structures’ can be replicated. Model parameters are estimated using weekly data on the term structure of swap spreads from several countries. The model fits the data well.