The Term Structure of Interest-Rate Future Prices
September 29, 1999
Marti G. Subrahmanyam, R.C. Stapleton
ABSTRACT
We derive general properties of two-factor models of the term structure of interest rates and, in particular, the
process for futures prices and rates. Then, as a special case, we derive a no-arbitrage model of the term structure
in which any two futures rates act as factors. The term structure shifts and tilts as the factor rates vary. The
cross-sectional properties of the model
derive from the solution of a two-dimensional autoregressive process for the short-term rate, which exhibits both
mean reversion and a lagged persistence parameter. We show that the correlation of the futures rates is restricted
by the no-arbitrage conditions of the model. In addition, we investigate the determinants of the volatility of
the futures rates of various maturities. These are shown to be related to the volatilities of the short rate, the
volatility of the second factor, the degree of mean reversion and the persistence of the second factor shock. We
obtain specific results for futures rates in the case where the logarithm of the short-term rate [e.g., the London
Inter-Bank Offer Rate (Libor)] follows a two-dimensional process. Our results lead to empirical hypotheses that
are testable using data from the liquid market for Eurocurrency interest rate futures contracts.
Subject: Investments/Fixed Income
Classification: Theoretical
Subrahmanyam: (212) 998-0348 msubrahm@stern.nyu.edu
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