FIN-01-040

The Term Structure of Interest-Rate Futures Prices.

September 14, 2001

Richard C. Stapleton and Marti G. Subrahmanyam

ABSTRACT

We derive general properties of two-factor models of the term structure of in- terest 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. In this model, the term struc- ture 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 volatilities and the correlations of the futures rates of various maturities. These are shown to be related to the volatility of the short rate, the volatility of the second factor, the de- gree of mean-reversion and the persistence of the second factor shock. We also discuss the extension of our model to three or more factors. We ob- tain specific results for futures rates in the case where the logarithm of the short-term rate [e.g., the London Inter-Bank Oer Rate (LIBOR)] follows a two-dimensional process. We calibrate the model using data from Eurocur- rency interest rate futures contracts, using alternative optimisation criteria. We then derive the term structures of volatilities and correlations implied by the model.


Richard C. Stapleton
Institution: Department of Accounting and Finance, University of Strathclyde, 100, Cathedral Street, Glasgow, Scotland.
Telephone: (44) 524-381172
Fax: (44) 524-846874
Email: rcs@staplet.demon.co.uk

Marti G. Subrahmanyam
Institution: Stern School of Business, New York University, 44th West 4th Street, New York, NY 10012
Telephone: (212) 998-0348
Fax: (212) 995-4233
Email: msubrahm@stern.nyu.edu
Homepage:http://www.stern.nyu.edu/~msubrahm

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