Interest rate futures: estimation of volatility parameters in an arbitrage-free framework

Abstract

Hedging interest rate exposures using interest rate futures contracts requires some knowledge of the volatility function of the interest rates. Use of historical data as well as interest rate options like caps and swaptions to estimate this volatility function, have been proposed in the literature. The interest rate futures price is modelled within an arbitrage-free framework for a volatility function which includes a stochastic variable, the instantaneous spot interest rate. The resulting system is expressed in a state space form which is solved using an extended Kalman filter. The technique is applied to short-term interest rate futures contracts trading on the Sydney Futures Exchange as well as on the Tokyo International Financial Futures Exchange. The residual diagnostics indicate suitability of the model and the bootstrap resampling technique is used to obtain small sample properties of the parameters of the volatility function.