Volatility and maturity effects in the Nikkei index futures

Abstract

Many financial data series are found to exhibit stochastic volatility. Some of these time series are constructed from contracts with time-varying maturities. In this paper, we focus on index futures, an important subclass of such time series. We propose a bivariate GARCH model with the maturity effect to describe the joint dynamics of the spot index and the futures-spot basis. The setup makes it possible to examine the Samuelson effect as well as to compare the hedge ratios under scenarios with and without the maturity effect. The Nikkei-225 index and its futures are used in our empirical analysis. Contrary to the Samuelson effect, we find that the volatility of the futures price decreases when the contract is closer to its maturity. We also apply our model to futures hedging, and find that both the optimal hedge ratio and the hedging effectiveness critically depend on both the maturity and GARCH effects. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 895–909, 1999