Allowing for basis convergence and long memory in volatility when dynamic hedging the Australian All Ordinaries Index

This paper supplements Dark (2003c) where bivariate error correction GARCH and FIGARCH models between the All Ordinaries Index and its Share Price Index (SPI) futures are used to estimate dynamic minimum variance hedge ratios (MVHRs). Dark (2003c) documents the importance of allowing for long memory in volatility and time varying correlations when estimating MVHRs, however the approach does not exploit the convergence between the All Ordinaries Index and its SPI futures over the life of the futures contract. To allow for basis convergence we employ bivariate GARCH and FIGARCH models with maturity effects to model the joint dynamics of the All Ordinaries Index and the basis. The model results illustrate the importance of allowing for basis convergence and long memory in volatility when modelling the joint dynamics. These effects are also shown to be important when estimating dynamic MVHRs