Before going to measure conditional volatility utilizing different ARCH family of models, an effort has been made to compare the descriptive time invariant measures in both the markets. As far as the standard deviation of underlying NIFTY index in spot and futures markets are concerned, it has been found to be higher in the futures index. Underlying stock return variability in most of the stocks in the futures market is found to be slightly higher than that in the spot market.
Conditional volatility both in spot and futures markets are measured in different ARCH framework for the underlying index and stocks. The results from the ARCH (1) and GARCH (1,1) models clearly revealed that both the ARCH and GARCH coefficients for the underlying spot index and majority no. of stocks in the spot market are found to be significant. Apart from these, the old news (GARCH) coefficient is found to be stronger for more no. of stocks.
The results on the conditional volatility in futures market reveal that the ARCH and GARCH coefficients representing recent news and old news respectively in a GARCH (1,1) framework are found to be statistically significant for futures index as well as for most of the underlying stocks. Within these two coefficients, the old news (GARCH) coefficient is found to be significant for all the stocks. This is the same observation what we found in spot market also.
Volatility estimation separately in spot and futures markets is followed by a comparison of conditional and unconditional volatility in these markets in a GARCH (1,1) framework. It is observed that the unconditional as well as the conditional volatility is lower in futures market compared to spot market for the underlying index and nine out of ten stocks. Only exception here is HINDALCO stock. Thus, it can be concluded that the returns in futures market exhibit lesser volatility than returns in underlying spot market as being found through the utilization of GARCH class of models.
As far as the forecasting results for the index as well as stock returns are considered, most of the test statistics reveal that GARCH (1,1) model has lesser forecasting error compared to ARCH (1) framework, though the difference is very marginal. Volatility forecasting for stocks in both spot and futures markets are also found to have little difference in the forecasting error among the ARCH (1) and GARCH (1,1) frameworks.