An Investigation of the Causal Relationships Between Index and Component Stock Implied Volatility

Abstract

We investigate the causal relationships between volatility implied in Major Market Index (MMI) options and its component stocks' options from January, 1987 to October, 1989. We find that MMI implied volatility Granger causes component stock implied volatility for all twenty component stocks, which is consistent with the hypothesis that changes in volatility in index options markets leads volatility in underlying component (cash) markets. When we further analyze the sample by subperiod, we find that the causal relationships are insignificant in the period after the October 1987 crash, which is consistent with the hypothesis that exchange and regulatory actions taken after the crash weakened the influence of index options markets on cash markets. Trading strategies and programs involving stock index options and futures have been blamed for increasing volatility of the stock market. Indeed, trading in index futures and options markets has been blamed for much of the drop in stock prices in the crash of October 1987. After the crash, regulators took several actions to reduce the influence of futures and options market volatility on cash market volatility. If regulators' fears were legitimate and their efforts were successful, the volatility linkage between index options markets and their underlying cash markets should have been weakened. This paper provides two important contributions to our understanding of the volatility implications of index options markets. First, we examine the causality relationships between index and component stock implied volatility to assess whether or not changes in volatility in the index option market lead changes in volatility in the underlying component stock markets. Second, we test whether the causal relationships differ before and after the October 1987 crash to assess whether or not regulatory actions after the crash caused a change in these relationships. We measure volatility using implied standard deviations (ISDs) from options on the Major Market Index (MMI) and its component stocks. We form time series of ISDs for both the MMI and its component stocks, and then apply Granger causality tests to the series. For the full sample period of January 1987 to October 1989, we find that changes in index ISDs do Granger cause changes in component stock ISDs for all twenty component stocks, evidence consistent with the notion that volatility in index option market leads volatility in the component (cash) market. When we analyze the sample by subperiod, however, we find that the significant Granger causality holds only in the period before the October 1987 crash. Post‐crash subperiods show insignificant causality relationships, which suggests that efforts taken by exchange officials and regulators to reduce the influence of volatility in the index options and futures markets on cash market volatility were successful. The remainder of the paper is structured as follows. In Section I we discuss the potential for causal relationships between index option markets and their component markets and review related literature. Section II contains a discussion of our methodology and a description of our data. Section III contains a discussion of our results and Section IV concludes.

Citation

Laatsch, F.E. and Johnson, S.A. (1995), "An Investigation of the Causal Relationships Between Index and Component Stock Implied Volatility", Managerial Finance, Vol. 21 No. 10, pp. 26-40. https://doi.org/10.1108/eb018537