The Greek implied volatility index: construction and properties

Abstract

There is a growing literature on implied volatility indices in developed markets. However, no similar research has been conducted in the context of emerging markets. In this paper, an implied volatility index (GVIX) is constructed for the fast developing Greek derivatives market. Next, the properties of GVIX are explored. In line with earlier results, GVIX can be interpreted as a gauge of the investor's sentiment. In addition, it is found that the underlying stock market can forecast the future movements of GVIX. However, the reverse relationship does not hold. Finally, a contemporaneous spillover between GVIX and the US volatility indices VXO and VXN is detected. The results have implications for portfolio management.

Acknowledgements

I am particularly grateful to Nikos Porfiris who kindly provided the data set for this study, and to Carol Alexander, Chris Brooks, Harris Linaras, Stewart Mayhew, Nikolaos Panigirtzoglou, Peter Pope, Mark Shackleton, and Robert Whaley for many helpful discussions. I would also like to thank Christos Dadamis, Athanasios Episkopos, Dimitris Flamouris, Gikas Hardouvelis, Iakovos Iliadis, Katerina Panopoulou, Dimitris Papas, Costas Petsas, and the participants at the 2003 University of Piraeus-ADEX Research Seminar Series, and at the 2003 Hellenic Finance and Accounting Association Meeting for useful discussions and comments. This paper was part of the project ‘Volatility Derivatives’ funded by the Athens Derivatives Exchange (ADEX). Financial support from the Research Centre of the University of Piraeus is also gratefully acknowledged. The views expressed herein are those of the author and do not necessarily reflect those of ADEX. Any remaining errors are my responsibility alone.

Notes

A volatility derivative can also be written on an asset that has a payoff closely related to the volatility swings, e.g. a straddle. See Brenner et al. (2002) who propose an option on a straddle.

For example, MONEP constructs its volatility indices using only call prices that trade more frequently. However, this may introduce severe biases in the construction of the implied volatility index since it is well documented that the implied volatilities of calls and puts may differ significantly (Gemmill, 1996). See also Moraux et al. (1999) for a discussion of the measurement errors in the construction of the French volatility indices.

In September 2003, CBOE introduced two new volatility indices, termed VIX and VXN, respectively. These are based on an alternative to the ‘old’ VIX and VXN construction method. Among other differences, the new method also uses only OTM options.

The option prices quoted as ‘closing’ in ADEX are not the last-traded prices. They are settlement prices in the sense that ADEX uses an algorithm to calculate them. For the shortest expiry, the three nearest-to-the-money call and puts are used. For the second expiry series only the closest-to-the-money call and put is required. Then, Black's (1976) model is used to back out the implied volatility using the last traded future price and a constant interest rate of 3%. In the next step, the arithmetic average of the implied volatility is obtained. Finally, the settlement option price is calculated using the average implied volatility and the future settlement price.

A distinguishing characteristic of the Greek derivatives market is that the settlement and margining are performed at an end-client level, allowing a transparent monitoring of the transactions that facilitates risk management. This is in contrast to the ‘omnibus’ practice followed by other exchanges.

Figlewski and Wang (2000) confirm this asymmetric relationship by treating the changes (of the logarithm) of implied volatility as the dependent variable, and the index returns as the independent variable, in a linear regression setup.

As such a measure of fear, VXO can help to determine whether OEX options are undervalued or overvalued (see Stendahl, 1994, for a discussion on using VXO for volatility trading purposes).

Whaley (2000) uses also an intercept in his regression formulation. We found that the intercept component was insignificant and thus we omitted it.

Y is said to be Granger-caused by X if X helps in the prediction of Y, or equivalently if the coefficients on the lagged Xs are statistically significant. It is important to note that the statement ‘X Granger causes Y’ does not imply that Y is the effect or the result of X. Granger causality measures precedence and information content but does not by itself indicate causality in the more common use of the term (see Hamilton, 1994, for a detailed description of the Granger causality test).

We applied the Granger causality test to squared returns, as well. However, the results did not change.