In this paper a new measure of Greek stock market volatility based on the prices of FTSE/ATHEX-20 index options is proposed. Greek Implied Volatility Index is calculated using the model-free methodology that involves option prices summations and is independent from the Black and Scholes pricing formula. The specific method is applied for the first time in a peripheral and illiquid market as the Athens Exchange. The empirical findings of this paper show that the proposed volatility index includes information about future realized volatility beyond that contained in past volatility and in addition, show that there is a statistically significant negative and asymmetric contemporaneous relationship between the returns of the implied volatility index and the underlying equity index. Finally, the volatility transmission effects on the Greek stock exchange from two leading markets, namely the New York Stock Exchange and the Deutsche Borse, are tested and documented.