International Transmission of Volatility: A Study on the Volatility Indexes Vx1, Vdax and VIX

Abstract

The relation between risk and return is very well documented in financial literature. While Sharpe (1964) proposed a linear relation between risk and return through the CAPM, Black (1976) pointed out later an asymmetric relation between these variables. Indeed, he noted that volatility was higher after a stock market fall than after a rise. From this observation, many articles were written on the transmission mechanism of price and on volatility spillovers across different markets. All these papers modeled returns and historical variance through different models and generally with GARCH models.

In this paper, we propose a precise description of volatility spillovers based on the international transmission of implied volatility. Indeed, we examine the possible interactions between returns and implied volatility and between implied volatilities belonging to different markets. To do so, we use three implied volatility indexes, the French VX1, the German VDAX and the American VIX.

We find very interesting results concerning the impact of news on the implied volatility behavior and also on the interaction between implied volatility and realized volatility. We get rich information on the nature of the underlying process of implied volatility and historical volatility.

Keywords: GARCH model, Implied Volatility, Risk Management

JEL Classification: G13, G14, C53