Common stochastic volatility trend in European exchange rates

Abstract

This paper examines the nature of stochastic volatility in the deutschemark/dollar and French franc/dollar exchange rates. In particular using a multivariate random walk stochastic volatility model the study examined whether volatility in each series can be ascribed to a single common trend. Results for univariate stochastic volatility models show very high persistence in the autoregressive component of volatility supporting the model specification where volatility follows a random walk. Estimation of the multivariate model reveals a very high correlation between the volatility innovations, and suggests that they follow a common trend, in essence the volatilities are cointegrated. A multivariate model with a single volatility trend is then estimated. Finally, support for this specification is further received when estimation of a stochastic volatility model for the ratio of the two series reveals no stochastic volatility present.