This paper examines the nature of stochastic volatility in the deutschemark
/dollar and French franc/dollar exchange rates. In particular using a multi
variate 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 specificati
on where volatility follows a random walk. Estimation of the multivariate m
odel reveals a very high correlation between the volatility innovations', a
nd suggests that they follow a common trend, in essence the volatilities ar
e cointegrated. A multivariate model with a single volatility trend is then
estimated. Finally, support for this specification is further received whe
n estimation of a stochastic volatility model for the ratio of the two seri
es reveals no stochastic volatility present.