Cross-Dynamics of Volatility Term Structures Implied by Foreign Exchange Options

Abstract

This paper examines the cross-dynamics of volatility term structures implied by foreign exchange options. The data used in the empirical analysis consist of daily observations of implied volatilities for OTC options on the euro, Japanese yen, British pound, Swiss franc, and Canadian dollar, quoted against the U.S. dollar. The empirical findings demonstrate that two common factors can explain a vast proportion of the variation in volatility term structures across currencies. Furthermore, the results indicate that the euro is the dominant currency, as the implied volatility term structure of the euro is found to affect all the other volatility term structures, while the term structure of the euro appears to be virtually unaffected by the other currencies. Finally, our results reveal a rather deviant relation between the volatility term structures of the euro and Swiss franc by providing evidence of significant nonlinearities in the relationship between these two currencies.