Multi-Currency Quadratic Models : Theory and Evidence

The challenge of international term structure models is to simultaneously account for the properties of interest rate term structures and foreign exchange rates within an arbitrage-free framework. We extend the quadratic term structure models proposed in Leippold and Wu (2002) to multiple currencies and illustrate its flexibility and tractability in capturing the salient features of both interest rates and exchange rates. The model framework not only readily explains the stylized evidence on classic forecasting regressions based on various forms of expectation hypotheses (EH), but also accommodates rich time-varying dynamics for conditional variance of bond and currency returns. Furthermore, we propose an m+n model structure where the first m factors are term structure factors and the latter n factors are pure exchange rate factors independent of the movement of the term structure of either country. These independent currency risk factors account for the variation in the exchange rate that is independent of the variation in the interest rate term structure of either country. Equipped with a model that can accommodate these empirical facts, we use a relatively new filtering technique, the unscented Kalman filter, to estimate a series of multi-currency quadratic models (MCQM) with LIBOR and swap rates from US and Japan and the exchange rates between them. The estimation results shed further lights on the interaction between interest rates and exchange rates.