To simultaneously account for the properties of interest-rate term structure and foreign exchange rates within one arbitrage-free framework, we propose a class of multi-currency quadratic models (MCQM) with an (m + n) factor structure in the pricing kernel of each economy. The m factors model the term structure of interest rates. The n factors capture the portion of the exchange rate movement that is independent of the term structure. Our modeling framework represents the first in the literature that not only explicitly allows independent currency movement, but also guarantees internal consistency across all economies without imposing any artificial constraints on the exchange rate dynamics. We estimate a series of multi-currency quadratic models using U.S. and Japanese LIBOR and swap rates and the exchange rate between the two economies. Estimation shows that independent currency factors are essential in releasing the tension between the currency movement and the term structure of interest rates.

Using sovereign CDS spreads and currency option data for Mexico and Brazil, we document that CDS spreads covary with both the currency option implied volatility and the slope of the implied volatility curve in moneyness. We propose a joint valuation framework, in which currency return variance and sovereign default intensity follow a bivariate diffusion with contemporaneous correlation. Estimation shows that default intensity is much more persistent than currency return variance. The market price estimates on the two risk factors also explain the well-documented evidence that historical average default probabilities are lower than those implied from credit spreads.