Response of the term structure of forward exchange rate to jump in the interest rate

In this paper, we propose a dynamic model of the term structure of forward exchange rates and discuss the effects of jumps in interest rates on the term structure of forward exchange rates. First, we develop a dynamic three-factor model of forward exchange rates in continuous time that incorporates central bank policy. We model the policy-related events, especially the interest rate adjustment, as interest rate jumps. We apply the model framework to the pricing of USD/CAD and USD/JPY forward exchange rates. We use the Kalman filter approach to estimate the model and Markov Chain Monte Carlo (MCMC) algorithm to discriminate jumps in interest rates. The empirical results show strong evidence of jumps in interest rates related to macroeconomic announcements. Given these jumps, we conclude that our proposed model improves the performance of existing forward exchange rates models. Last but not least, when jumps in interest rates occur, whether the volatility curves of forward rates are asymmetric smile-shaped depends on the standard deviation of spot exchange rate, the speed of adjustment coefficient of foreign interest rate and the correlation coefficient between spot exchange rate and foreign interest rate.

► A dynamic three-factor model of the term structure is established. ► The effect of jumps on the term structure of forward exchange rates is analyzed. ► The Kalman filter approach is used to estimate the three-factor model. ► Strong evidence of jumps in interest rates related to macroeconomic announcements. ► The volatility curves of forward exchange rates are asymmetric smiled-shaped.