Modeling the Dynamic Process of the Forward Curve

Abstract

In this paper, we provide adjustments for liquidity and credit risk to the forward Libor rate in order to improve accuracy of the forward rate in forecasting the 3-month Libor rate. In particular, we introduce the adjusted forward curve (AFC) that models the update in the forward curve from one period to the next. A direct modeling of the dynamic process of the forward curve facilitates the specification of adjustment factors to the forward curve, and it underscores the role of mean reversion (stationarity) in the nexus between the forward rate and the future spot rate, The AFC factors that underpin the forward curve bias are statistically relevant with p-values that are less than .00001. The upward bias in the forward curve (i.e., when the forward curve exceeds the expected future spot rate) positively correlates with the steepness of the yield curve in the AFC model. A downward bias positively correlates with the credit spread and industrial capacity utilization. Furthermore, the effect of the instantaneous forward curve on the future spot rate tempers off with time. The predictive power of the AFC model, however, hinges on the forecastability of the underlying factors. The testing indicates that all the AFC model factors have a mean reversion component. Overall, our model effectively anticipates movements in the forward curve that tend to yield a better forecast of the future spot rate.