Working Paper No. 291
By Luca Benati
This paper uses two affine term structure models from the Duffie-Kan class—a three-factor Cox-Ingersoll-Ross model, and a three-factor model in the spirit of Longstaff and Schwartz—to extract historical estimates of foreign exchange risk premia for the pound with respect to the US dollar. The term structures of interest rates for the two countries are estimated jointly, together with the dynamics of the nominal exchange rates between them, via maximum likelihood. The likelihood function is computed via the Kalman filter, and is maximised numerically with respect to unknown parameters. Particular attention is paid to the robustness of the results across models; to the overall (filter plus parameter) econometric uncertainty associated with risk premia estimates; and to the ability of estimated structures to replicate Fama’s ‘forward discount anomaly’. The paper’s main results may be summarised as follows. First, risk premia estimates are not consistent across the two models. Second, both models fail to replicate the forward discount anomaly, with theoretical values of ß in the Fama regressions implied by estimated structures being consistently positive at all horizons from 1 to 12 months.
Affine term structure models for the foreign exchange risk premium