Approximating Risk Premium on a Parametric Arbitrage-free Term Structure Model

Abstract

In this paper we approximate the risk factors of a polynomial arbitrage-free dynamic term structure model by running a sequential set of linear regressions independent across time. This approximation avoids the cost of a full optimization procedure allowing for a simple method to extract the risk premium embedded in interest rate assets. Closed-form bond pricing formulas provide interpretation of each source of aggregate risk as known term structure movements. Assuming, for illustrative purposes, an economy with three sources of aggregate risk (level, slope and curvature), we test the validity of our approximation adopting a dataset of Brazilian zero coupon interest rates. The new methodology generates accurate parameters, standard deviations and risk premium dynamics when compared to the exact dynamic model. Moreover, an empirical illustration comparing the out-of-sample forecasting performance of the exact model, our approximation, and a standard Gaussian affine model against the Random Walk, reveals that the proposed approximation obtains favorable forecasting results providing a reliable substitute to the exact estimation method with a much smaller computational time.