Approximating risk premium on a parametric arbitrage-free term structure model
Resumo
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 full optimization in the estimation process allowing for a simple method to extract the risk premium embedded in interest rate instruments. Closed-form bond pricing formulas provide a clear interpretation of each source of aggregate risk as known term structure movements. Assuming, for illustrative purposes, the existence of three sources of aggregate risk (level, slope and curvature) in the economy, we test the validity of our approximation adopting a dataset of Brazilian zero coupon interest rate swaps. The new methodology generates accurate parameters, standard deviations and risk premium dynamics when compared to the exact dynamic model.
