A Practical Robust Long Term Yield Curve Model

Abstract

This paper describes the development and initial testing of the Black-corrected version of a workhorse 3-factor Gaussian yield curve (term structure) model, the economic factor model (Dempster et al., 2010) which we have used for many years with Monte Carlo scenario simulation for structured derivative valuation, investment modelling and asset liability management with various time steps and currencies. In common with most alternative approaches in the literature to generating non-negative yieldsusing Black's idea, we propose a simple approximation to the Black mathematical model using the nonlinear unscented Kalman filter (UKF). However, model calibration, unlike that of the current computationally intensive alternatives, requires not significantly more computing time than is needed for the linear Kalman filter with the underlying affine shadow rate model. Initial empirical testing of the new Black EFM model both in- and out-of-sampleshows acceptable accuracy, improved over that of the affine EFM model, which can be further improved by UKF tuning in future research. Migration of the system to the cloud can reduce calibration times for both models from a few hours to a few minutes by exploiting massive parallelization of the computationally intensive step.