Modelling Term and Inflation Risk Premia in the South African Bond Market

van Schaik, Luke

Modelling Term and Inflation Risk Premia in the South African Bond Market

Master Thesis

2022

Abstract

A variety of approaches has been used to estimate the term premium of bond yields. Early attempts include linear regression models, such as those of Fama and Bliss (1987) and Cochrane and Piazzesi (2005), but these have been shown to be inconsistent and lacking in robustness (Kim and Orphanides (2007)). Affine term structure models developed by Duffie and Kan (1996) and extended by Duffee (2002) provide a more sophisticated framework for modelling bond yields and term premia, with improved results over the aforementioned regressions. However, parameters of these models have historically been estimated using maximum likelihood methods which are computationally inefficient and have been shown to have problems in finding the global maximum of the likelihood function (Hamilton and Wu (2012), Adrian et al. (2013)). The framework and estimation procedure of Adrian, Crump and Moench, or ACM, addresses the above problems by using ordinary least-square regressions exclusively to estimate the parameters of an affine term structure model (Adrian et al. (2013)). This dissertation applies the ACM procedure to South African zero-coupon nominal bond yields to estimate the term premium embedded in these yields. Performance of the ACM procedure is tested under Monte Carlo simulation and under applications to the smoothed United States nominal bond yield curves of Gurkaynak et al. (2006) and bootstrapped nominal bond yield curves from the South African market. Dynamics of the level, slope and curvature components of the US yield curves are compared to each other and to the estimated term premia. Results show that the ACM procedure generates very accurate fits to observed yield curves, but has some trouble capturing idiosyncratic features of the South African yield curve. Further, magnitudes of the term premium estimate are shown to be affected by the choice of time series of yield curves. Despite these limitations, the ACM procedure is shown to be a fast estimation procedure which generates term premium dynamics consistent with other approaches.

Keywords

Mathematical Finance

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