South African Inflation Modelling Under the HJM Framework

Rizzo, Massimo

South African Inflation Modelling Under the HJM Framework

Master Thesis

2022

Abstract

Inflation modelling is typically done following an econometric approach, however this results in models being constructed that are not consistent with the observable bond market and as such they cannot be used in hedging market instruments or in pricing inflation-linked derivatives. Jarrow and Yildirim (2003) were one of the first to propose a framework under which nominal and real forward rates and an inflation index could be jointly modelled in a consistent manner, based on the Heath-Jarrow-Morton (HJM) framework as first developed by Heath et al. (1992). They showed that under this framework it is possible to recover observed nominal and inflation-linked bond prices, hedge these instruments, and price related inflation-linked derivatives. A shortfall of this framework however, as critiqued by Mercurio (2005) and Belgrade et al. (2004), is that it depends entirely on non observable parameters. As such, estimating the parameters of a model constructed under this framework is non-trivial. This dissertation applies the approach detailed by Jarrow and Yildirim (2003) to construct a model that fits the South African context, and makes use of the Kalman filter, as originally documented by Kalman (1960), to overcome the issues that arise in parameter estimation. Using the model constructed, forecasts of future inflation in South Africa are produced.

Keywords

Mathematical Finance

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