Implementing a filtered term structure model in the South African bond market

Master Thesis


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University of Cape Town

A key feature of the local bond market is that trade is concentrated in a few liquid government bonds. We review and implement the filtered term structure model proposed by Gombani, Jaschke and Runggaldier that defines an arbitrage free pricing system that is consistent with liquid bond prices. The model is derived in two stages called the underlying and perturbed models. The underlying model defines the theoretical arbitrage free term structure. It is assumed to be a multi-factor, affine HNM type model where the stochastic factors satisfy a linear diffusion equation. Gombani et al. argue that the differences between the theoretical and market prices should be interpreted as unobserved errors. The perturbed model the prices of the observed bonds as their theoretical values distorted by noise. Assuming that the information at any point in time is the market prices of a finite number of liquidly traded bonds, the perturbed model is used to derive a continually updated pricing system that is arbitrage free with respect to the observed prices. The method is based on the Kalman filter. We implement a particular three-factor version of the model and calibrate it to the South African market. We discuss the relevant data and numerical and statistical techniques including principal component analysis and yield curve construction. We apply the formulas for pricing European options on zero-coupon and coupon bearing bonds for Gaussian HJM models to the perturbed model and present two examples to demonstrate the application of the model to bond and option pricing.

Includes bibliographical references (leaves 72-75).