Browsing by Author "Dugmore, Brett"

Now showing 1 - 5 of 5
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    Implementing a filtered term structure model in the South African bond market
    (2007) Ririe, Angela; Dugmore, Brett
    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.
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    Open Access
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    Open Access
    Modelling credit spreads in an illiquid South African corporate debt market
    (2019) Jones, Samantha; Laurie, Henri; Fredericks, Ebrahim; Becker, Ronald; Dugmore, Brett
    The South African debt market suffers from severe illiquidity, as is common in most emerging markets. Infrequent trading leads to out-of-date market prices and stale, unreliable credit spreads. Since the coverage of the South African debt market by credit ratings agencies is poor, meaningful credit spreads become even more important in gauging credit worth. The illiquidity of corporate vanilla bonds traded on the Johannesburg Stock Exchange and the ensuing adverse effects on their credit spreads are rigourously illustrated. Lack of data poses a serious problem when modelling any system and this analysis provides motivation for the necessity of a framework that addresses the statistical complications that incomplete data sets present. A new model, which is a distinctive modification of the well-known mean-reverting Ornstein-Uhlenbeck or Vasicek process, is introduced. This innovative approach creates a mathematically and intuitively sound relationship between the credit spread process and that of the stock price of the bond issuer. This key feature is used in a Bayesian methodology to impute missing credit spread data for calibration, for more meaningful inference. On sparse simulated data and market observed credit spread time series, the model proves to deliver an improved quality of the estimations, with probabilities that are now statistically founded. Even on complete credit spread time series, the model is shown to have some merit over the traditional model in terms of goodness of fit, giving further credence to its validity and explanatory power.
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    The right exactness of the smooth right Puppe sequence
    (1996) Dugmore, Brett; Cherenack, Paul F
    It was our aim, in this thesis, to give a proof that the smooth right Puppe sequence exists and is right exact, following the methods used by Whitehead in (30], and where he shows that the usual continuous right Puppe sequence exists and is right exact. We have only partially been able meet this aim. We have attempted to follow the general approach of Steenrod [27], where he defines neighbourhood deformation retracts, but there are some difficulties involved in the theory of smooth neighbourhood deformation retracts that have made it necessary for us to assume the existence of a 'suitable' smooth structure on products such as I x X x Y, where (X, A), and (Y, B) are smooth neighbourhood deformation retracts, such that the product, defined as (X x Y, Ax Y U X x A), is an SNDR pair under this 'suitable' product structure. This enables us to develop the theory of smooth neighbourhood deformation retracts in a similar way to the theory of continuous neighbourhood deformation retracts.