Title page for ETD etd-06172009-085254

Document Type Master's Dissertation
Author Thomas, Michael Patrick
URN etd-06172009-085254
Document Title Long term extrapolation and hedging of the South African yield curve
Degree MSc
Department Mathematics and Applied Mathematics
Advisor Name Title
Prof E Mare Supervisor
  • hedging strategy
  • long term extrapolation
  • fixed interest rate market
  • extrapolation technique
Date 2009-04-28
Availability unrestricted
The South African fixed interest rate market has historically had very little liquidity beyond 15 - 20 years. Most financial institutions are currently prepared to quote and trade interest rate risk up to a maximum term of 30 years. Any trades beyond 30 years usually attract very onerous spreads and raise relevant questions regarding an appropriate level of mid-rates. However, there are many South African entities whose business involves taking on exposure to interest rates beyond 30 years, such as life insurance companies and pension funds. These entities have historically used very traditional approaches to hedging their interest rate exposures across the whole term structure and have typically done little to gain any further protection.

We can generalise the problems faced by any entity exposed to long term interest rate risk in South Africa:

1. The inadequacy of traditional matching methods (i.e. immunisation and bucketing) to cope with the long term interest rate risks.

2. The non-observability of interest rate data beyond the maximum term in the yield curve. Associated with this is the inability to adequately quantify interest rate risk.

3. The lack of liquidity in long term interest rate markets. Associated with this is the inability to adequately hedge long term interest rate risk.

We examine various traditional approaches to matching / hedging interest rate risk using information available at observable / tradable terms on the nominal yield curve. We then look at the reasons why these approaches are not suitable for hedging long term interest rate risk.

Some modern methods to forecast and hedge long term interest rate risks are then examined and the possibility of their use in managing long term interest risk is explored. On the back of these investigations, we propose a number of possible yield curve extrapolation procedures and methodology for performing calibrations.

Using some general theoretical hedging results, we perform a case study which analyses the performance of various theoretical hedges over a historical period from October 2001 to March 2007. The results indicate that extrapolation and hedging of the yield curve is able to significantly reduce Value-At-Risk of long term interest rate exposures.

A second case study is then performed which analyses performance of the various theoretical hedges using out-of-sample simulated yield curve data.

We find that there appears to be a significant benefit to the use of yield curve extrapolation techniques, specifically when used in conjunction with a hedging strategy. In some cases we find that the more simple extrapolation techniques actually increase risk (significantly) when used in conjunction with hedging. However, for some of the more advanced techniques, risk can be significantly reduced.

For an entity looking to deal with long term interest rate risk, we find that the choice of extrapolation technique and hedging strategy go hand-in-hand. For this reason the cost of hedging and reduction in risk are strongly correlated. The results we obtain suggest that it is necessary to weigh the benefits against the cost of hedging. Further, this cost seems to increase with increasing reduction in risk. The research and results presented here are related to those in the paper Long Term Forecasting and Hedging of the South African Yield Curve presented by Thomas and Maré at the 2007 Actuarial Convention in South Africa.

Copyright © 2008, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.

Please cite as follows:

Thomas, MP 2008, Long term extrapolation and hedging of the South African yield curve, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-06172009-085254/ >


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