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Hull-White Or Black-Karasinski? Implementation Note and Model Comparison for ALM A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Khan, Aisha; Guan, Eric; Poon, Ser-huang Working Paper Short rate models: Hull-White or Black-Karasinski? Implementation note and model comparison for ALM Manchester Business School Working Paper, No. 562 Provided in Cooperation with: Manchester Business School, The University of Manchester Suggested Citation: Khan, Aisha; Guan, Eric; Poon, Ser-huang (2008) : Short rate models: Hull- White or Black-Karasinski? Implementation note and model comparison for ALM, Manchester Business School Working Paper, No. 562, The University of Manchester, Manchester Business School, Manchester This Version is available at: http://hdl.handle.net/10419/50684 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu Working Paper Series Short Rate Models: Hull-White or Black-Karasinski? Implementation Note and Model Comparison for ALM Aisha Khan, Eric Guan and Ser-Huang Poon Manchester Business School Working Paper No. 562 September 2008 Manchester Business School Copyright © 2008, Khan, Guan and Poon. All rights reserved. Do not quote or cite without permission from the author. Manchester Business School The University of Manchester Booth Street West Manchester M15 6PB +44(0)161 306 1320 http://www.mbs.ac.uk/research/workingpapers/ ISSN 0954-7401 The working papers are produced by The University of Manchester - Manchester Business School and are to be circulated for discussion purposes only. Their contents should be considered to be preliminary. The papers are expected to be published in due course, in a revised form and should not be quoted without the authors’ permission. Author(s) and affiliation Professor Ser-Huang Poon Professor of Finance Manchester Business School University of Manchester Crawford House Oxford Road Manchester M13 9PL United Kingdom Tel: +44 161 275 0431 (direct) 0429/0436 (secretary) Fax: +44 161 275 4023 Email: [email protected] http://www.personal.mbs.ac.uk/ser-huang-poon/ http://ssrn.com/author=44637/ Aisha Khan and Eric Guan were postgraduate students at Manchester Business School. Keywords Asset-liability management, Hull-White, Black-Karasinski, Bermudan swaptions, 1-factor model Abstract In this paper, we compare two one-factor short rate models: the Hull White model and the Black- Karasinski model. Despite their inherent shortcomings the short rate models are being used quite extensively by the practitioners for risk-management purposes. The research, as part of students’ projects in collaboration with the Asset-Liability-Management (ALM) Group of ABN AMRO Bank, provides detail procedures on the implementation, and assesses model performance from an ALM perspective. In particular, we compare the two models for pricing and hedging Bermudan swaptions because of its resemblance to prepayment option in typical mortgage loans. To our knowledge, the implementation of the two short rate models (and the Black-Karasinski model in particular) is not well documented. We implemented the two models using interest rate derivatives on Euro and US rates over the period February 2005 to September 2007 and with the Hull-White trinomial tree. Our results show that in terms of the in-sample pricing tests, the one-factor Hull- White model outperforms the Black-Karasinski model. The estimated parameters of Hull-White model are also more stable than those of the Black-Karasinski model. On the other hand, the tests for the hedging performance show that the Black-Karasinski model is more effective in hedging the interest rate risk of the at-the-money 10x1 co-terminal Bermudan swaption. How to quote or cite this document Khan, Guan and Poon (2008). Short Rate Models: Hull-White or Black-Karasinski? Implementation Note and Model Comparison for ALM, Manchester Business School Working Paper, Number 562, available: http://www.mbs.ac.uk/research/workingpapers/ Short Rate Models: Hull-White or Black-Karasinski? Implementation Note and Model Comparison for ALM Aisha Khan, Eric Guan and Ser-Huang Poon June 14, 2008 All authors are at Manchester Business School, UK. Please send all correspondence to Professor Ser-Huang Poon, Manchester Business School Crawford House, University of Manchester, Oxford Road, Manchester M13 9PL, UK. Tel: +44 161 275 4021, Fax: +44 161 275 4023, Email: ser- [email protected]. We would like to thank Peter van der Wal, Vincent van Bergen and Jan Remmerswaal from ABN AMRO for manu useful suggestions and data, Michael Croucher for NAG software support, and Dick Stapleton and Marti Subrahmanyam for many helpful advice. 1 Short Rate Models: Hull-White or Black-Karasinski? Implementation Note and Model Comparison for ALM Abstract In this paper, we compare two one-factor short rate models: the Hull White model and the Black-Karasinski model. Despite their inherent shortcomings the short rate models are being used quite extensively by the practitioners for risk- management purposes. The research, as part of students’ projects in collaboration with the Asset-Liability-Management (ALM) Group of ABN AMRO Bank, provides detail procedures on the implementation, and assesses model performance from an ALM perspective. In particular, we compare the two models for pricing and hedging Bermudan swaptions because of its resemblance to prepayment option in typical mortgage loans. To our knowledge, the implementation of the two short rate models (and the Black- Karasinski model in particular) is not well documented. We implemented the two models using interest rate derivatives on Euro and US rates over the period February 2005 to September 2007 and with the Hull-White trinomial tree. Our results show that in terms of the in-sample pricing tests, the one-factor Hull- White model outperforms the Black-Karasinski model. The estimated parameters of Hull-White model are also more stable than those of the Black- Karasinski model. On the other hand, the tests for the hedging performance show that the Black-Karasinski model is more effective in hedging the interest rate risk of the at-the-money 10x1 co-terminal Bermudan swaption. 1 Short Rate Models: Hull-White or Black-Karasinski? Implementation Note and Model Comparison 1 Introduction In this paper, we study the choice of short rate models for asset-liability management in a global bank. In particular, we compare the performance of two one-factor short rate models, viz. Hull-White and Black-Karasinski, for hedging a 10x1 Bermudan swaption on an annual basis over a one and a half year period. The 10x1 Bermudan swaption is chosen because it resembles a loan portfolio with early redemption fea- ture, an important product for most banks. Unlike the short-term pricing problem, the one-factor model is often preferred for the longer term ALM purpose because of its simplicity. For long horizon hedging, the multi-factor model could produce more noise as it requires more parameters input. Pricing performance measures a model’s capability of capturing the current term structure and market prices of interest rate sensitive instruments. Pricing performance can always be improved, in an almost sure sense, by adding more explanatory variable and complexities to the dynamics. However, pricing performance alone cannot re‡ect the model’sability in capturing the true term structure dynamics. To assess the appropriateness of model dynamics, one has to study model forecasting and hedging performance. The last few decades have seen the development of a great variety of interest rate models for estimating prices and risk sensitivities of interest rate derivatives. These models can be broadly divided into short rate, forward rate and market models. The class of short-rate models, among others, includes Vasicek (1977), Hull and White (1990), and Black and Karasinski (1991). The Ho-Lee model is an early example of forward-rate modelling. A generalized framework for arbitrage free forward-rate modelling originates from the work of Heath, Jarrow and Morton (HJM, 1992). Market models are a class of models within the HJM framework that model the evolution of rates that are directly observable in the market. Example of such models are the Libor Market Model by Brace, Gatarek, and Musiela (1997) 2 and the Swap Market Model by Jamshidian (1997). All these models have their own strengths and weaknesses. Short-rate models are tractable, easy to understand and implement but do not provide complete freedom in choosing the volatility structure. The HJM framework is
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