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Essays on the Modeling of Risks in Interest-Rate and Inflation Markets A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Tang Andersen, Allan Sall Doctoral Thesis Essays on the Modeling of Risks in Interest-rate and Inflation Markets PhD Series, No. 20.2011 Provided in Cooperation with: Copenhagen Business School (CBS) Suggested Citation: Tang Andersen, Allan Sall (2011) : Essays on the Modeling of Risks in Interest-rate and Inflation Markets, PhD Series, No. 20.2011, ISBN 9788792842015, Copenhagen Business School (CBS), Frederiksberg, http://hdl.handle.net/10398/8339 This Version is available at: http://hdl.handle.net/10419/208785 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. 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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. https://creativecommons.org/licenses/by-nc-nd/3.0/ www.econstor.eu Essays on the modeling of risks in interest-rate and inflation markets Essays on the modeling of risks in interest-rate copenhagen business school handelshøjskolen solbjerg plads 3 dk-2000 frederiksberg danmark www.cbs.dk Essays on the modeling of risks in interest-rate and inflation markets Allan Sall Tang Andersen PhD Series 20.2011 ISSN 0906-6934 Print ISBN: 978-87-92842-00-8 Online ISBN: 978-87-92842-01-5 The PhD School of Economics and Management PhD Series 20.2011 Essays on the modeling of risks in interest-rate and inflation markets Allan Sall Tang Andersen Advisor : Bjarne Astrup Jensen Ph.D. dissertation Department of Finance Copenhagen Business School May, 2011 Allan Sall Tang Andersen Essays on the modeling of risks in interest-rate and inflation markets 1st edition 2011 PhD Series 20.2011 © The Author ISSN 0906-6934 Print ISBN: 978-87-92842-00-8 Online ISBN: 978-87-92842-01-5 “The Doctoral School of Economics and Management is an active national and international research environment at CBS for research degree students who deal with economics and management at business, industry and country level in a theoretical and empirical manner”. All rights reserved. No parts of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval system, without permission in writing from the publisher. Contents Contents iii Acknowledgements v Introduction 1 Summary 11 1 Modeling stochastic skewness in a Heath-Jarrow-Morton framework 19 1.1Introduction........................... 20 1.2Evidenceofstochasticskewness................ 21 1.3Modelingstochasticskewness................. 27 1.4SpecifyingtheModel...................... 33 1.5Modelcalibration........................ 35 1.6Results.............................. 38 1.7Conclusion............................ 43 1.8Appendix:Proofofproposition1 ............... 44 1.9Appendix:MCMCdetails................... 45 2 Inflation derivatives modeling using time changed L´evy processes 49 2.1Introduction........................... 50 2.2Inflationlinkedproducts.................... 52 2.3TheJarrow-Yildirimmodel.................. 56 2.4 Time changed L´evyprocesses................. 58 2.5 An inflation HJM framework based on time changed L´evy processes............................. 61 2.6 Pricing inflation products . 68 2.7Specificationofthetime-change................ 72 2.8Calibration........................... 74 2.9Conclusion............................ 79 iii 2.10Appendix:Proofs........................ 81 2.11Appendix:TheVarianceGammaprocess........... 85 3 Inflation risk premia in the term structure of interest rates: Evidence from Euro area inflation swaps 87 3.1Introduction........................... 88 3.2 Data: Inflation swap rates and the nominal term structure . 90 3.3 Inflation risk premia: What theory predicts . 97 3.4 A no-arbitrage model of nominal and inflation swap rates . 99 3.5ModelEstimation........................102 3.6Empiricalresults........................105 3.7Conclusion............................120 3.8 Appendix: Derivation of nominal ZCB prices, real ZCB prices andInflationexpectations...................122 3.9Appendix:MCMCestimationofthemodel..........126 4 Affine Nelson-Siegel Models and Risk Management Per- formance 131 4.1Introduction...........................132 4.2 The Danish Government Bond Term Structure . 133 4.3AffineTermStructureModels.................136 4.4Multi-factorCox-Ingersoll-Rossmodels............138 4.5AffineNelson-Siegelmodels..................140 4.6ModelEstimation........................143 4.7EmpiricalResults:In-Sample.................146 4.8EmpiricalResults:Out-of-Sample...............153 4.9Conclusion............................159 4.10 Appendix: Affine Nelson-Siegel models with stochastic volatil- ity................................161 4.11Appendix:MCMCdetails...................167 4.12Appendix:DensityForecasts..................172 4.13 Appendix: Tables with out-of-sample forecast results . 177 Conclusion 203 Bibliography 205 iv Acknowledgements With the hand-in of this thesis, I have now finished my years as a Ph.D. student at the Department of Finance at Copenhagen Business School and Danmarks Nationalbank. The years as a Ph.D. student have at times been hard work, but it has most definitely been a good experience. First of all, I would like to thank my supervisor Bjarne Astrup Jensen for encouraging me to consider a position as a Ph.D. student, for providing me with suggestions and pin-pointing errors and unclear reasoning in my work during the process. I would like to thank Danmarks Nationalbank for giving me the opportu- nity to enter into their Ph.D. programme and the Capital Markets/Financial structure division at the European Central Bank for giving me the possibil- ity to spend 6 months in Frankfurt. The stay in Frankfurt both spurred an interest in and deepened my understanding of inflation markets. I would also like to thank professor Rama Cont for providing the opportunity to stay a semester at the Center for Financial Engineering, Columbia University. Fellow Ph.D. students at the Department of Finance and Danmarks Nation- albank also deserve thanks for creating a good environment, both socially and professionally. From Danmarks Nationalbank I would especially like to thank my office-mate Jannick Damgaard for making the Ph.D. a pleasant time, despite non-overlapping research interests. From the Department of Finance I would like to thank Mads Stenbo Nielsen and Jens Dick-Nielsen for always having their door open if I needed to discuss a topic. Outside the world of Ph.D. students, I would like to thank Jacob Ejsing and Kasper Ahrndt Lorenzen for providing valuable insights, especially regarding infla- tion markets. I also want to thank Jesper Lund and Fred Espen Benth for participating in my pre-defence and providing me with valuable comments for my thesis. On a personal level, I want to thank my parents for supporting me my entire life and providing abstractions outside the world of finance. Finally, I would like to thank my fianc´ee Anne-Sofie for constant encouragement v and patience. Your insight into the life of a Ph.D. student, have made my life as a, at times slightly confused, Ph.D. student significantly better. Copenhagen, May 2011 Allan Sall Tang Andersen vi Introduction The topic of this thesis is the modeling of risks in interest-rate and inflation markets. Interest-rate risk is an important issue to investors. For instance, according to BIS (2010) the notional value of over-the-counter interest-rate derivatives markets is 465,260 billion US-dollar. This corresponds to 77 percent of the notional of the entire OTC derivatives market. Thus interest-rate deriva- tives is at the back-bone of the financial markets. According to ISDA (2009) 83 percent of Fortune 500 companies report using interest-rate derivatives in their risk management. Furthermore, many mortgage-based loans and pen- sion contracts contain either explicit or implicit interest-rate options. Thus a better understanding of the interest-rate derivative markets, and the risk associated with the traded products is of great value, both to financial and non-financial companies as well as individuals. The market for inflation linked products, such as bonds and swaps, is sig- nificantly smaller than the one for interest-rate derivatives. The market is also significantly newer than the nominal interest-rate market, with one of the prominent examples being US Treasury Inflation Protected Bonds (TIPS). TIPS were introduced in 1997 and with a notional outstanding of less than 50 billion US dollar. By 2010 the US Treasury has issued TIPS worth over 600 billion US dollar, see Christensen and Gillan (2011). The issuance of inflation
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