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The Dynamics of Swap Spreads and the Estimation of Volatility

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The Dynamics of Swap Spreads and the Estimation of Volatility Applied Financial Econometric Analysis: The Dynamics of Swap Spreads and the Estimation of Volatility David Mendez Vives The London School of Economics Thesis submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy at the University of London UMI Number: U615604 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI U615604 Published by ProQuest LLC 2014. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 Th eses F Z)Zb I01&732 1 Abstract This Thesis contains an examination of the time-series properties of swap spreads, their relation with credit spreads and an estimation of the risk premium embedded in the swap spread curve. Chapter 2 introduces the main institutional aspects of swap markets, and studies the time-series properties of swap spreads. These are shown to be non-stationary and display a time-varying conditional volatility. Chapter 3 provides evidence of cointegration between corporate bond spreads and swap spreads. We es­ timate an error-correction model, including additional variables such as the level and slope of the yield curve, taking into account the exogenous structural break due to the crisis of August 1998. We find evidence that the relation between swap and credit spreads arises from the swap cash flows being indexed to Libor rates. Chapter 4 stud­ ies the risk premium in the term structure of the swap spreads, obtaining evidence that it is time-varying. The slope of the swap spread curve is shown to predict the changes in swap spreads. These results are relevant for the study of the risk premium in credit markets, and extend the existing literature on riskless Treasury securities. Chapter 6 develops the asymptotic properties of the quadratic variation estimator of the volatility of a continuous time diffusion process. We explore the case in which the number of observations tends to infinity, while the time between them remains fixed. For the case of a geometric Brownian motion, we show that the estimator is asymptotically biased, but the bias is a random variable that converges. We study the behaviour of this ran­ dom variable via a simulation study, that shows that it typically has a “small” effect. We conclude by exploring some practical applications related the specification of the volatility for financial time series. 2 Acknowledgements I would like to express my gratitude to Jos6 Marin and Arturo Kohatsu (Universitat Pompeu Fabra), and Vasant Naik (Lehman Brothers). The guidance and help from Richard Payne (LSE), my Thesis advisor, are highly ap­ preciated. This Thesis would not have been possible without the support from the Economics De­ partment and the Centre de Recerca en Economia Financera of the Universitat Pompeu Fabra (Andreu Mas-Colell, Antoni Bosch, Xavier Freixas), the Bank of Spain, and the Financial Markets Group of the London School of Economics (David Webb). Also, I thank Lehman Brothers (Jamil Baz and Robert Campbell) for the use of substantial computer and data resources. Finally, I thank my family, for everything. Contents 1 Introduction 10 2 Time-Series Properties 18 2.1 Introduction to Swap Markets ............................................................. 18 2.1.1 The evolution of swap markets .................................................. 20 2.1.2 Trading swap spreads ................................................................. 21 2.1.3 The dynamics of swap spreads .................................................. 23 2.1.4 The effects of the financial crisis of August 1998 .................... 25 2.2 The Time Series Properties of Swap Spreads ........................................ 27 2.2.1 Persistence and stationarity........................................................ 28 2.2.2 Properties of the swap spreads in first differences .................... 31 2.2.3 Modelling the conditional volatility of swap sp re a d s 33 2.3 Conclusions ........................................................................................... 36 Tables and Figures ....................................................................................... 37 3 Swap and Credit Spreads 67 3.1 Introduction .......................................................................................... 67 3.2 The Dynamics of the US Credit M arkets .............................................. 69 3.2.1 The evolution of the spreads .................................................... 70 3.2.2 Statistics of the spread c u rv e s ................................................. 70 3.2.3 Properties of Libor spreads ....................................................... 71 3.3 Economics of the Relation Between Swap and Credit Markets .... 72 3.3.1 Swaps and credit ris k ................................................................. 72 3.3.2 Some empirical implications .................................................... 75 3.4 A Multivariate Analysis of Swap and Credit S p re ad s......................... 76 3 4 3.4.1 Economic drivers of swap spreads............................................ 76 3.4.2 Previous literatu re .................................................................. 77 3.4.3 An Error Correction model for swap s p re a d s ........................ 79 3.5 Conclusions.......................................................................................... 82 Tables and Figures ....................................................................................... 85 4 Term Structure of Swap Spreads 110 4.1 Introduction ......................................................................................... 110 4.2 The Risk Premium in Swap Spreads .................................................... 113 4.3 Estimation and Empirical Results ......................................................... 115 4.3.1 Description of the d a ta .............................................................. 115 4.3.2 Properties of the slope of the swap spread curve ....................... 116 4.3.3 Results of the predictive regression ......................................... 116 4.3.4 Further evidence on the predictability of swap spreads .... 118 4.4 Some Results on Trading Swap Spreads .............................................. 119 4.5 Conclusions and Further R esearch ....................................................... 121 Tables and Figures ....................................................................................... 121 5 Asymptotics of the QV Estimator 148 5.1 Introduction ......................................................................................... 148 5.2 The Basic Setup .................................................................................... 152 5.2.1 The QV estimator for a geometric Brownian m o tio n 152 5.2.2 The concept of quadratic variation ........................................... 153 5.2.3 Decomposing the quadratic variation estim ator ....................... 155 5.3 Asymptotics when n —► o o .................................................................. 156 5.3.1 The Main Theorem ................................................................... 156 5.3.2 Outline of the P r o o f ................................................................ 157 5.4 Simulation S tu d y ................................................................................ 158 5.5 A Simple Application .......................................................................... 160 5.6 Conclusions and Further R esearch ..................................................... 163 Tables and Figures ....................................................................................... 163 6 Conclusion 192 List of Tables 2.1 Statistics of USD and EUR swap spreads ............................................. 38 2.2 Statistics of USD swap spreads by subsamples .................................... 39 2.3 Statistics of EUR swap spreads by subsamples.................................... 40 2.4 Statistics of 10-year USD and EUR swap spreads .............................. 41 2.5 Autocorrelation function for 10-year USD swap spreads .................... 42 2.6 Autocorrelation function for 10-year EUR swap spreads .................... 43 2.7 Augmented Dickey-Fuller tests for 10-year USD and EUR swap spreads 44 2.8 Perron test for USD and EUR 10-year swap spreads ........................... 45 2.9 Statistics of daily changes in 10-year EUR and USD swap spreads . 46 2.10 Autocorrelation function for daily changes in 10-year USD swap spreads 47 2.11 Autocorrelation function for daily changes in 10-year EUR swap spreads 48 2.12 Augmented Dickey-Fuller tests for daily changes in USD and EUR 10- year fitted swap spreads ........................................................................ 49 2.13 Autocorrelation function for the residuals of an AR( 1) for daily changes in 10-year USD swap spreads ............................................................... 50 2.14 Autocorrelation function for the residuals of an AR(1) for daily changes in 10-year EUR swap spreads ..............................................................
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