school of HEC at University of Lausanne
Institute of Banking and Finance
Master of Science in Banking and Finance
Master Thesis
Capital Structure Arbitrage Strategies:
Models, Practice and Empirical Evidence
Oliver Berndt and Bruno Stephan Veras de Melo
November 2003, Lausanne, Switzerland
Supervised by
Professor Salih Neftci, CUNY, New York and School of HEC at University of Lausanne
Co-supervised by
Dr. Norbert Dörr, Credit Risk Management, Deutsche Bank AG, London
and
Dr. Wilhelm Trinder, Financial Risk Management, KPMG, Frankfurt/Main

Contents
Abstract vi
Introduction vii
Notation xvi
I DescriptivePart 1
1 Theoretical and Practical Background 2
1.1 Bond PricingModels based on Equity Price Behavior . . . . . . . . . . . . . . 2
1.1.1 Structural Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 Reduced-formModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2 Convertible Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.2.1 Brief Survey on PricingModels . . . . . . . . . . . . . . . . . . . . . . 28
1.2.2 Risks and theGreeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.2.3 Arbitrage Technique - DeltaHedging . . . . . . . . . . . . . . . . . . . 31
1.2.4 Portfolio RiskManagement . . . . . . . . . . . . . . . . . . . . . . . . 36
1.3 Credit Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.3.1 Basics about CreditDerivatives . . . . . . . . . . . . . . . . . . . . . . 38
1.3.2 Terminologies and Definitions . . . . . . . . . . . . . . . . . . . . . . . 39
1.3.3 CreditDerivative Types . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.3.4 CreditDerivative Structures andApplications . . . . . . . . . . . . . . 45
1.3.5 TheMarket and the Use of CreditDerivatives . . . . . . . . . . . . . . 50
1.3.6 CreditDerivatives can complete FinancialMarket Information . . . . . 55
1.3.7 CreditDefault Swap Basics . . . . . . . . . . . . . . . . . . . . . . . . 55
1.3.8 CreditDefault SwapValuation . . . . . . . . . . . . . . . . . . . . . . 62
1.3.9 CreditDefault Swap Summary . . . . . . . . . . . . . . . . . . . . . . 103
i
CONTENTS ii
2 Capital Structure Arbitrage and Hedging 105
2.1 Main Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.1.1 Equity andDebtMarket . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.1.2 Equity and CreditMarket . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.1.3 Credit andDebtMarkets . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.2 TheMarket for Capital Structure Arbitrage andHedging Strategies . . . . . . 122
2.2.1 The Participants of the Capital Structure Arbitrage Strategies Market . 123
2.2.2 The Rule of Banks and Hedge Funds in Capital Structure Arbitrage and
Hedging Strategiesmarket . . . . . . . . . . . . . . . . . . . . . . . . . 125
2.2.3 The Consequences to the Financial Market from Capital Structure Arbitrage
Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
II Empirical Analysis 132
3 Cointegration Analysis 133
3.1 The Rationale of empirical Capital StructureArbitrageAnalysis . . . . . . . . 133
3.1.1 Relationship between the Credit Spread and the Volatility Skew implied
by theMertonModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
3.2 Cointegration Econometrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
3.2.1 Stationary and Nonstationary Stochastic Process . . . . . . . . . . . . 142
3.2.2 Vector AutoregressiveModels . . . . . . . . . . . . . . . . . . . . . . . 146
3.2.3 Cointegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.3 Descriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
3.4 Cointegration Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
3.4.1 Description of the Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 155
3.4.2 Empirical Relationship between CDS Rates and the Volatility Skew . . 157
3.4.3 Empirical Relationship between CDS and Equity Prices . . . . . . . . . 170
4 Conclusion 178
A Detailed Proofs 182
A.1 Notations: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
A.2 Proof of formula (9) inHull et al. (2003a) . . . . . . . . . . . . . . . . . . . . 183
A.3 Proof of formula (8) inHull et al. (2003a) . . . . . . . . . . . . . . . . . . . . 188
A.4 The credit spread of a risky bond implied by theMertonmodel . . . . . . . . 189
A.5 Aformula for the implied put option volatilities . . . . . . . . . . . . . . . . . 190
CONTENTS iii
B VAR and VECM representations of section 3.4.2 192
C VAR and VECM representations of section 3.4.2 195
C.1 Unit Roots Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
C.2 Granger Causality Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
C.3 VAR Especification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
C.4 Innovation Accounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
C.5 Cointegration Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
C.6 VARand VECMrepresentations . . . . . . . . . . . . . . . . . . . . . . . . . 201
D VAR and VECM representations of section 3.4.3 204
Bibliography 207