IMPERIAL COLLEGE LONDON Counterparty Credit Risk, Funding Risk and Central Clearing Stephen Yang Zhang Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Finance for Imperial College London and the Diploma of Imperial College London Counterparty Credit Risk, Funding Risk and Central Clearing To Kate, Mum and Dad, for your support and encouragement throughout my life. To Alicia, who continually makes me proud to be a father. * I hereby certify that this thesis constitutes my own work and that all material, which is not my own work, has been properly acknowledged. * The copyright of this thesis rests with the author and is made available under a Creative Commons Attribution Non- Commercial No Derivatives licence. Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work. Page 1 Counterparty Credit Risk, Funding Risk and Central Clearing Contents Acknowledgement 3 List of Tables 4 List of Figures 6 1. Introduction 8 2. Counterparty Credit Risk and CVA/DVA 16 2.1 Introduction 16 2.2 General Pricing Formula of Unilateral CVA 24 2.3 No Arbitrage Pricing in Real Market 26 2.4 No Arbitrage Pricing across Different Asset Classes 39 2.5 No Arbitrage Pricing for Unilateral CVA 65 2.6 Bilateral CVA without First to Default Features 72 2.7 Approximations for CVA/DVA 76 2.8 General Pricing Formula ofof Bilateral CVA 80 2.9 CVA/DVA Pricing 83 3. Funding Risk and FVA 113 3.1 Background: Widening LIBOR-OIS Spread 113 3.2 FVA Pricing without Counterparty Credit Risk 116 3.3 Economic Drivers of FVA 124 3.4 FVA Pricing with Counterparty Credit Risk 135 3.5 CVA, DVA and FVA at Trade Level 145 3.6 CVA, DVA and FVA at Portfolio Level 152 3.7 xVA Accounting 159 3.8 FCA/FBA Accounting (FTP=ΔCA-ΔCL) 161 3.9 FVA/FDA Accounting (FTP=ΔCA) 164 3.10 DVA Hedging 168 4. Central Clearing and Initial Margins 189 4.1 Introduction to Central Clearing 189 4.2 A Brief Review of Clearing Mechanisms of Exchanges 191 4.3 Clearing for OTC Derivatives 193 4.4 Advantages and Disadvantages of Central Clearing 199 4.5 Regulatory Arbitrages Created by Central Clearing 206 4.6 xVA and Central Clearing 209 4.7 Risk Conversion by Margin Requirements 213 4.8 CVA, DVA, FVA and MVA Pricing 224 5. Conclusion 237 Appendix 238 Reference 253 Page 2 Counterparty Credit Risk, Funding Risk and Central Clearing Acknowledgement I would like to thank my supervisor, Prof. Enrico Biffis, for his support, encouragement and patience over my 4 years PhD studies at Imperial College. And I am grateful for many helpful discussions with Prof. Damiano Brigo, Dr. Laura Ballotta, Mr. Jonathan Durden, Mr. Tianyu Wang, Dr. Nicholas Burgess, and Dr. Warwick Palmer. Page 3 Counterparty Credit Risk, Funding Risk and Central Clearing List of Tables Table 2.1: Asymmetric Treatments of the Surviving Party in the Default State of Its Counterparty 67 Table 2.2: Term Structure of Derivative Dealer’s CDS Curve 83 Table 2.3: CVA and DVA for Uncollateralised 10 Years Spot Starting IRS Fixed Payer 86 Table 2.4: CVA and DVA for Uncollateralised 10 Years Spot Starting IRS Fixed Receiver 86 Table 2.5: CVA and DVA for Uncollateralised 5x15 Forward Starting IRS Fixed Payer 88 Table 2.6: CVA and DVA for Uncollateralised 5x15 Forward Starting IRS Fixed Receiver 88 Table 2.7: CVA and DVA for Collateralised 5x15 Forward Starting IRS Fixed Payer 90 Table 2.8: CVA and DVA for Collateralised 5x15 Forward Starting IRS Fixed Receiver 90 Table 2.9: CVA and DVA for Uncollateralised 5 into 10 Cash Settled European Payer Swaption 92 Table 2.10: CVA and DVA for Uncollateralised 5 into 10 Cash Settled European Receiver Swaption 92 Table 2.11: CVA and DVA for Uncollateralised 5 into 10 Physically Settled European Payer Swaption 94 Table 2.12: CVA and DVA for Uncollateralised 5 into 10 Physically Settled European Receiver Swaption 94 Table 2.13: CVA and DVA for Uncollateralised 5 into 10 Physically Settled Bermudan Payer Swaption 96 Table 2.14: CVA and DVA for Uncollateralised 5 into 10 Physically Settled Bermudan Receiver Swaption 96 Table 2.15: CVA and DVA for Collateralised 5 into 10 Physically Settled European Payer Swaption 99 Table 2.16: CVA and DVA for Collateralised 5 into 10 Physically Settled European Receiver Swaption 99 Table 2.17: CVA and DVA for Collateralised 5 into 10 Physically Settled Bermudan Payer Swaption 99 Table 2.18: CVA and DVA for Collateralised 5 into 10 Physically Settled Bermudan Payer Swaption 99 Table 2.19: CVA and DVA for Uncollateralised 15 Years FX (EURUSD) Forward Long EUR at Maturity 101 Table 2.20: CVA and DVA for Uncollateralised 15 Years FX (EURUSD) Forward Short EUR at Maturity 101 Table 2.21: CVA and DVA for Uncollateralised 15 Years FX (EURUSD) Swap Long EUR at Maturity 103 Table 2.22: CVA and DVA for Uncollateralised 15 Years FX (EURUSD) Swap Short EUR at Maturity 103 Table 2.23: CVA and DVA for Collateralised 15 Years FX (EURUSD) Forward Long EUR at Maturity 106 Table 2.24: CVA and DVA for Collateralised 15 Years FX (EURUSD) Forward Short EUR at Maturity 106 Table 2.25: CVA and DVA for Collateralised 15 Years FX (EURUSD) Swap Long EUR at Maturity 107 Table 2.26: CVA and DVA for Collateralised 15 Years FX (EURUSD) Swap Short EUR at Maturity 107 Table 2.27: CVA and DVA for Uncollateralised 15 Years EURUSD CCS Long EUR at Maturity 109 Table 2.28: CVA and DVA for Uncollateralised 15 Years EURUSD CCS Short EUR at Maturity 109 Table 2.29: CVA and DVA for Collateralised 15 Years EURUSD CCS Long EUR at Maturity 110 Table 2.30: CVA and DVA for Collateralised 15 Years EURUSD CCS Short EUR at Maturity 110 Table 2.31: Counterparty Credit Risk Reduction by Variation Margin for IRDs 111 Table 2.32: Counterparty Credit Risk Reduction by Variation Margin for FXDs 112 Table 3.1: Explanatory Power of Principal Components of GS, MS and JPM 175 Table 3.2: Summary of R^2 of CDS as Explanatory Variable for GS, MS and JPM 180 Table 3.3: Summary of R^2 of 1 Lag in CDS as Explanatory Variable for GS, MS and JPM 182 Table 3.4: Summary of R^2 of 1st Order Changes in CDS as Explanatory Variable for GS, MS and JPM 184 Table 3.5: Summary of R^2 of three different explanatory variables as Explanatory Variable for GS, MS and JPM 184 Table 3.6: Summary of R^2 of 1st Order Changes in CDS as Explanatory Variable for DVAs GS, MS and JPM 186 Table 3.7: DVA Book Sensitivity to CDS changes for GS, MS and JPM 187 Table 3.8: DVA Hedging Equity Portfolio Holdings 188 Table 3.9: Risk/Return Profile of DVA Hedging Equity Portfolio 188 Table 4.1: BCBS-ISOCO (2013) Standardised Initial Margin Schedule 222 Page 4 Counterparty Credit Risk, Funding Risk and Central Clearing Table 4.2: the Term Structure of Derivative Dealer’s Funding Spread 224 Table 4.3: xVA for 5x15 Froward Starting Fixed Payer under Different Margin Requirements 226 Table 4.4: xVA for 5x15 Froward Starting Fixed Receiver under Different Margin Requirements 227 Table 4.5: xVA for 5 into 10 European Payer Swaption under Different Margin Requirements 228 Table 4.6: xVA for 5 into 10 European Receiver Swaption under Different Margin Requirements 229 Table 4.7: xVA for 5 into 10 Bermudan Payer Swaption under Different Margin Requirements 230 Table 4.8: xVA for 5 into 10 Bermudan Receiver Swaption under Different Margin Requirements 231 Table 4.9: xVA for 15 Years EURUSD Cross Currency Swap Long EUR at Maturity under Different Margin Requirements 231 Table 4.10: xVA for 15 Years EURUSD Cross Currency Swap Short EUR at Maturity under Different Margin Requirements 233 Page 5 Counterparty Credit Risk, Funding Risk and Central Clearing List of Figures Figure 2.1: Uncollateralised 10 Years Spot Starting IRS Fixed Payer Exposure Profile 85 Figure 2.2: Uncollateralised 10 Years Spot Starting IRS Fixed Receiver Exposure Profile 85 Figure 2.3: Uncollateralised 5x15 Forward Starting IRS Fixed Payer Exposure Profile 87 Figure 2.4: Uncollateralised 5x15 Forward Starting IRS Fixed Receiver Exposure Profile 87 Figure 2.5: Collateralised 5x15 Forward Starting IRS Fixed Payer Exposure Profile 89 Figure 2.6: Collateralised 5x15 Forward Starting IRS Fixed Receiver Exposure Profile 89 Figure 2.7: Uncollateralised 5 into 10 Cash Settled European Payer Swaption Exposure Profile 91 Figure 2.8: Uncollateralised 5 into 10 Cash Settled European Receiver Swaption Exposure Profile 91 Figure 2.9: Uncollateralised 5 into 10 Physically Settled European Payer Swaption Exposure Profile 93 Figure 2.10: Uncollateralised 5 into 10 Physically Settled European Receiver Swaption Exposure Profile 93 Figure 2.11: Uncollateralised 5 into 10 Physically Settled Bermudan Payer Swaption Exposure Profile 95 Figure 2.12: Uncollateralised 5 into 10 Physically Settled Bermudan Receiver Swaption Exposure Profile 95 Figure 2.13: Collateralised 5 into 10 Physically Settled European Payer Swaption Exposure Profile 97 Figure 2.14: Collateralised 5 into 10 Physically Settled European Receiver Swaption Exposure Profile 97 Figure 2.15: Collateralised 5 into 10 Physically Settled Bermudan Payer Swaption Exposure Profile 98 Figure 2.16: Collateralised 5 into 10 Physically Settled Bermudan Payer Swaption Exposure Profile 98 Figure 2.17: Uncollateralised 15 Years FX (EURUSD) Forward Long EUR at Maturity Exposure Profile 100 Figure 2.18: Uncollateralised 15 Years FX (EURUSD) Forward Short EUR at Maturity Exposure Profile 101 Figure 2.19: Uncollateralised