# Measuring and Managing Liquidity Risk

# Measuring and Managing Liquidity Risk

ISBN: 978-1-119-99066-6 September 2013 600 Pages

**E-Book**

$66.99

## Description

**A fully up-to-date, cutting-edge guide to the measurement and management of liquidity risk**

Written for front and middle office risk management and quantitative practitioners, this book provides the ground-level knowledge, tools, and techniques for effective liquidity risk management. Highly practical, though thoroughly grounded in theory, the book begins with the basics of liquidity risks and, using examples pulled from the recent financial crisis, how they manifest themselves in financial institutions. The book then goes on to look at tools which can be used to measure liquidity risk, discussing risk monitoring and the different models used, notably financial variables models, credit variables models, and behavioural variables models, and then at managing these risks. As well as looking at the tools necessary for effective measurement and management, the book also looks at and discusses current regulation and the implication of new Basel regulations on management procedures and tools.

About the authors xvii

Abbreviations and acronyms xix

**PART I LIQUIDITY AND BANKING ACTIVITY 1**

**1 Banks as lemons? 3**

1.1 Introduction 3

1.2 The first wave 4

1.3 Banks as lemons? 7

1.4 The response 9

1.5 The second wave 13

1.6 Conclusion 15

**2 A journey into liquidity 17**

2.1 Introduction 17

2.2 Central bank liquidity 18

2.3 Funding liquidity 19

2.4 Market liquidity 22

2.5 The virtuous circle 24

2.6 The vicious circle 24

2.8 The role of the central bank, supervision and regulation 28

2.9 Conclusions 31

**3 Too big to fail 33**

3.1 Introduction 33

3.2 When giants fall 34

3.3 A hard lesson 36

3.4 Closer supervision 37

3.5 G-SIFI regulations 39

3.6 The next steps 41

3.7 Conclusion 44

**4 The new framework 47**

4.1 Introduction 47

4.2 Some basic liquidity risk measures 48

4.3 The first mover 50

4.4 Basel III: The new framework for liquidity risk measurement and monitoring 53

4.4.1 The liquidity coverage ratio 55

4.5 Inside the liquidity coverage ratio 63

4.6 The other metrics 66

4.7 Intraday liquidity risk 69

4.8 Beyond the ratios 72

4.9 Conclusion 74

**5 Know thyself! 75**

5.1 Introduction 75

5.2 Some changes on the liabilities side 75

5.3 The role of leverage 79

5.4 The originate-to-distribute business model 82

5.5 The liquidity framework 84

5.6 Stress-testing and contingency funding plan 89

5.7 The CEBS identity card 95

5.8 Conclusions 97

5.9 Appendix: The CEBS Identity Card Annex (CEBS) 98

**PART II TOOLS TO MANAGE LIQUIDITY RISK 109**

**6 Monitoring liquidity 111**

6.1 A taxonomy of cash flows 111

6.2 Liquidity options 114

6.3 Liquidity risk 115

6.4 Quantitative liquidity risk measures 118

6.4.1 The term structure of expected cash flows and the term structure of expected cumulated cash flows 119

6.4.2 Liquidity generation capacity 123

6.4.3 The term structure of available assets 127

6.5 The term structure of expected liquidity 134

6.6 Cash flows at risk and the term structure of liquidity at risk 135

**7 Liquidity buffer and term structure of funding 143**

7.1 Introduction 143

7.2 Liquidity buffer and counterbalancing capacity 143

7.3 The first cause of the need for a liquidity buffer: Maturity mismatch 145

7.3.1 Some or all stressed scenarios do not occur 149

7.3.2 The cost of the liquidity buffer for maturity mismatch 152

7.3.3 Liquidity buffer costs when stressed scenarios do not occur 158

7.3.4 A more general formula for liquidity buffer costs 163

7.4 Funding assets with several liabilities 168

7.5 Actual scenarios severer than predicted 169

7.6 The term structure of available funding and the liquidity buffer 171

7.6.1 The term structure of forward cumulated funding and how to use it 175

7.7 Non-maturing liabilities 179

7.7.1 Pricing of NML and cost of the liquidity buffer 182

7.8 The second cause of the liquidity buffer: Collateral margining 186

7.8.1 A method to set the liquidity buffer for derivative collateral 186

7.8.2 The cost of the liquidity buffer for derivative collateral 188

7.9 The third cause of the liquidity buffer: Off-balance-sheet commitments 192

7.10 Basel III regulation and liquidity buffer 194

**8 Models for market risk factors 199**

8.1 Introduction 199

8.2 Stock prices and FX rates 199

8.3 Interest rate models 201

8.3.1 One-factor models for the zero rate 201

8.3.2 Vasicek model 202

8.3.3 The CIR model 202

8.3.4 The CIRþþ model 209

8.3.5 The basic affine jump diffusion model 211

8.3.6 Numerical implementations 212

8.3.7 Discrete version of the CIR model 212

8.3.8 Monte Carlo methods 214

8.3.9 Libor market model 215

8.4 Default probabilities and credit spreads 219

8.4.1 Structural models 219

8.4.2 Reduced models 221

8.4.3 Credit spreads 223

8.5 Expected and minimum liquidity generation capacity of available bonds 224

8.5.1 Value of the position in a defaultable coupon bond 225

8.5.2 Expected value of the position in a coupon bond 226

8.5.3 Haircut modelling 227

8.5.4 Future value of a bond portfolio 228

8.5.5 Calculating the quantile: a (Delta - Tua) approximation of the portfolio 228

8.5.6 Estimation of the CIR++ model for interest rates 231

8.5.7 Estimation of the CIR++ model for default intensities 233

8.5.8 Future liquidity from a single bond 239

8.5.9 Future liquidity from more bonds 240

8.6 Fair haircut for repo transactions and collateralized loans 247

8.7 Adjustments to the value of illiquid bonds 256

8.7.1 Liquid equivalent adjustment 258

8.7.2 Price volatility adjustment 261

8.A Expectation value of the bond with selling probability and spread 270

**9 Behavioural models 277**

9.1 Introduction 277

9.2 Prepayment modelling 277

9.2.1 Common approaches to modelling prepayments 277

9.2.2 Hedging with an empirical model 278

9.2.3 Effective hedging strategies of prepayment risk 285

9.2.4 Conclusions on prepayment models 288

9.2.5 Modelling prepayment decisions 288

9.2.6 Modelling the losses upon prepayment 290

9.2.7 Analytical approximation for ELoP1 296

9.2.8 Valuing the ELoP using a VaR approach 299

9.2.9 Extension to double rational prepayment 303

9.2.10 Total prepayment cost 305

9.2.11 Expected cash flows 306

9.2.12 Mortgage pricing including prepayment costs 308

9.3 Sight deposit and non-maturing liability modelling 316

9.3.1 Modelling approaches 317

9.3.2 The stochastic factor approach 319

9.3.3 Economic evaluation and risk management of deposits 324

9.3.4 Inclusion of bank runs 334

9.4 Credit line modelling 337

9.4.1 Measures to monitor usage of credit lines 339

9.4.2 Modelling withdrawal intensity 340

9.4.3 Liquidity management of credit lines 341

9.4.4 Pricing of credit lines 360

9.4.5 Commitment fee 362

9.4.6 Adding the probability of default 364

9.4.7 Spread option 365

9.4.8 Incremental pricing 368

**PART III PRICING LIQUIDITY RISK 383**

**10 The links between credit risk and funding cost 385**

10.1 Introduction 385

10.2 The axiom 385

10.3 Cash flow fair values and discounting 386

10.4 Critique of debit value adjustment 389

10.4.1 Single-period case 389

10.4.2 Multi-period case 391

10.4.3 DVA as a funding benefit 394

10.5 DVA for derivative contracts 397

10.6 Extension to positive recovery and liquidity risk 402

10.7 Dynamic replication of DVA 404

10.7.1 The gain process 404

10.7.2 Dynamic replication of a defaultable claim 405

10.7.3 Objections to the statement ""no long position in a bank's own bonds is possible"" 409

10.7.4 DVA replication by the funding benefit 410

10.7.5 DVA replication and bank’s franchise 415

10.8 Recapitulation of results 419

10.9 Accounting standard and DVA 419

10.10 Distinction between price and value 421

**11 Cost of liquidity and fund transfer pricing 425**

11.1 Introduction 425

11.2 Principles of transfer pricing 425

11.2.1 Balance sheet 425

11.2.2 Bank’s profits and losses 426

11.3 Funding and banking activity 431

11.4 Building a funding curve 432

11.5 Including the funding cost in loan pricing 446

11.5.1 Pricing of a fixed rate bullet loan 450

11.6 Monitoring funding costs and risk control of refunding risk 452

11.7 Funding costs and asset/liability management 456

11.8 Internal fund transfer pricing system 457

11.8.1 Multiple curves 459

11.8.2 Single curve 461

11.8.3 Implementation of funding policies 465

11.9 Best practices and regulation 468

**12 Liquidity risk and the cost of funding in derivative contracts 473**

12.1 Pricing of derivative contracts under collateral agreements 473

12.1.1 Pricing in a simple discrete setting 475

12.1.2 The replicating portfolio in continuous time 480

12.1.3 Pricing with a funding rate different from the investment rate 483

12.1.4 Funding rate different from investment rate and repo rate 489

12.1.5 Interest rate derivatives 491

12.2 Pricing of collateralized derivative contracts when more than one currency is involved 499

12.2.1 Contracts collateralized in a currency other than the payoff currency 499

12.2.2 FX derivatives 505

12.2.3 Interest rate derivatives 511

12.2.4 Cross-currency swaps 514

12.3 Valuation of non-collateralized interest rate swaps including funding costs 518

12.3.1 The basic setup 518

12.3.2 Hedging swap exposures and cash flows 519

12.3.3 Funding spread modelling 521

12.3.4 Strategy 1: Funding all cash flows at inception 522

12.3.5 Strategy 2: Funding negative cash flows when they occur 524

12.3.6 Including counterparty credit risk 528

12.3.7 Practical examples 531

**13 A sort of conclusion: towards a new treasury? 539**

13.1 Introduction 539

13.2 Organization of the treasury and the dealing room 539

13.3 Banking vs trading book 542

13.3.1 Collateralization 542

13.3.2 Links amongst risks 543

13.3.3 Production costs 545

References 547

Index 553