Pricing and Hedging Interest and Credit Risk Sensitive Instruments (eBook)

Cover 1
Contents 5
1 AN INTRODUCTION TO INTEREST AND CREDIT RISKY INSTRUMENTS AND THEIR MARKETS 13
1.1 Bond conventions 13
1.1.1 Interest and credit risk 16
1.2 Bond markets 17
1.3 Trends in the global capital markets 20
1.4 Corporate bonds 21
1.4.1 Default risk 21
1.4.2 Bond covenants 24
1.4.3 Adverse selection 26
1.5 Scope of this book 27
1.6 Exercises 29
2 THE SOVEREIGN TERM STRUCTURE AND THE RISK STRUCTURE OF INTEREST RATES 30
2.1 Objectives pricing and hedging 30
2.1.1 Imperfections in perfect hedge ratios 32
2.2 Introduction to the term and risk structure of interest rates 33
2.3 The uses of the term structure and risk structure of interest rates 34
2.3.1 Which yield curve? 36
2.4 Theories of the sovereign term structure of interest rates 37
2.4.1 The expectations hypothesis 38
2.4.2 The liquidity and preferred habitat hypotheses 41
2.4.3 The Fisher effect 43
2.4.4 Cox Ingersoll and Ross (1981) 44
2.4.5 Information in the sovereign term structure of interest rates 45
2.5 Theory of the risk structure of interest rates 46
2.5.1 The relationship between changes in the sovereign term structure and the credit spread 48
2.6 How sovereign bonds are issued 48
2.6.1 American auction 49
2.6.2 Dutch auction 50
2.6.3 Variations 51
2.7 Repos 53
2.8 Summary 54
2.9 Exercises 55
3 MEASURING THE EXISTING SOVEREIGN TERM STRUCTURE AND THE RISK STRUCTURE OF INTEREST RATES 58
3.1 Measuring the sovereign term structure of interest rates 58
3.2 Frequently traded bonds 59
3.2.1 Other data problems 62
3.2.2 Estimating corporate yield curves 63
3.3 Zero coupon yields 64
3.3.1 Zero coupon yields and coupon bias 65
3.3.2 Bootstrapping 67
3.3.3 STRIPS are not the answer 71
3.4 Measuring continuous yield curves 72
3.4.1 Natural splines 72
3.4.2 The problem with splines 76
3.4.3 Parsimonious yield curve estimates 78
3.4.4 Which yield curve fitting technique is best? 82
3.5 Par coupon yield curves 82
3.6 Summary 83
3.7 Exercises 84
4 MODELLING THE SOVEREIGN TERM STRUCTURE OF INTEREST RATES: THE BINOMIAL APPROACH 86
4.1 The binomial approach 86
4.2 The simple model 87
4.3 Which short rate of interest should we model? 90
4.4 Pricing a bond using the interest rate tree 91
4.5 The problems with the simple model 95
4.6 Incorporating risk aversion 97
4.7 Exercises 102
5 INTEREST RATE MODELLING: THE TERM STRUCTURE CONSISTENT APPROACH 104
5.1 Desirable features of an interest rate model 104
5.2 Ho and Lee (1986) 105
5.2.1 State prices 106
5.2.2 Calibration 112
5.2.3 Implementing Ho and Lee 114
5.2.4 Using the calibrated interest rate tree 117
5.3 Black Derman and Toy: constant volatility 118
5.4 Black Derman and Toy (1990) 122
5.4.1 Implementing BDT 124
5.5 Some other one factor term structure consistent models 131
5.6 Summary 132
5.7 Exercises 132
6 INTEREST AND CREDIT RISK MODELLING 134
6.1 Evolutionary interest rate models 134
6.2 Vasicek (1977) 135
6.2.1 Implementing Vasicek 137
6.3 Cox Ingersoll and Ross (1985) 138
6.3.1 Implementing CIR 140
6.4 Other evolutionary models 140
6.5 Comparing the term structure consistent and evolutionary models 141
6.5.1 The seriousness of these problems from the practitioner’s perspective 143
6.6 The problem with interest rate (and credit risk) modelling 145
6.6.1 So which model is best? 147
6.7 Non-stochastic credit risk models 147
6.7.1 Bierman and Hass (1975) 148
6.7.2 Jonkhart (1979) 150
6.8 Jarrow and Turnbull (1995) 153
6.8.1 Implementing JT 155
6.8.2 Using the calibrated JT model 159
6.9 Duffie and Singleton (1999) 161
6.9.1 An example of Duffie and Singleton (1999) 162
6.9.2 Using the calibrated DS model 165
6.10 Other credit risk modelling approaches 166
6.11 Summary 169
6.12 Exercises 169
7 HEDGING SOVEREIGN BONDS: THE TRADITIONAL APPROACH 171
7.1 Introduction 171
7.2 Macaulay duration 171
7.3 Modified duration 175
7.4 Other measures of interest rate sensitivity 178
7.5 Convexity 179
7.5.1 Properties of convexity 179
7.6 Hedging 181
7.7 Regression-based hedge ratios 182
7.7.1 An example of regression-based hedging 184
7.7.2 Comments on the regression-based hedge ratio 186
7.8 Duration-based hedge ratio 186
7.8.1 Delivery squeezes and the need for bond futures contracts 188
7.8.2 An example of duration-based hedging 191
7.9 Basis risk 195
7.10 Appendix 198
7.10.1 Derivation of the regression-based hedge ratio 198
7.10.2 The (modified) duration hedge ratio 201
7.11 Exercises 202
8 ACTIVE AND PASSIVE STRATEGIES 206
8.1 Introduction 206
8.2 Adjusting the duration of a portfolio 206
8.3 Active and passive strategies 209
8.4 Implementing a rate anticipation swap 211
8.5 Implementing an asset substitution swap 213
8.5.1 Butterfly/barbell swaps 215
8.5.2 Butterfly/barbell arbitrage 216
8.6 Portfolio immunization 219
8.7 Balance sheet immunization 226
8.7.1 The duration gap model 228
8.7.2 How can we eliminate the duration gap? 230
8.8 Bond portfolio management 232
8.9 Exercises 236
9 ALTERNATIVE HEDGE RATIOS 239
9.1 Improvements in modified duration hedge ratios 239
9.2 Fisher Weil (1971) 240
9.2.1 Examples of Fisher Weil duration 242
9.3 Key rate duration 244
9.3.1 Example of key rate duration 245
9.3.2 Measuring the volatility of a portfolio 247
9.4 Duration for corporate bonds 249
9.4.1 Credit risk adjusted duration 250
9.5 Delta hedging 254
9.5.1 PVBP delta hedge 254
9.5.2 Binomial delta hedging 255
9.6 Exercises 256
10 PRICING AND HEDGING NON-FIXED INCOME SECURITIES 258
10.1 Introduction 258
10.2 Floaters 258
10.3 Inverse floaters 263
10.3.1 Pricing inverse floaters via value additivity 264
10.3.2 Duration of an inverse floater 267
10.4 Caps, floors and collars 270
10.4.1 Cap example 272
10.4.2 Floor example 275
10.4.3 Collar example 277
10.5 Interest rate swaps 278
10.5.1 Valuation of swaps 279
10.5.2 Hedging a long swap 282
10.6 Exercises 283
11 CREDIT DERIVATIVES 286
11.1 Introduction 286
11.2 Types of credit derivatives 287
11.2.1 Single name credit derivatives 287
11.2.2 Multi-name credit derivatives 288
11.3 Vulnerable derivatives 289
11.4 Credit default swaps 292
11.4.1 An example of a credit default swap 295
11.5 Issues in default swap pricing 298
11.5.1 Theory: floating rate reference bond 299
11.5.2 Theory: fixed rate reference bond 300
11.5.3 Market imperfections: liquidity 302
11.5.4 Market imperfections: moral hazard 303
11.5.5 Conclusions 304
11.6 Exercises 305
12 EMBEDDED OPTIONS 308
12.2 An introduction to callable/putable bonds 309
12.2.1 Valuing callable bonds 311
12.2.2 An example of valuing a callable bond 312
12.2.3 Valuing putable bonds 317
12.3 Measures of interest rate sensitivity for callable bonds 319
12.3.1 Negative convexity 322
12.4 Sinking fund bonds 326
12.4.1 Valuing a sinking fund bond: the sink by lottery only case 329
12.4.2 Sink by lottery or sink by open market purchase 331
12.5 Exercises 334
12.1 Introduction 308
ANSWERS TO SELECTED PROBLEMS 336
REFERENCES 373
INDEX 379