List of Tables xi List of Figures xv

Abbreviations xv11

Notation xxv

Preface xxix

Acknowledgement xxxi

Foreword xxxiii

Introduction xxxv

1. Review of Market Analytics 1

1.1. Bond Valuation 1

1.2. Simple Bond Analytics 3

1.3. Portfolio Analytics 5

1.4. Key Rate Durations 8

2. Term Structure of Rates 11

2.1. Linear and Non-linear Space 11

2.2. Basis Functions 13

2.3. Decay Coefficient 16

2.4. Forward Rates 17

2.5. Par Curve 18

2.6. Application to the US Yield Curve 18

2.7. Historical Yield Curve Components 20

2.8. Significance of the Term Structure Components 23

2.9. Estimating the Value of the Decay Coefficient 25

3. Comparison of Basis Functions 29

3.1. Polynomial Basis Functions 29

3.2. Exponential Basis Functions 30

3.3. Orthogonal Basis Functions 30

3.4. Key Basis Functions 31

3.5. Transformation of Basis Functions 32

3.6. Comparison with the Principal Components Analysis 39

3.7. Mean Reversion 44 3.8. Historical Tables of Basis Functions 45

4. Risk Measurement 47

4.1. Interest Rate Risks 47

4.2. Zero Coupon Bonds Examples 49

4.3. Eurodollar Futures Contracts Examples 51

4.4. Conventional Duration of a Portfolio 52

4.5. Risks and Basis Functions 53

4.6. Application to Key Rate Duration 56

4.7 Risk Measurement of a Treasury Index 60

5. Performance Attribution 63

5.1. Curve Performance 64

5.2. Yield Performance 65

5.3. Security Performance 65

5.4. Portfolio Performance 67

5.5. Aggregation of Contribution to Performance 73

6. Libor and Swaps 77

6.1. Term Structure of Libor 79

6.2. Adjustment Table for Rates 80

6.3. Risk Measurement and Performance Attribution of Swaps 83

6.4. Floating Libor Valuation and Risks 84

6.5. Repo and Financing Rate 86

6.6. Structural Problem of Swaps 87

7. Trading 91

7.1. Liquidity Management 91

7.2. Forward Pricing 95

7.3. Curve Trading 95

7.4. Synthetic Securities 101

7.5. Real Time Trading 104

8. Linear Optimization and Portfolio Replication 107

8.1. Portfolio Optimization Example 110

8.2. Conversion to and from Conventional KRD 112

8.3. KRD and Term Structure Hedging 113

9. Yield Volatility 115

9.1. Price Function of Yield Volatility 116

9.2. Term Structure of Yield Volatility 118

9.3. Volatility Adjustment Table 122

9.4. Forward and Instantaneous Volatility 124

10. Convexity and Long Rates 127

10.1. Theorem: Long Rates Can Never Change 127

10.2. Convexity Adjusted TSIR 130

10.3. Application to Convexity 134

10.4. Convexity Bias of Eurodollar Futures 138

11. Real Rates and Inflation Expectations 145

11.1. Term Structure of Real Rates 145

11.2. Theorem: Real Rates Cannot Have Log-normal Distribution 146

11.3. Inflation Linked (IL) Bonds 149

11.4. Seasonal Adjustments to Inflation 155

11.5. Inflation Swaps 160

12. Credit Spreads 165

12.1. Equilibrium Credit Spread 165

12.2. Term Structure of Credit Spreads 167

12.3. Risk Measurement of Credit Securities 167

12.4. Credit Risks Example 168

12.5. Floating Rate Credit Securities 170

12.6. TSCS Examples 172

12.7. Relative Values of Credit Securities 174

12.8. Performance Attribution of Credit Securities 176

12.9. Term Structure of Agencies 178

12.10. Performance Contribution 179

12.11. Partial Yield 181

13. Default and Recovery 185

13.1. Recovery, Guarantee and Default Probability 185

13.2. Risk Measurement with Recovery 189

13.3. Partial Yield of Complex Securities 195

13.4. Forward Coupon 197

13.5. Credit Default Swaps 197

14. Deliverable Bond Futures and Options 201

14.1. Simple Options Model 202

14.2. Conversion Factor 204

14.3. Futures Price on Delivery Date 205

14.4. Futures Price Prior to Delivery Date 205

14.5. Early versus Late Delivery 209

14.6. Strike Prices of the Underlying Options 209

14.7. Risk Measurement of Bond Futures 210

14.8. Analytics for Bond Futures 211

14.9. Australian Bond Futures 213

14.10. Replication of Bond Futures 213

14.11. Backtesting of Bond Futures 216

15. Bond Options 217

15.1. European Bond Options 218

15.2. Exercise Boundary of American Options 221

15.3. Present Value of a Future Bond Option 222

15.4. Feedforward Pricing 226

15.5. Bond Option Greeks 230

15.6. Risk Measurement of Bond Options 231

15.7. Treasury and Real Bonds Options 233

15.8. Bond Options with Credit Risk 234

15.9. Theorem: Credit Prices Are Not Arbitrage-free 236

15.10. Correlation Model 238

15.11. Credit Bond Options Examples 239

15.12. Risk Measurement of Complex Bond Options 241

15.13. Remarks on Bond Options 242

16. Currencies 245

16.1. Currency Forwards 246

16.2. Currency as an Asset Class 247

16.3. Currency Trading and Hedging 248

16.4. Valuation and Risks of Currency Positions 249

16.5. Currency Futures 251

16.6. Currency Options 251

17. Prepayment Model 253

17.1. Home Sale 254

17.2. Refinancing 255

17.3. Accelerated Payments 256

17.4. Prepayment Factor 257

18. Mortgage Bonds 259

18.1. Mortgage Valuation 260

18.2. Current Coupon 262

18.3. Mortgage Analytics 264

18.4. Mortgage Risk Measurement and Valuation 268

19. Product Design and Portfolio Construction 273

19.1. Product Analyzer 275

19.2. Portfolio Analyzer 278

19.3. Competitve Universe 279

19.4. Portfolio Construction 280

20. Calculating Parameters of the TSIR 287

20.1. Optimizing TSIR 289

20.2. Optimizing TSCR 292

20.3. Optimizing TSCR with No Convexity 294

20.4. Estimating Recovery Value 295

20.5. Robustness of the Term Structure Components 295

20.6. Calculating the Components of the TSYV 296

21. Implementation 299

21.1. Term Structure 299

21. 1.1. Primary Curve 299

21. 1.2. Real Curve 300

21. 1.3. Credit Curve and Recovery Value 301

21.2. Discount Function and Risk Measurement 302

21.3. Cash Flow Engine 303

21.4. Invoice Price 306

21.5. Analytics 306

21.6. Trade Date versus Settle Date 308

21.7. American Options 309

21.8. Linear Programming 313

21.9. Mortgage Analysis 314

References 317

Index 319