Yield Curve Modeling and Forecasting

Francis X. Diebold is the Paul F. and Warren S. Miller Professor of Economics at the University of Pennsylvania and professor of finance and statistics at the university's Wharton School. Glenn D. Rudebusch is executive vice president and director of economic research at the Federal Reserve Bank of San Francisco. They are the coauthors of Business Cycles: Durations, Dynamics, and Forecasting (Princeton).

• List of Illustrations ix Introduction xi Preface xiii Additional Acknowledgment xvii 1 Facts, Factors, and Questions 1 *1.1 Three Interest Rate Curves 2 *1.2 Zero-Coupon Yields 3 *1.3 Yield Curve Facts 4 *1.4 Yield Curve Factors 7 *1.5 Yield Curve Questions 13 *1.6 Onward 22 2 Dynamic Nelson-Siegel 23 *2.1 Curve Fitting 23 *2.2 Introducing Dynamics 26 *2.3 State-Space Representation 30 *2.4 Estimation 34 *2.5 Multicountry Modeling 42 *2.6 Risk Management 46 *2.7 DNS Fit and Forecasting 49 3 Arbitrage-Free Nelson-Siegel 55 *3.1 A Two-Factor Warm-Up 58 *3.2 The Duffie-Kan Framework 62 *3.3 Making DNS Arbitrage-Free 64 *3.4 Workhorse Models 78 *3.5 AFNS Restrictions on A0(3) 83 *3.6 Estimation 86 *3.7 AFNS Fit and Forecasting 90 4 Extensions 96 *4.1 Variations on the Basic Theme 96 *4.2 Additional Yield Factors 105 *4.3 Stochastic Volatility 113 *4.4 Macroeconomic Fundamentals 117 5 Macro-Finance 126 *5.1 Macro-Finance Yield Curve Modeling 126 *5.2 Macro-Finance and AFNS 131 *5.3 Evolving Research Directions 144 6 Epilogue 149 *6.1 Is Imposition of No-Arbitrage Helpful? 151 *6.2 Is AFNS the Only Tractable A0(3) Model? 153 *6.3 Is AFNS Special? 155 Appendixes 159 Appendix A Two-Factor AFNS Calculations 161 * A.1 Risk-Neutral Probability 161 * A.2 Euler Equation 163 Appendix B Details of AFNS Restrictions 166 * B.1 Independent-Factor AFNS 168 * B.2 Correlated-Factor AFNS 171 Appendix C The AFGNS Yield-Adjustment Term 174 Bibliography 179 Index 197

"Diebold and Rudebusch have succeeded in writing a milestone book that will be used variously as a standard reference, a guide for future research topics, a text book, or as a convenient introduction to the topics of yield curve modeling and macro-finance. Hence, while forecasting (especially about the future) is always fraught with peril, I'm confident that copies of the book will find their way into many collections, and that they will be actively used when they get there."--Leo Krippner, International Review of Economics and Finance "[T]he methods presented in the book are of great importance in financial market practice. The book is designed for academics, students, and practitioners working in yield curve modeling and forecasting, and it will be useful for all interested in bond markets and their links with the macroeconomic environment."--Malgorzata Doman, Zentralblatt MATH