Yield Curve Modeling and Forecasting: The Dynamic Nelson-Siegel Approach (The Econometric and Tinbergen Institutes Lectures) - Hardcover

Diebold, Francis X.; Rudebusch, Glenn D.

Hardcover

ISBN 10: 0691146802 ISBN 13: 9780691146805

Verlag: Princeton University Press, 2013

Inhaltsangabe

Understanding the dynamic evolution of the yield curve is critical to many financial tasks, including pricing financial assets and their derivatives, managing financial risk, allocating portfolios, structuring fiscal debt, conducting monetary policy, and valuing capital goods. Unfortunately, most yield curve models tend to be theoretically rigorous but empirically disappointing, or empirically successful but theoretically lacking. In this book, Francis Diebold and Glenn Rudebusch propose two extensions of the classic yield curve model of Nelson and Siegel that are both theoretically rigorous and empirically successful. The first extension is the dynamic Nelson-Siegel model (DNS), while the second takes this dynamic version and makes it arbitrage-free (AFNS). Diebold and Rudebusch show how these two models are just slightly different implementations of a single unified approach to dynamic yield curve modeling and forecasting. They emphasize both descriptive and efficient-markets aspects, they pay special attention to the links between the yield curve and macroeconomic fundamentals, and they show why DNS and AFNS are likely to remain of lasting appeal even as alternative arbitrage-free models are developed. Based on the Econometric and Tinbergen Institutes Lectures, Yield Curve Modeling and Forecasting contains essential tools with enhanced utility for academics, central banks, governments, and industry.

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Francis X. Diebold & Glenn D. Rudebusch

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"This lucid and concise book is unique in the field of term structure modeling. It leads readers from yield curve basics, with a popular and intuitive term structure model, to the frontiers of academia in associated fields. By the end of the book, readers will be inspired and enlightened enough to push those frontiers in the many open research directions noted by the authors, particularly in the emerging field of macro-finance."--Leo Krippner, Reserve Bank of New Zealand

"This timely and enlightening book covers the latest developments in the cutting-edge field of yield curve modeling in financial economics and macro-finance. Even active researchers in this area undoubtedly will learn something new. The book is clearly written by two distinguished scholars who share their insights and provide many refreshing clear-cut messages about theoretical and empirical issues in yield curve modeling and forecasting."--Lasse Bork, Aalborg University, Denmark

Aus dem Klappentext

"This lucid and concise book is unique in the field of term structure modeling. It leads readers from yield curve basics, with a popular and intuitive term structure model, to the frontiers of academia in associated fields. By the end of the book, readers will be inspired and enlightened enough to push those frontiers in the many open research directions noted by the authors, particularly in the emerging field of macro-finance."--Leo Krippner, Reserve Bank of New Zealand

"This timely and enlightening book covers the latest developments in the cutting-edge field of yield curve modeling in financial economics and macro-finance. Even active researchers in this area undoubtedly will learn something new. The book is clearly written by two distinguished scholars who share their insights and provide many refreshing clear-cut messages about theoretical and empirical issues in yield curve modeling and forecasting."--Lasse Bork, Aalborg University, Denmark

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Yield Curve Modeling and Forecasting

The Dynamic Nelson-Siegel ApproachBy Francis X. Diebold Glenn D. Rudebusch

Princeton University Press

Copyright © 2013 Princeton University Press
All right reserved.
ISBN: 978-0-691-14680-5

Contents

List of Illustrations..........................................ixIntroduction...................................................xiPreface........................................................xiiiAdditional Acknowledgment......................................xvii1 Facts, Factors, and Questions................................12 Dynamic Nelson-Siegel........................................233 Arbitrage-Free Nelson-Siegel.................................554 Extensions...................................................965 Macro-Finance................................................1266 Epilogue.....................................................149Appendixes.....................................................159Appendix A Two-Factor AFNS Calculations........................161Appendix B Details of AFNS Restrictions........................166Appendix C The AFGNS Yield-Adjustment Term.....................174Bibliography...................................................179Index..........................................................197

Chapter One

Facts, Factors, and Questions

In this chapter we introduce some important conceptual, descriptive, and theoretical considerations regarding nominal government bond yield curves. Conceptually, just what is it that are we trying to measure? How can we best understand many bond yields at many maturities over many years? Descriptively, how do yield curves tend to behave? Can we obtain simple yet accurate dynamic characterizations and forecasts? Theoretically, what governs and restricts yield curve shape and evolution? Can we relate yield curves to macroeconomic fundamentals and central bank behavior?

These multifaceted questions are difficult yet very important. Accordingly, a huge and similarly multifaceted literature attempts to address them. Numerous currents and cross-currents, statistical and economic, flow through the literature. There is no simple linear thought progression, self-contained with each step following logically from that before. Instead the literature is more of a tangled web; hence our intention is not to produce a "balanced" survey of yield curve modeling, as it is not clear whether that would be helpful or even what it would mean. On the contrary, in this book we slice through the literature in a calculated way, assembling and elaborating on a very particular approach to yield curve modeling. Our approach is simple yet rigorous, simultaneously in close touch with modern statistical and financial economic thinking, and effective in a variety of situations. But we are getting ahead of ourselves. First we must lay the groundwork.

1.1 Three Interest Rate Curves

Here we fix ideas, establish notation, and elaborate on key concepts by recalling three key theoretical bond market constructs and the relationships among them: the discount curve, the forward rate curve, and the yield curve. Let P(τ) denote the price of a τ-period discount bond, that is, the present value of $1 receivable τ periods ahead. If y(τ) is its continuously compounded yield to maturity, then by definition

P(τ) = e^-τy(τ). (1.1)

Hence the discount curve and yield curve are immediately and fundamentally related. Knowledge of the discount function lets one calculate the yield curve.

The discount curve and the forward rate curve are similarly fundamentally related. In particular, the forward rate curve is defined as

f(τ) = -P'(τ)/P(τ). (1.2)

Thus, just as knowledge of the discount function lets one calculate the yield curve, so too does knowledge of the discount function let one calculate the forward rate curve.

Equations (1.1) and (1.2) then imply a relationship between the yield curve and forward rate curve,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.3)

In particular, the zero-coupon yield is an equally weighted average of forward rates.

The upshot for our purposes is that, because knowledge of any one of P(τ), y(τ), and f(τ) implies knowledge of the other two, the three are effectively interchangeable. Hence with no loss of generality one can choose to work with P(τ), y(τ), or f(τ). In this book, following much of both academic and industry practice, we work with the yield curve, y(τ). But again, the choice is inconsequential in theory.

Complications arise in practice, however, because although we observe prices of traded bonds with various amounts of time to maturity, we do not directly observe yields, let alone the zero-coupon yields at fixed standardized maturities (e.g., six-month, ten-year, ...), with which we work throughout. Hence we now provide some background on yield construction.

1.2 Zero-Coupon Yields

In practice, yield curves are not observed. Instead, they must be estimated from observed bond prices. Two historically popular approaches to constructing yields proceed by fitting a smooth discount curve and then converting to yields at the relevant maturities using formulas (1.2) and (1.3).

The first discount curve approach to yield curve construction is due to McCulloch (1971, 1975), who models the discount curve using polynomial splines. The fitted discount curve, however, diverges at long maturities due to the polynomial structure, and the corresponding yield curve inherits that unfortunate property. Hence such curves can provide poor fits to yields that flatten out with maturity, as emphasized by Shea (1984).

An improved discount curve approach to yield curve construction is due to Vasicek and Fong (1982), who model the discount curve using exponential splines. Their clever use of a negative transformation of maturity, rather than maturity itself, ensures that forward rates and zero-coupon yields converge to a fixed limit as maturity increases. Hence the Vasicek-Fong approach may be more successful at fitting yield curves with flat long ends.

Notwithstanding the progress of Vasicek and Fong (1982), discount curve approaches remain potentially problematic, as the implied forward rates are not necessarily positive. An alternative and popular approach to yield construction is due to Fama and Bliss (1987), who construct yields not from an estimated discount curve, but rather from estimated forward rates at the observed maturities. Their method sequentially constructs the forward rates necessary to price successively longer-maturity bonds. Those forward rates are often called "unsmoothed Fama-Bliss" forward rates, and they are transformed to unsmoothed Fama-Bliss yields by appropriate averaging, using formula (1.3). The unsmoothed Fama-Bliss yields exactly price the included bonds. Unsmoothed Fama-Bliss yields are often the "raw" yields to which researchers fit empirical yield curves, such as members of the Nelson-Siegel family, about which we have much to say throughout this book. Such fitting effectively smooths the unsmoothed Fama-Bliss yields.

1.3 Yield Curve Facts

At any time, dozens of different yields may be observed, corresponding to different bond maturities. But yield curves evolve dynamically; hence they have not only a cross-sectional, but also a temporal, dimension. In this section we address the obvious descriptive question: How do yields tend to behave across...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 0691146802
• ISBN 13: 9780691146805
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 224
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: gpsr@libri.de; gpsr@libri.de; ; Europaallee 1; Bad Hersfeld; 36244; Deutschland