Yield Curve Modeling and Forecasting

Yield Curve Modeling and Forecasting: The Dynamic Nelson-Siegel Approach

Francis X. Diebold
Glenn D. Rudebusch
Copyright Date: 2013
Pages: 176
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  • Book Info
    Yield Curve Modeling and Forecasting
    Book Description:

    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 Forecastingcontains essential tools with enhanced utility for academics, central banks, governments, and industry.

    eISBN: 978-1-4008-4541-5
    Subjects: Economics, Business, Finance

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. List of Illustrations
    (pp. ix-x)
  4. Introduction
    (pp. xi-xii)
    Philip Hans Franses and Herman K. van Dijk

    The Econometric and Tinbergen Institute Lectures deal with topics in econometrics that have important policy implications. The lectures cover a wide range of topics and are not confined to any one area or subdiscipline. Leading international scientists in the fields of econometrics in which applications play a major role are invited to give three-day lectures on a topic to which they have contributed significantly.

    The 2012 lectures deal with the topic of describing and modeling the dynamic behavior of a large cross section of financial assets, such as Treasury bonds. Understanding their evolution is crucial for implied policy analysis. The...

  5. Preface
    (pp. xiii-xvi)
    Francis X. Diebold and Glenn D. Rudebusch
  6. Additional Acknowledgment
    (pp. xvii-xx)
  7. 1 Facts, Factors, and Questions
    (pp. 1-22)

    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...

  8. 2 Dynamic Nelson-Siegel
    (pp. 23-54)

    Here we begin our journey. We start with static Nelson-Siegel curve fitting in the cross section, but we proceed quickly to dynamic Nelson-Siegel modeling, with all its nuances and opportunities. Among other things, we emphasize the model’s state-space structure, we generalize it to the multicountry context, and we highlight aspects of its use in risk management and forecasting.

    As we will see, Nelson-Siegel fits a smooth yield curve to unsmoothed yields. One can arrive at a smooth yield curve in a different way, fitting a smooth discount curve to unsmoothed bond prices and then inferring the implied yield curve. That’s...

  9. 3 Arbitrage-Free Nelson-Siegel
    (pp. 55-95)

    Because bonds trade in deep and well-organized markets, the theoretical restrictions that eliminate opportunities for riskless arbitrage across maturities and over time hold powerful appeal, and they provide the foundation for a large finance literature on arbitrage-free models that started with Vasicek (1977) and Cox et al. (1985). Those models specify the risk-neutral evolution of the underlying yield curve factors as well as the dynamics of risk premia. Following Duffie and Kan (1996), the affine versions of those models are particularly popular, because yields are convenient affine functions of underlying latent factors with factor loadings that can be calculated from...

  10. 4 Extensions
    (pp. 96-125)

    In this chapter, we highlight aspects of the vibrant ongoing research program associated with the ideas developed in earlier chapters. We begin with a collage-style sketch of work involving Bayesian analysis, functional form for factor loadings, term structures of credit spreads, and nonlinearities. We then discuss in greater detail a time-honored topic that has received attention both historically and presently, incorporation of more than three yield factors. Third, we treat stochastic volatility in both DNS and AFNS environments, with some attention to the issue of unspanned stochastic volatility. Finally, we also discuss in detail a crucially important topic for the...

  11. 5 Macro-Finance
    (pp. 126-148)

    From the vantage point of incorporating macroeconomic considerations into yield curve modeling, one can view the approaches introduced previously in section 4.4 as preparatory, paving the way for more extensive explorations. In this chapter, we move in that direction, discussing a variety of AFNS macro-finance yield curve approaches.

    A key feature of the recent global financial crisis and recession is the close feedback between the real economy and financial conditions. In many countries, the credit and asset price boom that preceded the crisis coincided with strong spending and production. Similarly, during the crash, deteriorating financial conditions both contributed to the...

  12. 6 Epilogue
    (pp. 149-158)

    We begin with a bit of history, as what we have done in this book blends the old and the new. In particular, we sketch and contrast what we will call the “traditional” and “modern” approaches to yield curve modeling, to heighten our understanding of where and how DNS/AFNS fits.

    Early on, bond markets were few and far between, so the term structure of bond yields remained a dormant issue. But as financial markets developed, and as economic theory and measurement advanced, issues related to the yield curve emerged as central in asset allocation, asset pricing, and risk management.


  13. Appendix A Two-Factor AFNS Calculations
    (pp. 161-165)
  14. Appendix B Details of AFNS Restrictions
    (pp. 166-173)
  15. Appendix C The AFGNS Yield-Adjustment Term
    (pp. 174-178)
  16. Bibliography
    (pp. 179-196)
  17. Index
    (pp. 197-204)