Zero Lower Bound Term Structure Modeling

A Practitioner's Guide

L. Krippner

• Publisher: Palgrave Macmillan
• Year: 2015
• ISBN:
  9781137401823
• Topic: Economics
• Subtopic: Macroeconomics
• Index: Economics

Nominal yields on government debt in several countries have fallen very near their zero lower bound (ZLB), causing a liquidity trap and limiting the capacity to stimulate economic growth. This book provides a comprehensive reference to ZLB structure modeling in an applied setting.

1

Introduction

The purpose of this book is to introduce practical term structure frameworks and associated monetary policy measures that are explicitly designed to accommodate near-zero nominal interest rates. It is motivated by the prevailing global situation in which interest rates in the world’s six largest economies, except China, and many other economies have now essentially been at zero for five years since late 2008/early 2009. Furthermore, guidance from central banks and different measures of market expectations indicate that interest rates are likely to remain at or near zero in some economies for several more years.

Interest rates near zero, or more specifically nominal interest rates that are constrained by the zero lower bound (ZLB), are unprecedented historically, apart from in Japan a decade ago. Therefore, the behavior of interest rates and their relationships with the macroeconomy in a ZLB environment are likely to be unfamiliar to central bankers. Similarly, financial market participants are likely to be uncertain how term structure models or related frameworks that are not designed to respect the ZLB constraint will perform in a ZLB environment. Term structure modelers will already be aware of the theoretical deficiencies in standard Gaussian term structure models, but may not be aware of relatively straightforward solutions that are available for such models.

In short, new term structure frameworks are required for the new environment, and that is what I have written this book to deliver. I have designed the book to appeal to several distinct groups of potential readers:

• General monetary policy readers. I envisage that this first group will include people such as central bank practitioners and applied economists with a general interest in the topic, but more specifically in using the output from the models for applications related to monetary policy. For example, the shadow short rates and/or the Effective Monetary Stimulus results from the ZLB term structure models may be used for monitoring the stance of monetary policy and as data for related analysis.

• General financial market readers. I envisage that this second group will be people such as financial market practitioners and applied financial researchers with a general interest in the topic, but more specifically using the output from the models for applications related to financial markets. For example, the estimated state variables and parameters for the ZLB term structure models can be used for a risk framework in fixed interest portfolios, and the parameters for the estimated models can be used to value options on bonds.

• Term structure modelers. The third group will be those interested in learning about the specifics of term structure modeling and its extension into ZLB environments, so they can develop and apply their own ZLB term structure models. I expect this group will include people such as central bank researchers, financial market quantitative analysts, academic researchers, and students.

In the following section I provide an overview of the remaining eight chapters of the book, and then in section 1.2, I provide my reading suggestions for the three different groups. Sections 1.3 to 1.5 provide some further preliminaries that help to put the book in context.

1.1 Chapter overview

The following list provides a brief overview of the chapters in this book:

• Chapter 2: A new framework for a new environment. I provide background and motivation appropriate to the book by introducing some basic principles about monetary policy and term structure modeling, and the complications introduced by the ZLB. As a solution to those complications, I introduce the shadow/ZLB class of term structure models, which will be the predominant focus of the remaining chapters.

• Chapter 3: Gaussian affine term structure models. I outline the Gaussian affine term structure model (GATSM) framework, including the popular and parsimonious subclass of arbitrage-free Nelson and Siegel (1987) models (ANSMs). The outline first serves to establish the present standard for term structure modeling, and I also use GATSMs to represent the shadow term structure in the shadow/ZLB-GATSMs in the remainder of the book. Related to that point, I can then present the shadow/ZLB-GATSM framework and its estimation in chapter 4 as a relatively tractable modification to the GATSM class.

• Chapter 4: Krippner framework for ZLB term structure modeling. I develop the Krippner (2011, 2012b,c, 2013d,e) shadow/ZLB framework based on GATSMs outlined in chapter 3. I begin with the Krippner shadow/ZLB-GATSM, or K-AGM, framework because it is relatively tractable compared to the Black (1995) framework that I will discuss in chapter 5. In particular, the K-AGM is designed to use many of the standard results directly from the GATSM literature.

• Chapter 5: Black framework for ZLB term structure modeling. I provide an exposition of the shadow/ZLB-GATSM framework based on the approach first suggested in Black (1995) and using a GATSM to represent the shadow term structure. The Black shadow/ZLB-GATSM, or B-AGM, framework is seen by many as the benchmark for shadow/ZLB-GATSMs, but I argue that there is a strong case for using the K-AGM framework as an alternative, at least from a practical perspective and potentially also on theoretical grounds. Providing readers with a complete overview of the B-AGM framework and an explicit comparison to the K-AGM framework will best enable them to make an informed choice of which framework to use.

• Chapter 6: K-ANSM foundations and “Effective Monetary Stimulus.” I outline a generic economic foundation, based on well-accepted principles from the term structure literature, for ANSMs. There are several motivations for providing this ANSM economic foundation:

– It provides a justification for using ANSMs generally as a parsimonious and realistic representation of the shadow term structure.

– It provides a theoretical perspective for considering the pricing foundations of the K-ANSM and the B-ANSM frameworks.

– It helps justify the “Effective Monetary Stimulus” or EMS summary measure for the stance of monetary policy.

• Chapter 7: Monetary policy applications. I discuss some of the practical applications of shadow/ZLB-GATSMs to various aspects of monetary policy. In particular, chapter 7 will discuss how several outputs from shadow/ZLB-GATSMs can be used to indicate the stance of monetary policy or as data for related analysis.

• Chapter 8: Financial market applications. I discuss the practical application of shadow/ZLB-GATSMs within financial markets. In particular, I have selected two topics for which applying standard methods and GATSMs suitable for a non-ZLB environment would be very unsuitable in a ZLB environment, and for which shadow/ZLB-GATSMs can be used to bridge the gap. The first topic is the quantification of mark-to-market risk in fixed interest portfolios, and the second topic is the pricing of options on bonds in a ZLB environment.

• Chapter 9: Conclusion and future research directions. I provide a brief summary of the key points from each of the main chapters, and then give an overview of the case for using K-ANSMs as a standard term structure model that will accommodate both non-ZLB and ZLB environments. I conclude with a list of future research that remains to be undertaken for K-ANSMs.

1.2 Suggested reading

In the following subsection I provide suggested reading from the perspective of the three groups mentioned earlier.

1.2.1 Group 1: General monetary policy readers

I suggest that members of this group begin in chapter 2 where I provide the key intuition of non-ZLB and ZLB term structure modeling without resorting to the somewhat specialized mathematics that typically, and necessarily, accompanies the term structure literature. With the intuition from reading chapter 2, readers can turn directly to chapter 7 for an overview of the ZLB term structure models that I develop and estimate, and the applications of the output from those models to issues associated with monetary policy. The summary in chapter 9 will be useful to obtain an overview of the key results from other chapters. Note that both chapter 7 and chapter 9 include cross-references to intervening chapters and sections, so it is easy for readers to follow up on particular topics in more detail if they wish.

1.2.2 Group 2: General financial market readers

I suggest that members of this group also begin in chapter 2 to obtain the intuition of the topic, and then read at least section 7.1 from chapter 7 to obtain the overview of the shadow/ZLB term structure models that I develop and estimate. With the intuition from chapter 2 and the overview from chapter 7, readers can turn to chapter 8 for practical applications of shadow/ZLB term structure models to topics more specifically related to financial markets. The cross-references to the intervening chapters and sections that I have included in chapters 8 and 9 allow readers to easily seek out further details on particular topics if they wish.

1.2.3 Group 3: Term structure modelers

Those interested in learning more about developing and estimating shadow/ZLB term structure models will be able to work through all the chapters, and particularly the details on term structure models contained in chapters 3 to 6. The applications in chapters 7 and 8 provide illustrations on how the output from those models can be applied to various topics, and chapter 9 gives a summary, including a list of topics for future research.

Within chapters 3 to 6, I make few assumptions about the background knowledge of readers or their proficiency with the theory and practice of term structure modeling. Those with more proficiency can obviously skip through the familiar material more quickly. For example, those already familiar with GATSMs and their estimation need only read sections 3.1 and 3.2 to familiarize themselves with the notation I carry through to the remainder of the book.

I have included a very detailed focus on the estimation of all the models I present, for two reasons. First, a theoretical model is of no particular use in practice if it hasn’t been parametrized to adequately represent the actual data that are of relevance to the practitioner. Second, a practitioner is less likely to proceed to an estimation if the connection from a specified term structure model to a form that can be estimated is not clearly established or if it is left implicit. I prefer to have the book self-contained, so the reader can follow the development of the...

Table of contents

• Cover
• Title
• 1 Introduction
• 2 A New Framework for a New Environment
• 3 Gaussian Affine Term Structure Models
• 4 Krippner Framework for ZLB Term Structure Modeling
• 5 Black Framework for ZLB Term Structure Modeling
• 6 K-ANSM Foundations and Effective Monetary Stimulus
• 7 Monetary Policy Applications
• 8 Financial Market Applications
• 9 Conclusion and Future Research Directions
• Appendix A: Matrix Notation
• Notes
• Bibliography
• Index