This Element is intended for students and practitioners as a gentle and intuitive introduction to the field of discrete-time yield curve modelling. I strive to be as comprehensive as possible, while still adhering to the overall premise of putting a strong focus on practical applications. In addition to a thorough description of the Nelson-Siegel family of model, the Element contains a section on the intuitive relationship between P and Q measures, one on how the structure of a Nelson-Siegel model can be retained in the arbitrage-free framework, and a dedicated section that provides a detailed explanation for the Joslin, Singleton, and Zhu (2011) model.
Author(s): Ken Nyholm
Series: Elements in Quantitative Finance
Publisher: Cambridge University Press
Year: 2021
Language: English
Pages: 75
City: Cambridge
Cover
Title page
Copyright page
A Practitioner’s Guide to Discrete-Time Yield CurveModelling
Contents
1 Empirical Analysis of Term Structure Data
1.1 Introduction
1.2 Exploring Yield Curve Data
1.3 A First Look at Principal Component Models
1.4 Adding Time-Series Dynamics to the Factors
2 P and Q Measures
2.1 Introduction
2.2 Switching between Measures
2.3 A Simplified Empirical Example
2.4 A Generic Discrete-Time One-Factor Model
2.4.1 Estimating the Short-Rate Model
2.5 Summary
3 The Basic Yield Curve Modelling Set-Up
3.1 Introduction
3.2 The Factor Structure of Yields
3.3 Rotating the Yield Curve Factors
3.3.1 A Short-Rate Based Model
3.3.2 Using Yields as Factors
3.4 The Building Blocks That Shape the Yield Curve
3.5 Modelling Yields at the Lower Bound
3.6 Summary
4 Modelling Yields under the Q Measure
4.1 Introduction
4.2 A Discrete-Time Four-Factor SRB Model
4.2.1 The Relationship between the SRB Model and the Joslin, Singletonand Zhu (2011) Framework
4.2.2 The Relationship between the Four-Factor SRB Model and theSvensson-Söderlind Model
5 Model Implementation
5.1 Introduction
5.2 A Brief Note on Model Implementation
5.3 Implementing the Joslin, Singleton and Zhu (2011) Model
5.4 Implementing the Arbitrage-Free SRB Model
5.5 Constructing a Model with the Short Rate and the Ten-YearTerm Premium as Underlying Factors
6 Scenario Generation
6.1 Introduction
6.1.1 The Horse Race
6.1.2 Conditional Projections
6.1.3 Fix-Point Scenarios
Appendix: On the Included MATLAB Codes and Scripts
References
Acknowledgements
