Abstract

Since zero-coupon rates are rarely directly observable, they have to be estimated from market data. In this paper we review several widely-used parametric term structure estimation methods. We propose a weighted constrained optimization procedure with analytical gradients and a globally optimal start parameter search algorithm. Moreover, we introduce the <b>R</b> package <b>termstrc</b>, which offers a wide range of functions for term structure estimation based on static and dynamic coupon bond and yield data sets. It provides extensive summary statistics and plots to compare the results of the different estimation methods. We illustrate the application of the package through practical examples using market data from European government bonds and yields.

Highlights

  • The term structure of interest rates or the zero-coupon yield curve is the relationship between fixed income investments with only one payment at maturity and the time to maturity of this cashflow

  • It is used in different areas of application, e.g. risk management, financial engineering, monetary policy issues

  • Before we come to the problem of zero-coupon yield curve estimation, let us introduce the definitions of a few basic terms used in the fixed income literature

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Summary

Introduction

The term structure of interest rates or the zero-coupon yield curve is the relationship between fixed income investments with only one payment at maturity and the time to maturity of this cashflow. It is used in different areas of application, e.g. risk management, financial engineering, monetary policy issues. The fair price of a bond is the sum of its discounted future coupon and redemption payments. By comparing this fair price to the price on the market, we can identify mispriced securities. The numerous areas of application for the term structure of interest rates have lead to a fairly large amount of publications by researchers and practitioners

Fixed income basics
Literature review
Notation
Estimation procedure
Cubic splines
Knot point selection
Basis functions for cubic splines
Confidence intervals for the discount function
Practical application
Parametric methods
Spline-based methods
Summary statistics for the fitted models:
Rolling estimation procedure
Conclusion
Full Text
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