Bayesian smoothing spline models and their application in estimating yield curves

2015 ◽  
Author(s):  
◽  
Xiaojun Tong
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Smoothing Spline ◽  
Calendar Time ◽  
Yield Data ◽  
Yield Curves ◽  
Adaptive Smoothing ◽  
Spline Models ◽  
Bayesian Smoothing

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The term structure of interest rates, also called the yield curve, is the series of interest rates ordered by term to maturity at a given time. The smoothing spline as a nonparametric regression method has been used widely for fitting a smooth curve due to its flexibility and smoothing properties. In this dissertation, a class of Bayesian smoothing spline models is developed for the yield curve estimation under different scenarios. These include the Bayesian smoothing spline model for estimating the Treasury yield curves, the Bayesian multivariate smoothing spline model for estimating multiple yield curves jointly, the Bayesian adaptive smoothing spline model for dealing with the yield data in which the smoothness varies significantly, the Bayesian smoothing spline model for extracting the zero-coupon yield curve from coupon bond prices, and the Bayesian thin-plate splines for modeling the yield curves on both the calendar time and the maturity. In addition, the Bayesian model selection in the smoothing spline models is developed to test the nonlinearity of the yield curves.

Yield Curves, Swap Curves, and Term Structure of Interest Rates

2019 ◽  
pp. 203-228
Author(s):  
Tom P. Davis ◽  
Dmitri Mossessian
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Yield Curves ◽  
No Arbitrage ◽  
Interest Rate Swap ◽  
The Interest Rate ◽  
Rate Swap ◽  
The U.S

This chapter discusses multiple definitions of the yield curve and provides a conceptual understanding on the construction of yield curves for several markets. It reviews several definitions of the yield curve and examines the basic principles of the arbitrage-free pricing as they apply to yield curve construction. The chapter also reviews cases in which the no-arbitrage assumption is dropped from the yield curve, and then moves to specifics of the arbitrage-free curve construction for bond and swap markets. The concepts of equilibrium and market curves are introduced. The details of construction of both types of the curve are illustrated with examples from the U.S. Treasury market and the U.S. interest rate swap market. The chapter concludes by examining the major changes to the swap curve construction process caused by the financial crisis of 2007–2008 that made a profound impact on the interest rate swap markets.

scholarly journals Title: analysis of term structure of interest rates in Latin America countries from 2006 to 2014

2015 ◽  
Vol 13 (4) ◽  
pp. 650
Author(s):  
Felipe Stona ◽  
Jean Amann ◽  
Maurício Delago Morais ◽  
Divanildo Triches ◽  
Igor Clemente Morais
Keyword(s):  
Latin America ◽  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Principal Component ◽  
Vector Model ◽  
Yield Curves ◽  
Macroeconomic Factors ◽  
The Relationship ◽  
Latin America Countries

This article aims to investigate the relationship between the term structure of interest rates and macroeconomic factors in selected countries of Latin America, such as Brazil, Chile and Mexico, between 2006 and 2014, on an autoregressive vector model. Specifically, we perform estimations of Nelson-Siegel, Diabold-Li and principal component analysis to test how the change of macroeconomic factors, e.g. inflation, production and unemployment levels affect the yield curves. For Brazil and Mexico, GDP and inflation variables are relevant to change the yield curves, with the former shifting more the level, and the latter with greater influence on the slope. For Chile, inflation had the greatest impact on the level and, specifically for Mexico, the unemployment variable also changed the slope of the yield curve.

Partially informative normal and partial spline models

2015 ◽  
Author(s):  
◽  
Sifan Liu
Keyword(s):  
Yield Curve ◽  
Smoothing Splines ◽  
Smoothing Spline ◽  
Linear Component ◽  
Function Estimation ◽  
Regression Problem ◽  
Adaptive Smoothing ◽  
University Of Missouri ◽  
Spline Models ◽  
Large P Small N

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] There is a well-known Bayesian interpretation of function estimation by spline smoothing using a limit of proper normal priors. This limiting prior has the same form with Partially Informative Normal (PIN), which was introduced in Sun et al. (1999). In this dissertation, we first discuss some properties of PIN. In terms of improper priors, we consider q-vague convergence as the convergence mode. Then, we apply the properties to several extensions of smoothing spline problems. Partial spline model, which contains a non-parametric part as regular smoothing spline together with a linear parametric part, is discussed. We perform simulation studies and applications on yield curves. Specifically, Nelson-Siege (NS) model is considered to construct the linear component. NS partial spline model is used for fitting single yield curve, while partial parallel and non-parallel spline models are used for multiple curves. Then, large p, small n regression problem associated with the generalized univariate smoothing spline, some studies on bin smoothing splines, adaptive smoothing splines and correlated smoothing splines are discussed.

scholarly journals Yield curve dynamics with macroeconomic factors in Iberian economies

2020 ◽  
Vol 10 (3) ◽  
pp. 193-203
Author(s):  
Isabel Maldonado ◽  
Carlos Pinho
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Error Variance ◽  
Impact Factors ◽  
Strong Impact ◽  
Impulse Response Functions ◽  
Macroeconomic Factors ◽  
Vector Autoregressive ◽  
Future Evolution

Abstract The aim of this paper is to analyse the bidirectional relation between the term structure of interest rates components and macroeconomic factors. Using a factor augmented vector autoregressive model, impulse response functions and forecasting error variance decompositions we find evidence of a bidirectional relation between yield curve factors and the macroeconomic factors, with increased relevance of yield factors over it with increased forecasting horizons. The study was conduct for the two Iberian countries using information of public debt interest rates of Spain and Portugal and macroeconomic factors extracted from a set of macroeconomic variables, including indicators of activity, prices and confidence. Results show that the inclusion of confidence and macroeconomic factors in the analysis of the relationship between macroeconomics and interest rate structure is extremely relevant. The results obtained allow us to conclude that there is a strong impact of changes in macroeconomic factors on the term structure of interest rates, as well as a significant impact factors of the term structure in the future evolution of macroeconomic factors.

Does the slope of the yield curve of the interbank market influence prices on the Warsaw Stock Exchange? A sectoral perspective

2021 ◽  
Vol 67 (4) ◽  
pp. 294-307
Author(s):  
Ewa Majerowska ◽  
Jacek Bednarz
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Stock Exchange ◽  
Rate Curve ◽  
Daily Data ◽  
Warsaw Stock Exchange ◽  
The Interest Rate ◽  
Relationship Of

The interest rate curve is often viewed as the leading indicator of economic prosperity in a broad sense. This paper studies the ability of the slope of the yield curve in the term structure of interest rates to impact the sectoral indices on the Warsaw Stock Exchange, using daily data covering the period from 1 January 2001 to 30 September 2020. The results of the research indicate an ambiguous dependence of the logarithmic rates of return of sub-indices on the change of the interbank interest rate curve. The only sectors showing a clear relationship of this type is energy and pharmaceuticals.

scholarly journals A Nonparametric Approach to Bond Portfolio Immunization

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1121
Author(s):  
Victor Lapshin
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Best Practice ◽  
Yield Curve ◽  
Model Parameters ◽  
Dimensional Manifold ◽  
Nonparametric Approach ◽  
Hedging Portfolio ◽  
Practice Approach ◽  
Low Dimensional

We consider the problem of short term immunization of a bond-like obligation with respect to changes in interest rates using a portfolio of bonds. In the case that the zero-coupon yield curve belongs to a fixed low-dimensional manifold, the problem is widely known as parametric immunization. Parametric immunization seeks to make the sensitivities of the hedged portfolio price with respect to all model parameters equal to zero. However, within a popular approach of nonparametric (smoothing spline) term structure estimation, parametric hedging is not applicable right away. We present a nonparametric approach to hedging a bond-like obligation allowing for a general form of the term structure estimator with possible smoothing. We show that our approach yields the standard duration based immunization in the limit when the amount of smoothing goes to infinity. We also recover the industry best practice approach of hedging based on key rate durations as another particular case. The hedging portfolio is straightforward to calculate using only basic linear algebra operations.

scholarly journals The gilt-edged market reformulated

1977 ◽  
Vol 104 (2) ◽  
pp. 227-240
Author(s):  
K. S. Feldman
Keyword(s):  
Interest Rates ◽  
Yield Curve ◽  
Yield Curves ◽  
Market Prices ◽  
Simple Assumption ◽  
New Model ◽  
Uniform Rate ◽  
Conventional Analysis ◽  
The Future ◽  
Yield Calculation

1.1. In this note it is argued that models of the gilt-edged market which are based on yield curves are unnecessarily restrictive and should not be expected to give a satisfactory statistical ‘fit’ in current conditions. The new model which is formulated relates market prices directly to the life and coupon without diverting into the computation of redemption yields. Indeed, it is suggested that the yield calculation destroys the inherent simplicity of the underlying equations—which follow from a simple assumption concerning the return from different portfolios. The method avoids the inconsistency inherent in the conventional analysis of discounting future investment proceeds at a uniform rate of interest when the yield curve itself implies that interest rates will vary in the future.

scholarly journals Testes da Hipótese de Expectativas na Estrutura a Termo das Taxas de Juros Brasileiras

2003 ◽  
Vol 1 (1) ◽  
pp. 19
Author(s):  
Benjamin Miranda Tabak ◽  
Sandro Canesso de Andrade
Keyword(s):  
Monetary Policy ◽  
Interest Rates ◽  
Term Structure ◽  
Risk Premium ◽  
Rational Expectations ◽  
Yield Curve ◽  
Single Equation ◽  
Expectations Hypothesis ◽  
Macro Modeling ◽  
Daily Data

We test the Expectations Hypothesis (EH) plus Rational Expectations (RE) in the Brazilian term-structure of interest rates, using maturities ranging from 1 month to 12 months, and daily data from 1995 to 2000. We rely on two methodologies based on single-equation regressions. Our results indicate a rejection of the EH plus RE, specially at the longer maturity. This may have important implications for the rational expectations macro-modeling currently being used to evaluate the conduct of monetary policy in Brazil. We also show the risk premium in the yield curve are positively related to the covered interest rate differential and to the volatility of interest rates.

Sign in / Sign up

Export Citation Format

Share Document