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 MODELING TERM STRUCTURE DYNAMICS: AN INFINITE DIMENSIONAL APPROACH

2005 ◽  
Vol 08 (03) ◽  
pp. 357-380 ◽  
Author(s):  
RAMA CONT
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Dimensional Space ◽  
Forward Rate ◽  
Model Parameters ◽  
Stochastic Pde ◽  
Forward Rates ◽  
Infinite Dimensional ◽  
Average Shape

Motivated by stylized statistical properties of interest rates, we propose a modeling approach in which the forward rate curve is described as a stochastic process in a space of curves. After decomposing the movements of the term structure into the variations of the short rate, the long rate and the deformation of the curve around its average shape, this deformation is described as the solution of a stochastic evolution equation in an infinite dimensional space of curves. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates, the structure of principal components of forward rates and their variances. In particular we show that a flat, constant volatility structures already captures many of the observed properties. Finally, we discuss parameter estimation issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.

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.

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 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.

A Consumption Based Term Structure Model w ith Habit Utility

2018 ◽  
Vol 9 (6) ◽  
pp. 484-496
Author(s):  
Jun Lou ◽  
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Bond Yields ◽  
Expectations Hypothesis ◽  
Term Structure Model ◽  
Bond Risk Premia ◽  
The Interest Rate ◽  
Bond Risk

This paper proposes a term structure of interest rates model that modifies and extends the Campbell and Cochrane (1999) surplus consumption framework. The distinguishing contributions are tractable, continuous-time analytical solutions for the term structure of interest rate generating a realistic upward sloping yield curve. Despite the focus on the term structure, the model matches plausible equity quantities. For the interest rate, the model is able to account for the moments of bond yields at numerous maturities and produce countercyclical bond risk premia as seen in the data. Moreover, the model captures reasonable time series fluctuation on real interest rates. However, the model has difficulties reproducing empirical deviations from the expectations hypothesis.

scholarly journals Some Lessons from the Yield Curve

1995 ◽  
Vol 9 (3) ◽  
pp. 129-152 ◽  
Author(s):  
John Y Campbell
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Yield Curve ◽  
Bond Market ◽  
Expectations Hypothesis ◽  
Expectation Hypothesis ◽  
Maturity Structure ◽  
Short And Long Term ◽  
The U.S

This paper reviews the literature on the relation between short- and long-term interest rates. It summarizes the mixed evidence on the expectation hypothesis of the term structure: when long rates are high relative to short rates, short rates tend to rise as implied by the expectations hypothesis, but long rates tend to fall, which is contrary to the expectations hypothesis. The paper discusses the response of the U.S. bond market to shifts in monetary policy in the spring of 1994 and reviews the debate over the optimal maturity structure of the U.S. government debt.

scholarly journals Dynamic spillovers between the term structure of interest rates, bitcoin, and safe-haven currencies

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
David Y. Aharon ◽  
Zaghum Umar ◽  
Xuan Vinh Vo
Keyword(s):  
Exchange Rate ◽  
Exchange Rates ◽  
Dynamic Analysis ◽  
Interest Rates ◽  
Static Analysis ◽  
Term Structure ◽  
Yield Curve ◽  
Empirical Support ◽  
Safe Haven ◽  
The Exchange Rate

AbstractThis study examines the connectedness between the US yield curve components (i.e., level, slope, and curvature), exchange rates, and the historical volatility of the exchange rates of the main safe-haven fiat currencies (Canada, Switzerland, EURO, Japan, and the UK) and the leading cryptocurrency, the Bitcoin. Results of the static analysis show that the level and slope of the yield curve are net transmitters of shocks to both the exchange rate and its volatility. The exchange rate of the Euro and the volatility of the Euro and the Canadian dollar exchange rate are net transmitters of shocks. Meanwhile, the curvature of the yield curve and the Japanese Yen, Swiss Franc, and British Pound act mainly as net receivers. Our static connectedness analysis shows that Bitcoin is mainly independent of shocks from the yield curve’s level, slope, and curvature, and from any main currency investigated. These findings hint that Bitcoin might provide hedging benefits. However, similar to the static analysis, our dynamic analysis shows that during different periods and particularly in stressful times, Bitcoin is far from being isolated from other currencies or the yield curve components. The dynamic analysis allows us to observe Bitcoin’s connectedness in times of stress. Evidence supporting this contention is the substantially increased connectedness due to policy shocks, political uncertainty, and systemic crisis, implying no empirical support for Bitcoin’s safe-haven property during stress times. The increased connectedness in the dynamic analysis compared with the static approach implies that in normal times and especially in stressful times, Bitcoin has the property of a diversifier. The results may have important implications for investors and policymakers regarding their risk monitoring and their assets allocation and investment strategies.

scholarly journals Brazilian term structure of interest rate modeling: A Nelson-Siegel approach

2016 ◽  
Vol 14 (1) ◽  
pp. 414-432
Author(s):  
Adalto Barbaceia Gonçalves ◽  
Felipe Tumenas Marques
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Future Research ◽  
Model Parameters ◽  
Extensive Literature ◽  
Bond Markets ◽  
Fixed Rate ◽  
Yield Curves ◽  
Vec Model ◽  
Parsimonious Models

Forecasting interest rates structures plays a fundamental role in the fixed income and bond markets. The development of dynamic modeling, especially after Nelson and Siegel (1987) work, parsimonious models based in a few parameter shed light over a new path for the market players. Despite the extensive literature on the term structure of interest rates modeling and the existence in the Brazilian market of various yield curves from different traded asset classes, the literature focused only in the fixed rate curve. In this work we expand the existing literature on modeling the term structure of Brazilian interest rates evaluating all the yield curves of Brazilian market using the methodology proposed by Nelson and Siegel. We use Non Linear Least Squares (NLLS) to estimate the model parameters for almost 10 years of monthly data and model these parameters with the traditional VAR/VEC model. The results show that it is possible to estimate the Nelson Siegel model for the Brazilian curves. It remains for future research the modeling of their variances as well as the possibility to develop a global Brazilian model using Kalman Filter using the Diebold. Li. and Yue (2006) approach.

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