Estimation of the yield curve and the forward rate curve starting from a finite number of observations

1992 ◽  
Vol 11 (4) ◽  
pp. 259-269 ◽  
Author(s):  
F. Delbaen ◽  
Sabine Lorimier
Keyword(s):  
Finite Number ◽  
Yield Curve ◽  
Rate Curve ◽  
Forward Rate

Descriptive Bond-Yield and Forward-Rate Models for the British Government Securities' Market: [forms Part Of: Report of the Fixed-Interest Working Group, B.A.J. 4, II Pg.213–383]

1998 ◽  
Vol 4 (2) ◽  
pp. 265-321 ◽  
Author(s):  
A.J.G. Cairns
Keyword(s):  
Least Squares ◽  
Working Group ◽  
Yield Curve ◽  
Securities Market ◽  
Rate Curve ◽  
Forward Rate ◽  
Bond Yield ◽  
Least Squares Fit ◽  
Curve Model ◽  
First Time

ABSTRACTThis paper discusses possible approaches to the construction of gilt yield indices published by the Financial Times. The existing method, described by Dobbie & Wilkie (1978) splits bonds into high, medium and low-coupon bands and fits separate yield curves to each. This method has been identified as susceptible to ‘catastrophic’ jumps when the least-squares fit jumps from one set of parameters to another set of quite different values. This problem is a result of non-linearities in the least-squares formula which can give rise to more than one local minimum. A desire to remove the risk of catastrophic changes prompted this research, which is being carried out as part of the work of the Fixed Interest Working Group.Recent changes in the taxation of bonds has, further, prompted the need for a review of the yield indices. Significantly, since the announcement of the new tax regime, the old coupon effect has been removed. This has made the use of a single forward-rate curve appropriate for the first time.A particular form of forward-rate curve is proposed as the basis for a revision of the gilt yield indices. This curve appears to give a significantly better fit than the present yield–curve model. It is also argued that the risk of catastrophic jumps has been reduced significantly.

Interest rate volatility and the shape of the term structure

1994 ◽  
Vol 347 (1684) ◽  
pp. 563-576 ◽  
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Yield Curve ◽  
Factor Models ◽  
The State ◽  
Rate Curve ◽  
Forward Rate ◽  
State Variables ◽  
Single Factor ◽  
Interest Rate Volatility

This paper analyses the effect of interest rate uncertainty on the shape of the forward rate curve. We consider a broad class of term structure models characterized by an affine relation between the drift and diffusion coefficients of the stochastic process describing the evolution of the state variables and the level of the state variables. For these models, a simple relation exists between the shape of the forward rate curve, the sensitivity of the zero-coupon yield curve to the state variables and the variance-covariance matrix of the state variables. In single factor models this relation implies that minus the convexity of the forward rate curve with respect to a measure of ‘duration’ is equal to the variance of the short rate. The paper explores why it is that, despite the well known shortcomings of single factor models, attempts to fit such models to cross-sections of nominal bond prices nonetheless produce reasonable estimates of interest rate volatility.

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.

Fitting a Smooth Forward Rate Curve to Coupon Instruments

1996 ◽  
Vol 6 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Volf Frishling ◽  
Junko Yamamura
Keyword(s):  
Rate Curve ◽  
Forward Rate

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.

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