ADAPTIVE AND MONOTONE SPLINE ESTIMATION OF THE CROSS-SECTIONAL TERM STRUCTURE

2003 ◽  
Vol 06 (02) ◽  
pp. 195-212 ◽  
Author(s):  
ALESSANDRO RAMPONI
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Piecewise Polynomial ◽  
Discount Function ◽  
Cross Sectional ◽  
Piecewise Polynomial Approximation ◽  
Forward Rates ◽  
Regression Spline ◽  
Adaptive Regression ◽  
Spline Estimation

A number of numerical methods based on a piecewise polynomial approximation have been proposed for the estimation of the term structure of interest rates. Some drawbacks have been pointed out, such as a possible non monotonic estimated discount function and a highly fluctuating spot and forward rates. In order to overcome these kind of problems, we study the feasibility of an adaptive regression spline technique which use a monotone basis together with two alternative knot location procedures: a deterministic greedy algorithm and its randomized version in a simulated annealing framework. The features of the proposed method are tested on a set of data.

scholarly journals Term Structure, Inflation, and Real Activity

2009 ◽  
Vol 44 (4) ◽  
pp. 987-1011 ◽  
Author(s):  
Andrea Berardi
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Structural Model ◽  
Output Growth ◽  
Cross Sectional ◽  
Real Activity ◽  
Conditional Mean ◽  
Inflation Rates ◽  
Out Of Sample ◽  
Inflation Risk Premia

AbstractThis paper estimates an internally consistent structural model that imposes cross-sectional restrictions on the dynamics of the term structure of interest rates, inflation, and output growth. Distinct from previous term structure settings, this model introduces both time-varying central tendencies and a stochastic conditional mean of output growth. The estimation of the model, which is based on U.S. data over a 1960 to 2005 sample period, provides reliable estimates for the implicit term structures of real interest rates, expected inflation rates, and inflation risk premia, as well as for expectations of macroeconomic variables. The model has better out-of-sample forecasting properties than a number of alternative models, and it contradicts the puzzling evidence that during the “Great Moderation” in inflation subsequent to the mid-1980s, the forecasting ability of structural models deteriorated with respect to atheoretic statistical models.

scholarly journals Forward Rates and Future Policy: Interpreting the Term Structure of Interest Rates

1983 ◽  
Vol 1983 (1) ◽  
pp. 173 ◽  
Author(s):  
Robert J. Shiller ◽  
John Y. Campbell ◽  
Kermit L. Schoenholtz ◽  
Laurence Weiss
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Forward Rates ◽  
Future Policy

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.

Information Content of Implied Forward Exchange Rates

2003 ◽  
Vol 11 (1) ◽  
pp. 1-23
Author(s):  
Seong Hun Kim ◽  
Dong Se Cha
Keyword(s):  
Exchange Rates ◽  
Interest Rates ◽  
Error Correction ◽  
Information Content ◽  
Term Structure ◽  
Error Correction Model ◽  
Fisher Effect ◽  
Interest Rate Parity ◽  
Correction Model ◽  
Forward Rates

This paper analyzes the information content of the forward exchange rates implied by the interest rate parity, using the Korea and U.S. interest rates and Won/dollar exchange rates observed during the period of March 1991 to December 2002. First, we test the cointegration between implied forward exchange rates and future spot exchange rates to examine their longrun relationship, and find the existence of cointegration. Next, we examine the international Fisher effect and estimate an error correction model for their shortrun relationship. Our analysis supports the international Fisher effect for longer maturities. Our result also supports the error correction model that states that the future spot exchange rates will be adjusted reflecting the information contained in the past-period implied forward rates which is not fully reflected to current spot rates. Finally, we also find that the term structure of implied forward exchange rates is associated with the changes in future spot rates for longer maturities. Based on our findings, we conclude that the longrun relationship exists between the implied forward exchange rates and future spot exchange rates, and the shortrun deviation from the relationship tend to disappear as they return to the longrun relationship in the course of time.

Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset

2011 ◽  
Vol 101 (4) ◽  
pp. 1514-1534 ◽  
Author(s):  
Jonathan H Wright
Keyword(s):  
Interest Rates ◽  
Empirical Evidence ◽  
Term Structure ◽  
Industrialized Countries ◽  
Bond Yields ◽  
Inflation Uncertainty ◽  
Term Structure Model ◽  
Forward Rates ◽  
International Panel ◽  
Term Premia

This paper provides cross-country empirical evidence on term premia. I construct a panel of zero-coupon nominal government bond yields spanning ten industrialized countries and nearly two decades. I hence compute forward rates and use two different methods to decompose these forward rates into expected future short-term interest rates and term premiums. The first method uses an affine term structure model with macroeconomic variables as unspanned risk factors; the second method uses surveys. I find that term premiums declined internationally over the sample period, especially in countries that apparently reduced inflation uncertainty by making substantial changes in their monetary policy frameworks. (JEL E13, E43, E52, G12, H63)

A MARKOVIAN DEFAULTABLE TERM STRUCTURE MODEL WITH STATE DEPENDENT VOLATILITIES

2007 ◽  
Vol 10 (01) ◽  
pp. 155-202 ◽  
Author(s):  
CARL CHIARELLA ◽  
CHRISTINA NIKITOPOULOS SKLIBOSIOS ◽  
ERIK SCHLÖGL
Keyword(s):  
Diffusion Process ◽  
Interest Rates ◽  
Term Structure ◽  
Forward Rate ◽  
Term Structure Model ◽  
Forward Rates ◽  
Defaultable Bond ◽  
Term Structures ◽  
State Dependent ◽  
Path Independence

The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t,T) cause jumps and defaults to the defaultable bond prices Pd(t,T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates. In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.

THE CARMA INTEREST RATE MODEL

2014 ◽  
Vol 17 (02) ◽  
pp. 1450008 ◽  
Author(s):  
ARNE ANDRESEN ◽  
FRED ESPEN BENTH ◽  
STEEN KOEKEBAKKER ◽  
VALERIY ZAKAMULIN
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Moving Average ◽  
Forward Rate ◽  
Autoregressive Moving Average ◽  
Option Prices ◽  
Term Structure Model ◽  
Forward Rates ◽  
Closed Form Solutions ◽  
Bond Option

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

TERM STRUCTURE OF VANILLA OPTIONS

2007 ◽  
Vol 10 (08) ◽  
pp. 1323-1337
Author(s):  
DORJE C. BRODY ◽  
IRENE C. CONSTANTINOU ◽  
BERNHARD K. MEISTER
Keyword(s):  
Term Structure ◽  
Implied Volatility ◽  
Volatility Smile ◽  
Discount Function ◽  
Forward Rates ◽  
Black Scholes Model ◽  
Initial Term ◽  
Complete Market ◽  
Black Scholes ◽  
Structure Density

Every maturity-dependent derivative contract entails a term structure. For example, when the value of the portfolio consisting of a long position in a stock and a short position in a vanilla option is expressed in units of its instantaneous exercise value, the resulting quantity defines a discount function. Thus, the derivative of the discount function with respect to the time left until maturity defines a term structure density function, and the "hazard rate" associated with the discount function determines the forward rates for the vanilla option portfolio. The dynamics associated with these quantities are obtained in the complete market setting. In particular, one can model vanilla options based on the associated forward rates. The formulation based on forward rates for options extends the approach based on modeling the implied volatility process. As an illustrative example, the initial term structure of the Black–Scholes model is considered. It is shown in this example that the implied volatility smile has the effect of making the option forward rates homogeneous across different strikes.

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