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 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.

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.

scholarly journals The Term Structure of Interest Rates and its Impact on the Liability Adequacy Test for Insurance Companies in Brazil

2015 ◽  
Vol 26 (68) ◽  
pp. 223-236
Author(s):  
Antonio Aurelio Duarte ◽  
Aldy Fernandes da Silva ◽  
Luciano Vereda Oliveira ◽  
Elionor Farah Jreige Weffort ◽  
Betty Lilian Chan
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Cash Flow ◽  
Yield Curve ◽  
Spline Interpolation ◽  
Insurance Companies ◽  
Forward Rate ◽  
Insurance Company ◽  
Current Estimate ◽  
The Impact

<p>The Brazilian regulation for applying the Liability Adequacy Test (LAT) to technical provisions in insurance companies requires that the current estimate is discounted by a term structure of interest rates (hereafter TSIR). This article aims to analyze the LAT results, derived from the use of various models to build the TSIR: the cubic spline interpolation technique, Svensson's model (adopted by the regulator) and Vasicek's model. In order to achieve the objective proposed, the exchange rates of BM&FBOVESPA trading days were used to model the ETTJ and, consequently, to discount the cash flow of the insurance company. The results indicate that: (i) LAT is sensitive to the choice of the model used to build the TSIR; (ii) this sensitivity increases with cash flow longevity; (iii) the adoption of an ultimate forward rate (UFR) for the Brazilian insurance market should be evaluated by the regulator, in order to stabilize the trajectory of the yield curve at longer maturities. The technical provision is among the main solvency items of insurance companies and the LAT result is a significant indicator of the quality of this provision, as this evaluates its sufficiency or insufficiency. Thus, this article bridges a gap in the Brazilian actuarial literature, introducing the main methodologies available for modeling the yield curve and a practical application to analyze the impact of its choice on LAT.</p>

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 Models

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Term Structure ◽  
Yield Curve ◽  
Model Parameters ◽  
Bond Yields ◽  
Expectations Hypothesis ◽  
Forward Rates ◽  
Affine Models ◽  
Deterministic Function ◽  
Root Model ◽  
Quadratic Models

Bond yields and forward rates are defined. The fundamental PDE is derived. Affine term strucure models are explained, including the Vasicek model and the Cox‐Ingersoll‐Ross square root model. Gaussian affine models, completely affine models, and multifactor CIR models are explained. Quadratic models are described. The various versions of the expectations hypothesis are explained. We can fit a given yield curve by adding a deterministic function of time to an interest rate model or allowing model parameters to be time varying. Heath‐Jarrow‐Morton models are explained, and it is shown that drifts of forward rates under the risk neutral probability are determined by their volatilities.

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 CDO TERM STRUCTURE MODELLING WITH LÉVY PROCESSES AND THE RELATION TO MARKET MODELS

2012 ◽  
Vol 15 (01) ◽  
pp. 1250008 ◽  
Author(s):  
THORSTEN SCHMIDT ◽  
JERZY ZABCZYK
Keyword(s):  
Term Structure ◽  
Forward Rate ◽  
Collateralized Debt Obligations ◽  
Top Down ◽  
Market Models ◽  
Forward Rates ◽  
Finite Dimensional ◽  
Generalized Framework ◽  
Collateralized Debt ◽  
Absence Of Arbitrage

This paper considers the modelling of collateralized debt obligations (CDOs). We propose a top-down model via forward rates generalizing Filipović, Overbeck and Schmidt (2009) to the case where the forward rates are driven by a finite dimensional Lévy process. The contribution of this work is twofold: we provide conditions for absence of arbitrage in this generalized framework. Furthermore, we study the relation to market models by embedding them in the forward rate framework in spirit of Brace, Gatarek and Musiela (1997).

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