Affine Term Structure Models
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Author | : Damir Filipovic |
Publisher | : Springer Science & Business Media |
Total Pages | : 259 |
Release | : 2009-07-28 |
Genre | : Mathematics |
ISBN | : 3540680152 |
Changing interest rates constitute one of the major risk sources for banks, insurance companies, and other financial institutions. Modeling the term-structure movements of interest rates is a challenging task. This volume gives an introduction to the mathematics of term-structure models in continuous time. It includes practical aspects for fixed-income markets such as day-count conventions, duration of coupon-paying bonds and yield curve construction; arbitrage theory; short-rate models; the Heath-Jarrow-Morton methodology; consistent term-structure parametrizations; affine diffusion processes and option pricing with Fourier transform; LIBOR market models; and credit risk. The focus is on a mathematically straightforward but rigorous development of the theory. Students, researchers and practitioners will find this volume very useful. Each chapter ends with a set of exercises, that provides source for homework and exam questions. Readers are expected to be familiar with elementary Itô calculus, basic probability theory, and real and complex analysis.
Author | : David Bolder |
Publisher | : |
Total Pages | : 60 |
Release | : 2001 |
Genre | : Geometry, Affine |
ISBN | : |
Affine models describe the stylized time-series properties of the term structure of interest rates in a reasonable manner, they generalize relatively easily to higher dimensions, and a vast academic literature exists relating to their implementation. This combination of characteristics makes the affine class a natural introductory point for modelling interest rate dynamics. The author summarizes and synthesizes the theoretical and practical specifics relating to this analytically attractive class of models. This summary is accomplished in a self-contained manner with sufficient detail so that relatively few technical points will be left for the reader to ponder. As such, this paper represents a first step towards advancing the Bank of Canada's research agenda in this area, with a view to using these models to assist with practical debt and risk-management problems currently under study.
Author | : Qiang Dai |
Publisher | : |
Total Pages | : 51 |
Release | : 1997 |
Genre | : Geometry, Affine |
ISBN | : |
This paper characterizes, interprets, and tests the over-identifying restrictions imposed in affine models of the term" structure. Letting r(t) = ë Y(t), where Y is an unobserved vector affine process, our analysis proceeds in three steps. First, we show that affine models can be categorized according to the different over-identifying restrictions they impose on (i) ë, and (ii) the parameters of the diffusion matrices. Second, this formulation is shown to be equivalent to a model in which there is a terraced drift structure with one of the state variables being the stochastic long-run mean of r. This equivalence allows direct comparisons of the substantive restrictions on the dynamics of interest rates imposed in CIR-style models and models in which the state variables are the stochastic long-run mean and volatility of r. Third, we compute simulated method of moments estimates of a three-factor affine term structure model, and test the over-identifying restrictions on the joint distribution of long- and short-term interest rates implied by extant affine models of r. We find allowing for correlated factors is key to simultaneously describing the short and long ends of the yield curve. This finding is interpreted in terms of the properties of the risk factors underlying term structure movements
Author | : Frank de Jong |
Publisher | : |
Total Pages | : 56 |
Release | : 1999 |
Genre | : Interest rates |
ISBN | : |
Author | : Bovorn Vichiansin |
Publisher | : |
Total Pages | : 116 |
Release | : 2006 |
Genre | : Interest rates |
ISBN | : |
Author | : Mario Alessandro Maggi |
Publisher | : |
Total Pages | : 116 |
Release | : 2001 |
Genre | : |
ISBN | : |
Author | : Anders Brandt Wulff-Andersen |
Publisher | : |
Total Pages | : 100 |
Release | : 2000 |
Genre | : |
ISBN | : |
Author | : Pierre Collin-Dufresne |
Publisher | : |
Total Pages | : 53 |
Release | : 2011 |
Genre | : |
ISBN | : |
Building on the approach of Duffie and Kan (1996) who use finite maturity yields as the state vector, we propose a new representation of affine models in which the state vector is composed of infinitesimal maturity yields and their quadratic covariations. Because these variables possess unambiguous economic interpretations, they generate a representation that is globally identifiable. Further, this representation is more flexible than the maximal model of Dai and Singleton (2000) in that there are more identifiable parameters. We implement this new representation for two different three-factor models. The fact that our state vector can be estimated model-independently from yield curve data presents advantages for the estimation and interpretation of multi-factor models.
Author | : Adam Golinski |
Publisher | : |
Total Pages | : 61 |
Release | : 2017 |
Genre | : |
ISBN | : |
We develop a Gaussian discrete time essentially affine term structure model with long memory state variables. This feature reconciles the strong persistence observed in nominal yields and inflation with the theoretical implications of affine models, especially for long maturities. We characterise in closed-form the dynamic and cross-sectional implications of long memory for our model. We explain how long memory can naturally arise within the term structure of interest rates, providing a theoretical underpinning for our model. Despite the infinite-dimensional structure that long memory implies, we show how to cast the model in state space and estimate it by maximum likelihood. An empirical application of our model is presented.
Author | : Rajna Gibson |
Publisher | : Now Publishers Inc |
Total Pages | : 171 |
Release | : 2010 |
Genre | : Business & Economics |
ISBN | : 1601983727 |
Modeling the Term Structure of Interest Rates provides a comprehensive review of the continuous-time modeling techniques of the term structure applicable to value and hedge default-free bonds and other interest rate derivatives.