412 research outputs found
Modeling interest rate dynamics: an infinite-dimensional approach
We present a family of models for the term structure of interest rates which
describe the interest rate curve as a stochastic process in a Hilbert space. We
start by decomposing the deformations of the term structure into the variations
of the short rate, the long rate and the fluctuations of the curve around its
average shape. This fluctuation is then described as a solution of a stochastic
evolution equation in an infinite dimensional space. 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 and the structure of principal components of
term structure deformations. Finally, we discuss calibration issues and show
that the model parameters have a natural interpretation in terms of empirically
observed quantities.Comment: Keywords: interest rates, stochastic PDE, term structure models,
stochastic processes in Hilbert space. Other related works may be retrieved
on http://www.eleves.ens.fr:8080/home/cont/papers.htm
Identification of affine term structures from yield curve data
We consider a slight perturbation of the Hull-White short rate model and the resulting modified forward rate equation. We identify the model coefficients by using the martingale property of the normalized bond price. The forward rate and the system parameters are then estimated by using the maximum likelihood method
Parameter estimations for SPDEs with multiplicative fractional noise
We study parameter estimation problem for diagonalizable stochastic partial
differential equations driven by a multiplicative fractional noise with any
Hurst parameter . Two classes of estimators are investigated:
traditional maximum likelihood type estimators, and a new class called
closed-form exact estimators. Finally the general results are applied to
stochastic heat equation driven by a fractional Brownian motion
Liquidity and its impact on bond prices
In this paper, we propose a theoretical continuous-time model to analyze the impact of liquidity on bond prices. This model prices illiquid bonds relative to liquid bonds and provides a testable theory of illiquidity induced price discounts. The model is tested using 1992-1994 data from bonds issued by the german government.These bonds define a market segment that is homogeneous in bankruptcy risk, taxes, age, and coupons, but the bonds differ with respect to their liquidity. The empirical findings suggest that bond prices not only depend on the dynamics of interest rates, but also on the liquidity of bonds. Therefore, bond liquidity should be used as an additional pricing factor. The findings of the out-of-sample test demonstrate the superiority of the model in comparison with traditional pricing models
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Nonparametric Recovery of the Yield Curve Evolution from Cross-Section and Time Series Information
We develop estimation methodology for an additive nonparametric panel model that is suitable for capturing the pricing of coupon-paying government bonds followed over many time periods. We use our model to estimate the discount function and yield curve of nominally riskless government bonds. The novelty of our approach is the combination of two different techniques: cross-sectional nonparametric methods and kernel estimation for time varying dynamics in the time series context. The resulting estimator is able to capture the yield curve shapes and dynamics commonly observed in the fixed income markets. We establish the consistency, the rate of convergence, and the asymptotic normality of the proposed estimator. A Monte Carlo exercise illustrates the good performance of the method under different scenarios. We apply our methodology to the daily CRSP bond dataset, and compare with the popular Diebold and Li (2006) method
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