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Modeling Term Structure Dynamics: An Infinite Dimensional Approach.
, 1999
"... We present a family of models for term structure dynamics in an attempt to describe several statistical features observed in empirical studies of forward rate curves by decomposing the deformations of the term structure into the variations of the short rate, the long rate and the fluctuations of ..."
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Cited by 21 (0 self)
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We present a family of models for term structure dynamics in an attempt to describe several statistical features observed in empirical studies of forward rate curves 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.
LONGTERM RETURNS IN STOCHASTIC INTEREST RATE MODELS: APPLICATIONS B¥
"... We extend the CoxIngersollRoss (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have s ..."
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Cited by 9 (3 self)
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We extend the CoxIngersollRoss (1985) model of the short interest rate by assuming a stochastic reversion level, which better reflects the time dependence caused by the cyclical nature of the economy or by expectations concerning the future impact of monetary policies. In this framework, we have studied the convergence of the longterm return by using the theory of generalised Besselsquare processes. We emphasize the applications of the convergence results. A limit theorem proves evidence of the use of a Brownian motion with drift instead of the integral fg rudu. For practice, however, this approximation turns out to be only appropriate when there are no explicit formulae and calculations are very timeconsuming.
To appear in Mathematical Finance GENERALIZATION OF THE DYBVIG–INGERSOLL–ROSS THEOREM AND ASYMPTOTIC MINIMALITY
, 2010
"... Abstract. The longterm limit of zerocoupon rates with respect to the maturity does not always exist. In this case we use the limit superior and prove corresponding versions of the Dybvig–Ingersoll–Ross theorem, which says that longterm spot and forward rates can never fall in an arbitragefree mo ..."
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Abstract. The longterm limit of zerocoupon rates with respect to the maturity does not always exist. In this case we use the limit superior and prove corresponding versions of the Dybvig–Ingersoll–Ross theorem, which says that longterm spot and forward rates can never fall in an arbitragefree model. Extensions of popular interest rate models needing this generalization are presented. In addition, we discuss several definitions of arbitrage, prove asymptotic minimality of the limit superior of the spot rates, and illustrate our results by several continuoustime shortrate models. 1.
her experience in interest rate modeling. I also thank Toufik Abboud, JeanPhilippe
, 1999
"... Russo and Agnès Sulem for useful indications and encouragement. All remaining errors are mine. We present a family of models for term structure dynamics in an attempt to describe several statistical features observed in empirical studies of forward rate curves by decomposing the deformations of the ..."
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Russo and Agnès Sulem for useful indications and encouragement. All remaining errors are mine. We present a family of models for term structure dynamics in an attempt to describe several statistical features observed in empirical studies of forward rate curves 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
MODELING TERM STRUCTURE DYNAMICS:
, 2004
"... 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 ..."
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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.
ON THE DYBVIGINGERSOLLROSS THEOREM CONSTANTINOS KARDARAS AND ECKHARD PLATEN
, 901
"... Abstract. The DybvigIngersollRoss (DIR) theorem states that, in arbitragefree term structure models, longterm yields and forward rates can never fall. We present a unifying approach with a refined version of the DIR theorem, where we identify the reciprocal of the maturity date as the maximal or ..."
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Abstract. The DybvigIngersollRoss (DIR) theorem states that, in arbitragefree term structure models, longterm yields and forward rates can never fall. We present a unifying approach with a refined version of the DIR theorem, where we identify the reciprocal of the maturity date as the maximal order that longterm rates at earlier dates can dominate longterm rates at later dates. The viability assumption imposed on the market model is significantly weaker than those appearing previously in the literature. 1.
ECKHARD PLATEN
"... The DybvigIngersollRoss (DIR) theorem states that, in arbitragefree term structure models, longterm yields and forward rates can never fall. We present a refined version of the DIR theorem, where we identify the reciprocal of the maturity date as the maximal order that longterm rates at earlie ..."
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The DybvigIngersollRoss (DIR) theorem states that, in arbitragefree term structure models, longterm yields and forward rates can never fall. We present a refined version of the DIR theorem, where we identify the reciprocal of the maturity date as the maximal order that longterm rates at earlier dates can dominate longterm rates at later dates. The viability assumption imposed on the market model is weaker than those appearing previously in the literature. KEY WORDS: long maturities, forward rates, DybvigIngersollRoss.