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2000): “Specification Analysis of Affine Term Structure Models
 Journal of Finance
"... This paper explores the structural differences and relative goodnessoffits of affine term structure models ~ATSMs!. Within the family of ATSMs there is a tradeoff between flexibility in modeling the conditional correlations and volatilities of the risk factors. This tradeoff is formalized by our ..."
Abstract

Cited by 337 (30 self)
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This paper explores the structural differences and relative goodnessoffits of affine term structure models ~ATSMs!. Within the family of ATSMs there is a tradeoff between flexibility in modeling the conditional correlations and volatilities of the risk factors. This tradeoff is formalized by our classification of Nfactor affine family into N � 1 nonnested subfamilies of models. Specializing to threefactor ATSMs, our analysis suggests, based on theoretical considerations and empirical evidence, that some subfamilies of ATSMs are better suited than others to explaining historical interest rate behavior. IN SPECIFYING A DYNAMIC TERM STRUCTURE MODEL—one that describes the comovement over time of short and longterm bond yields—researchers are inevitably confronted with tradeoffs between the richness of econometric representations of the state variables and the computational burdens of pricing and estimation. It is perhaps not surprising then that virtually all of the empirical implementations of multifactor term structure models that use time series data on long and shortterm bond yields simultaneously have focused on special cases of “affine ” term structure models ~ATSMs!.AnATSM accommodates timevarying means and volatilities of the state variables through affine specifications of the riskneutral drift and volatility coefficients. At the same time, ATSMs yield essentially closedform expressions for zerocouponbond prices ~Duffie and Kan ~1996!!, which greatly facilitates pricing and econometric implementation. The focus on ATSMs extends back at least to the pathbreaking studies by Vasicek ~1977! and Cox, Ingersoll, and Ross ~1985!, who presumed that the instantaneous short rate r~t! was an affine function of an Ndimensional state vector Y~t!, r~t! � d 0 � d y Y~t!, and that Y~t! followed Gaussian and squareroot diffusions, respectively. More recently, researchers have explored formulations of ATSMs that extend the onefactor Markov represen
Optimal Consumption and Portfolio Selection with Stochastic Differential Utility
, 1999
"... We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuoustime version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the firstorder ..."
Abstract

Cited by 60 (3 self)
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We develop the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuoustime version of recursive utility due to D. Duffie and L. Epstein (1992, Econometrica 60, 353 394). We characterize the firstorder conditions of optimality as a system of forward backward SDEs, which, in the Markovian case, reduces to a system of PDEs and forward only SDEs that is amenable to numerical computation. Another contribution is a proof of existence, uniqueness, and basic properties for a parametric class of homothetic SDUs that can be thought of as a continuoustime version of the CES Kreps Porteus utilities studied by L. Epstein and A. Zin (1989, Econometrica 57, 937 969). For this class, we derive closedform solutions in terms of a single backward SDE (without imposing a Markovian structure). We conclude with several tractable concrete examples involving the type of ``affine'' state price dynamics that are familiar from the term structure literature.