Ahn, D-H, Dittmar R F, Gallant A R, (2002), 'Quadratic Term Structure Models: Theory and Evidence', Review of Financial Studies, 15, 243-288  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a number of authors (see, eg, Ait Sahalia (1996) Chan et al. 1992) find evidence that the exponent # in the di#usion equation dr = r dt r #dw (48) should be greater than 1. As for the estimation of the market price of risk, Dai and Singleton (2000) Jagannathan et al. (2000) [Ahn et al. 2002)] Bansal and Zhou (2002) and [Du#ee (2002) suggest that a complex specification may be required to account for the observed yield curve dynamics. In reality, since the term in #P T in Equation 47 contains the expression [ k# ##) kr] Vasicek) or [k# (## k)r] CIR) the market ....

Ahn, D-H, Dittmar R F, Gallant A R, (2002), 'Quadratic Term Structure Models: Theory and Evidence', Review of Financial Studies, 15, 243-288

....or probabilities advanced in Section 1. But there 25 is an exception. As shown by Due, Pan, and Singleton (2000) the Fourier transform is quite useful for pricing options on ane di usions. Ane di usions are rejected as models for both equities and bonds (Chernov, Gallant, Ghysels, Tauchen 2001; Ahn, Dittmar, and Gallant, 2001) so that estimating these models can be regarded as calibration. Matching characteristic functions does seem to be a reasonable metric for calibrating ane di usions for the purpose of asset pricing. 7 ....

Ahn, D-H., R. F. Dittmar, and A. R. Gallant (2001) \Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, forthcoming.

....that expected excess returns to other assets, such as stocks, do not appear to exhibit sign changes. Thus the covariance term must change sign. There is no apriorireason to reject models that require the sign of Cov t (r b t 1 , #c t 1 ) to depend on the slope of the term structure. In fact, Ahn, Dittmar, and Gallant (1999) construct a general equilibrium consumption based model that accomodates such a relation. Empirically, however, we are brought back to the problem noted with power utility and recursive utility there is no empirical evidence that covariances move with expected excess returns, let al..one that they ....

Ahn, Dong-Hyun, Robert F. Dittmar, and A. Ronald Gallant, 1999, Quadratic term structure models: Theory and evidence, Working paper, University of North Carolina.

....when data are si mulated. 2 (1997) While these are able to overcome some of the empirical drawbacks of existing a#ne models, mostu nfortu natelylack the analytical tractabilityof these models. This is not the case for the recent qu adratic term stru ctu re models proposed by, for example, Ahn, Dittmar, and Gallant (2000) and Leippold and Wu (2000) bu t these requ ire the estimation of many more parameters than the a#ne models. In this paper, we take an alternative, more parsimoniou rouy , first su ggested byDai and Singleton (1998) We retain the a#ne form ofDu #e and Kan, and generalize the fu nctional form for ....

Ahn, D.-H., R. F. Dittmar, and A. R. Gallant, 2000, Qu adratic term stru ctu re models: Theoryand evidence, Working paper, Universityof North Carolina.

....easily demonstrate that the CIR factor is equivalent to the square of the Gaussian factor in its contribution to the volatility. 4 Thus in terms of generating volatility, A n (n) is equivalent to Q(n) 5 The last class which could be of importance is the inverted square root model (ISRM) of Ahn and Gao (1999). This model is based on the notion that the interest rate is the inverse of a state variable which follows a square root process. This model is unique in the sense that the drift of the interest rate is a quadratic function of the underlying state variables and its volatility is governed by a ....

....between correlation and level dependence. By replacing a correlated quadratic factor with an independent inverted square root factor, we loose flexibility in correlation structure. However, as strongly evidenced by Chan, Karolyi, Longsta#, and Sanders (1992) A it Sahalia (1996a, 1996b) and Ahn and Gao (1999), interest rate volatility increases at an increasing rate in interest rate levels with a level dependence on the order of approximately 1.5. The inverted square root factor exhibits this stronger level dependence (the order of the di#usion term is 1.5 vs. 1.0) and thus may potentially result in ....

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Ahn, D., Dittmar, R., and A. R. Gallant, "Quadratic Term Structure Models: Theory and Evidence, " unpublished manuscript, University of North Carolina. Ahn, D., and B. Gao, 1999, "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, 12, 721-762.

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