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By Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira

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1. Therefore, if we choose the drift terms so they reproduce the forward rate structure of the true model, this will result in expected future log short rates declining without bound as we increase the horizon, while the true model implies that the expected future log short rates converge to a nite constant. 12) unless ! e. unless the state variable follows a random walk in the true model. Moreover, for n > 1, the conditional variance of log bond prices implied by the assumed model is larger than the conditional variance implied by the true model and, while the true model implies that the conditional variance of log bond prices is bounded at 2 =(1 ; )2 as n !

4) by the Principle of Invariance (see Zehna 1966]). 3 47 From here we will assume that the trend is known exactly. 12) n(^ 2 ; 2 ) a N 0 2 4 1 + 2e 2 h2 1 ; e;2 h (1 + 2 h)]2 : To derive the continuous-record asymptotics of ^ and ^ 2 , we let n ! 1 while T is held xed, hence h = T=n ! 0. 17) ZT 0 0 (p(s) ; s)2 ds (p(s) ; s) dp(s) ; ZT 0 (p(s) ; s) ds: R T (p(s) ; s) dp(s) ; R T (p(s) ; s) ds ^a; 0 : R T (p(s) ; s)02 ds 0 48 which simpli es to PROBLEMS IN CHAPTER 9 R T q (s) dq (s) ^ a ; R0 T 2 : 0 q (s) ds where q(t) p(t) ; t.

Backus, Foresi and Zin (1996) use this result to caution against the popular practice among practitioners of augmenting standard arbitrage-free bond pricing models with time-dependent parameters to t exactly the yield curve. This augmentation may seriously misprice state-contingent claims, even though it is able to exactly reproduce the prices of some derivative securities.

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A Solution Manual To The Econometrics Of Financial Markets by Petr Adamek, John Y. Campbell, Andrew W. Lo, A. Craig Mackinlay, Luis M. Viceira


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