请教一个利率模型(升水)的问题

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1. 关于即期利率(instantaneous interest rate) 和到期收益率的区分, bloomberg 上给出的 1-yr, 3-yr, 5-yr...等等应该是即期利率对吧? 到期收益率应该是要自己根据票面价格,利息算出来的?

2. 我要求term premium(流动性升水), 理论上应该是 forward rate - instantaneous interest rate (对吧?) 无套利情况下forward rate可以通过 1-yr, 5-yr(打比方) 算出来 4-yr的, 那么再减去1-yr的就能得到了. 是不是就这么简单?

如果instantaneous interest rate 不能直接得到了话(如果bloomberg给出的不是instantaneous interest rate的话), 那应该怎么求得?

我看了 Don H. Kim and Jonathan H. Wright 写的 An Arbitrage-Free Three-Factor Term Structure Model and the Recent Behavior of Long-Term Yields and Distant-Horizon Forward Rate 这篇文章, 他好象很复杂的样子, 先估计bond price, 从中得出forward rate, 然后求得三因子(我不知道他用啥方法,说得很少), 三因子得出instantaneous interest rate(也不知道哪里来的系数), 最后forward rate - instantaneous interest rate求得term premium.

总之,我没怎么看明白,有高手懂的话帮我说一下吧! 应该是怎么求term premium的

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关键词：利率模型 Bloomberg Structure Arbitrage interest 请教 利率 模型

Generally speaking, the model described in Kim and Wright(2005)paper belongs to the Gaussian 3 factor model[i didn't see any specification in the volatility term, which means the latent factors does not enter the volatility, for different specification of the short rate diffusion see Duffee(2002) and Duffie and Kan(1996), discrete models are refered to Campbell,Lo and MacKinlay(1997) and Backus,Foresi and Telmer(1996,1998)]. And as a result, the short rate[or instantaneous rate in the paper]term premium is a linear/affine function of the factors.

Now the latent factors.The latent factors are obtained using Kalman filter and maximum likelihood estimation[for other estimation methods, see Piazzesi (2003)].You can find many places using Kalman filter and this technique was originally used in engineering and physics.[Kalman filter can be found in Eviews package, see Eviews manual for Kalman filter updating or Chapter 13 in Hamilton's time series analysis].

Once you get through these, all these analytical solutions, due to this tractability enbeded in this model, for forward rates, expected average short rate and term premium are not difficult to grab[see Campbell,Lo and MacKinlay(1997) for those derivations].

hope these can give you some clues in interest rate term structure models.