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金融民工阿聪 · 2021年03月07日

D里面的均衡和套利模型的问题

NO.PZ2018122701000067

问题如下:

Model 1 assumes zero drift and is also called a normal model. Model 2 add a term for drift. Each of the following is true about these two models except for:

选项:

A.

A weakness of Model 1 is that the short-term rate can become negative.

B.

Model 1 implies a term structure that is perfectly flat at the current rate for all maturities, including the long-term rates.

C.

Model 2 is more capable of producing an upward-sloping term structure, which is often observed.

D.

Model 2 is an equilibrium model, rather than an arbitrage-free model, because no attempt is made to match the term structure closely.

解释:

B is correct.

考点 Term Structure Models

解析 Under Model 1, it is true that the middle node recombines to the same current node. But these are future short-term rates; they are not the term structure: the term structure is spot rates at all maturities. Models that take the initial term structure implied by market prices are called arbitrage-free models. A different approach, however, is to start with assumptions about the interest rate process and about the risk premium demanded by the market for bearing interest rate risk and then derive the risk-neutral process. Models of this sort do not necessarily match the initial term structure and are called equilibrium models.

1.套利模型和无套利模型其实指的是一个东西对吗?

2.我的理解是,套利模型中,term structure是输入变量;均衡模型中,term structure是输出变量。但是HL model为什么是属于套利模型,而不是套利模型呢?HL model作为model2的广义形式,更应该是均衡模型吧?

3.如果一个模型是均衡模型,那么它可以同时也是套利模型吗

感谢老师解答~

1 个答案

品职答疑小助手雍 · 2021年03月08日

嗨,努力学习的PZer你好:


1.是一个东西

2.我查了原版书对这两个模型区别的描述,他俩的核心区别在于是不是以匹配市场价格为目的来建立模型,均衡模型就像model1和2一样,不在乎市场利率是多少,自己我行我素的进行趋势发展和波动。而arbitrage-free的模型,其目的是为了让利率的走向匹配市场利率的,所以它每期的趋势项会根据市场利率主动调节,根据这个目的,HL就算是arbitrage-free的模型了。

其实也有点你说的那个意思,就是套利模型中,市场利率是一个决定因素(算是输入变量,只不过是作为参考为主),我们的模型最终目的是让模型的结果接近市场利率。而均衡模型则不考虑当前市场利率是什么情况。

3.根据上述那个目的,我觉得不同同时既是X又是Y。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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