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六姑娘 · 2021年11月17日

这题四个选项能都解释一下吗

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.

还是不太懂,麻烦解答一下

1 个答案

李坏_品职助教 · 2021年11月17日

嗨,从没放弃的小努力你好:


题干说的Model 1是没有漂移项drift的(Drift其实就是μ),model 2加入了drift。让你选出描述错误的选项。


model 1因为是没有Drift,是随机波动的,所以短期利率有可能是负数,这是他的缺陷。所以A正确。


Model 1完全是基于短期利率的波动去预测interest rate的,和term structure没关系,所以B错误。


model 2因为包含了drift,等于是在随机波动的基础上有一个向上走的趋势项,所以model 2正常情况下会产生向上倾斜的期限结构,C正确。


model 2没有用到初始的市场定价(市场利率)的数据,而是假定利率符合某种趋势,服从某个走势,然后推导出利率的期限结构。所以model 2不是无套利定价的模型, D 正确

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