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Shuangshuang · 2024年08月03日

equilibrium models

NO.PZ2023100703000085

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:

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.

是除了Model 1 都是equilibrium models么

2 个答案
已采纳答案

品职答疑小助手雍 · 2024年08月03日

同学你好,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,而ho-lee这么做了,根据这个目的,它是无套利的。

不过我觉得根据原版书说的,根据这些模型的公式本身是推不出均衡还是无套利的,只能加个目的来约束模型的性质,目前看到只有ho-lee是无套利的。

它甚至还说model2是均衡,但model2形成的过程是无套利,感觉加的这个目的还是挺模糊的,我觉得只能硬记ho-lee是无套利,其他是均衡的了。(除非你翻到原版书还有啥别的发现)

品职答疑小助手雍 · 2024年08月04日

是的

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