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410140980 · 2022年10月08日

二叉树利率有负的时候做的调整

NO.PZ2018122701000065

问题如下:

A risk manager is pricing a 10-year call option on 10-year Treasury using a successfully tested pricing model. Current interest rate volatility is high and the risk manager is concerned about the effect this may have on short-term rates when pricing the option. Which of the following actions would best address the potential for negative short-term interest rates to arise in themodel?

选项:

A.

The risk manager uses a normal distribution of interest rates.

B.

When short-term rates are negative, the risk manager adjusts the risk-neutral probabilities.

C.

When short-term rates are negative, the risk manager increases the volatility.

D.

When short-term rates are negative, the risk manager sets the rate to zero.

解释:

D is correct.

考点 Interest Rate Tree (Binominal) Model

解析 Negative short-term interest rates can arise in models for which the terminal distribution of interest rates follows a normal distribution. The existence of negative interest rates does not make much economic sense since market participants would generally not lend cash at negative interest rates when they can hold cash and earn a zero return. One method that can be used to address the potential for negative interest rates when constructing interest rate trees is to set all negative interest rates to zero. This localizes the change in assumption s to points in the distribution corresponding to negative interest rates and preserves the original rate tree for all other observations. In comparison, adjusting the risk neutral probabilities would alter the dynamics across the entire range of interest rates and therefore not be an optimal approach.

When a model displays the potential for negative short-term interest rates, it can still be a desirable model to use in certain situations, especially in cases where the valuation depends more on the average path of the interest rate, such as in valuing coupon bonds. Therefore, the potential for negative rates does not automatically rule out the use of the model.

老师这道题针对利率为负进行调整,解析给出两个方法,第二个我没看懂是怎么做的。能解释一下吗

1 个答案
已采纳答案

李坏_品职助教 · 2022年10月08日

嗨,爱思考的PZer你好:


In comparison, adjusting the risk neutral probabilities would alter the dynamics across the entire range of interest rates and therefore not be an optimal approach. 这个就是第二种方法。这个意思是调整风险中性概率会改变整个利率二叉树的进程,不是最佳方法。


如果risk neutral rate被改变了,那么原来那些positive的利率值也全都被改变了。最好的办法应该是把negative values调整到合适的水平(比如0),尽量少改变利率二叉树的过程。

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NO.PZ2018122701000065 这题不懂,麻烦解答,谢谢

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NO.PZ2018122701000065 这题没看懂,麻烦解答一下

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