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六姑娘 · 2021年09月01日

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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.

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1 个答案

李坏_品职助教 · 2021年09月02日

嗨,努力学习的PZer你好:


这道题目说的是一个经理正在对10年期的国债的call option进行定价。当下的利率波动性非常大,这个经理很担心出现负的利率对于他的定价模型会有什么不利的影响。题目让我们选出哪一项可以解决负利率对于模型的不利影响?


A项的normal distribution尤其容易收到负利率negative interest rate的不利影响,所以不能选A。


B项:如果经理调整了风险中性概率,那么整个利率的期限结构以及interest rate tree决策树都会被改变,为了应付一个负利率而调整整个模型,这是不合适的。


C项:其实C的缺陷和B类似,都是会改变整个利率模型,是不合适的


D项:把负利率在模型里强制设为0,既保留了模型原本的结构,又避免了负利率对模型的不利影响,正确~


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