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六姑娘 · 2021年09月01日

求解

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.

这题不懂,麻烦解答,谢谢

1 个答案

DD仔_品职助教 · 2021年09月01日

嗨,从没放弃的小努力你好:


同学你好~

这道题问,有个风险经理在给一个10年期的call option定价,这个call option的基础资产是10年期的国债。当前的利率水平波动非常大,这个风险经理但心在为这个期权进行定价的时候,会因为短期的利率水平受到影响。问下面哪个选项最好的解决,在使用模型时短期利率是一个负数?

这个题说了一大堆,但其实是在考一个期权定价时默认的规则:给期权进行定价的时候,如果碰到利率是负数时(一般情况利率都是正数),直接将这个负数利率用0代替就可以。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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