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hhhwdk · 2024年04月11日

这个题解析有点形而上

NO.PZ2023100703000081

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 the model?

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:

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.

能不能有更清晰的解析说明呀,谢谢!

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pzqa39 · 2024年04月11日

嗨,努力学习的PZer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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加油吧,让我们一起遇见更好的自己!

hhhwdk · 2024年04月12日

感谢,回去翻了知识点,确实

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NO.PZ2023100703000081问题如下A risk manager is pricing a 10-yecall option on 10-yeTreasury using a successfully testepricing mol. Current interest rate volatility is high anthe risk manager is concerneabout the effethis mhave on short-term rates when pricing the option. Whiof the following actions woulbest aress the potentifor negative short-term interest rates to arise in the mol?A.The risk manager uses a normstribution of interest rates.B.When short-term rates are negative, the risk manager austs the risk-neutrprobabilities.C.When short-term rates are negative, the risk manager increases the volatility.When short-term rates are negative, the risk manager sets the rate to zero.Negative short-term interest rates carise in mols for whithe terminstribution of interest rates follows a normstribution. The existenof negative interest rates es not make mueconomic sense sinmarket participants woulgenerally not lencash negative interest rates when they cholcash anearn a zero return. One methothcuseto aress the potentifor 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 stribution corresponng to negative interest rates anpreserves the originrate tree for all other observations. In comparison, austing the risk neutrprobabilities woulalter the namiacross the entire range of interest rates antherefore not optimapproach.When a mol splays the potentifor negative short-term interest rates, it cstill a sirable mol to use in certain situations, especially in cases where the valuation pen more on the average path of the interest rate, suin valuing coupon bon. Therefore, the potentifor negative rates es not automatically rule out the use of the mol.A为什么不对zzzzz

2024-08-01 23:39 1 · 回答