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张书记 · 2022年10月18日

上涨概率

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000066

问题如下：

A 2-year zero-coupon bond with a face value of USD 1,000 is currently priced at USD 952.48. The firm uses a binominal pricing model with a 1-year time step for all of its valuations. If interest rates go down over the next year, the model estimates the bond’s value to be USD 970, and if interest rates go up over the next year, the model estimates the bond’s value to be USD 950. Using the risk-neutral probabilities implied by the model, and assuming the risk-free rate of interest is 1% per year, what should be the current value of a 1-year European call option on this bond with a strike price of USD 960?

选项：

A.

USD 3.96

B.

USD 5.94

C.

USD 6.00

D.

USD 9.90

解释：

B is correct.

考点 ： Interest Rate Tree (Binominal) Model

解析：假设价格上涨的概率为πu ，价格下跌的概率为πd =1- πu

[970*πu +950*（1-πu ）]/(1+1%)=952.48，求出πu=60%,πd =40%.

对于欧式看涨期权，执行价格为960，所以C+ =max(970-960,0)=10, C- =max(950-960,0)=0.

于是C0 =(10*60%+0*40%)/(1+1%)=5.94

这里面的上涨概率为什么不用 u−d1+r−d​ 

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DD仔_品职助教 · 2022年10月19日

嗨，爱思考的PZer你好：


同学可以看我下图写的推到，上面的回答里写的是利用复利来求，单利也是一样的，求出来的结果一致

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

DD仔_品职助教 · 2022年10月19日

嗨，努力学习的PZer你好：


同学你好，这列求法是一样的，答案也是一样的，如果用你写的这个公式计算的话，如下：

u=970/952.48=1.0184

d=950/952=0.9979

p上升概率=(e^rf-d)/(u-d)=(e^1%-0.9979)/(1.0184-0.9979)=0.01215/0.0205=60%

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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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