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Danlei · 2021年11月20日

为何不选A

  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

在计算向上概率和向下概率时，利率向下概率对应的是970，利率向上概率对应的是950。

在计算call value时，为什么10（即利率向下那一支对应的call的payoff）对应的概率却是向上的概率呢？

请老师解答。

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李坏_品职助教 · 2021年11月20日

嗨，从没放弃的小努力你好：


答案里面的π_u 对应的是bond价格上涨的概率，也是C加号 对应的10的概率。

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努力的时光都是限量版，加油！

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