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Enno · 2021年08月02日

题干里写的是int rate goes down的价格是970，那么C1-才是10吧？是不是应该用πd=40%来算，最后选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

如题，感觉应该选A吧

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1 个答案

品职答疑小助手雍 · 2021年08月02日

嗨，爱思考的PZer你好：


算出来的概率是债券价格上涨的概率，不是利率上升的概率。

bond上涨概率是60%，所以答案没错。

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