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粉红战狼 · 2022年04月20日

风险中性概率的公式是在一级哪里学过的啊，不太记得了。二级还会再考吗？

  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

我怎么记得分母是u-d的啊

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2 个答案

DD仔_品职助教 · 2022年04月21日

嗨，努力学习的PZer你好：


前提条件是u=1/d，图里的assumption第三个。

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DD仔_品职助教 · 2022年04月21日

嗨，努力学习的PZer你好：


这不是一个类型的题，你说的分母是u-d是股票价格上升的概率，u和d是股价上升幅度，然后求上升概率，一级学过如下图


用上面的共是有前提条件，d=1/u

这题d明显不等于1/u,所以不能用


这里是直接设上升概率是πu

股价上升970，概率是πu，下降是950概率是1-πu

这俩预期值是970*πu+950*（πu）

然后折现到0时刻是价格952.48

反求出πu

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