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Yvonne0719 · 2024年10月08日

请问一下这里的r是一整年的，为什么不用除以2呢？

  1. CFA I
  2. Derivative

NO.PZ2023040401000080

问题如下：

Suppose the strike price of a one-year call option is CAD100, the risk free rate is 2%. At time 0, the underlying asset, S0, trades at CAD98, now six months have passed, the underlying asset, St, trades at CAD102. Which of the following calculations of the upper and lower bounds of the call option is correct?

选项：

A.

The upper bound of the call option is CAD102; the lower bound of the call option is 0.

B.

The upper bound of the call option is CAD102; the lower bound of the call option is CAD2.9852.

C.

The upper bound of the call option is CAD2.9852; the lower bound of the call option is 0.

解释：

ct,Lower bound = Max(0, St − X(1 + r)−(T−t)) = Max (0, 102 – 100(1+2%)-0.5) = CAD2.9852

ct,Upper bound = St = CAD102.

请问一下这里的r是一整年的，为什么不用除以2呢？

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李坏_品职助教 · 2024年10月09日

嗨，从没放弃的小努力你好：


因为“半年”是体现在T里面，T=0.5就行了。 这个是复利的算法，不需要r除以2.


r是一年的利率，时间只有半年，所以（1+r）^(-0.5)，这就是半年的复利折现。


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李坏_品职助教 · 2024年10月08日

嗨，从没放弃的小努力你好：


期权的计算用的是复利形式，也就是(1+r)^T，因为距离到期还剩半年，所以这个T用0.5。


既然T已经用了半年的，那么r就不需要再除以2了。

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Yvonne0719 · 2024年10月08日

我的问题是关于r的部分，因为给出的r是年化利率，这里只有半年到期了，为什么不用把r除以2？

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