为什么ct upper bound是102

NO.PZ2021061002000065

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, S_t, trades at CAD102.

Which of the following calculations of the upper and lower bounds of the call option is correct?

选项：

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

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

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

解释：

中文解析：

计算如下：

c_{t,Lower bound} = Max(0, S_t − X(1 + r)^−(T^−t) ) = Max (0, 102 – 100(1+2%)^-0.5) = CAD2.9852

c_{t,Upper bound} = S_t= CAD102

为什么ct upper bound是102呢

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Lucky_品职助教 · 2023年08月17日

嗨，努力学习的PZer你好：

期权的定价一般用BSM模型，你的疑惑点应该是答案中的公式，这个公式是“now six months have passed”这个时点，也就是在6个月这个小t 时刻求value，那就是用市价和“行权价折现到t时点”的差，与0相比，因此St是不需要折现的，当下就是t时点

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加油吧，让我们一起遇见更好的自己！

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为什么ct upper bound是102

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