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台风来了 · 2023年02月03日

欧式看涨期权定价公式，上下限如何推导的？为什么St不用折现？

  1. CFA I
  2. Derivative

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, 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：

中文解析：

计算如下：

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

欧式看涨期权定价公式，上下限如何推导的？为什么St不用折现？

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1 个答案

Lucky_品职助教 · 2023年02月04日

嗨，从没放弃的小努力你好：


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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