为什么不用98

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

可以讲一下为什么不用98而用100吗，我理解的100是面值，t=0时刻的价值不是98吗

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1 个答案

李坏_品职助教 · 2024年09月08日

嗨，爱思考的PZer你好：

100是strike price，也就是执行价格。意思是在1年后（到期日的时候），期权的买方有权利按照100的价格的执行价格从对方手里买入一份underlying asset。

题目说现在是six months have passed，也就是现在已经不是0时刻了，而是6个月之后了。那么计算当前期权价格的“upper and lower bounds ”，自然也要用当前的underlying asset的价格St （就是102）。

而98是0时刻的underlying asset的价格，已经过时了，没有用。

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NO.PZ2021061002000065问题如下 Suppose the strike priof a one-yecalloption is CA00, the risk free rate is 2%. time 0, the unrlying asset, S0,tras CA8, now six months have passe the unrlying asset, St,tras CA02. Whiof thefollowing calculations of the upper anlower boun ofthe call option is correct? A.The upper bounof the call option is CA02;the lower bounof the call option is 0;B.The upper bounof the call option is CA02;the lower bounof the call option is CA.9852;C.The upper bounof the call option is CA.9852; the lower bounof the call option is 0; 中文解析计算如下ct,Lower boun = Max(0, St − X(1 + r)−(T−t) ) = M(0, 102 – 100(1+2%)-0.5)= CA.9852ct,Upper boun= St = CA02 为什么T-t是0.5

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