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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

最好能帮忙用画图大法分析一下或者哪里有讲解我去听

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1 个答案

pzqa35 · 2024年03月02日

嗨，爱思考的PZer你好：

这个是期权的上线限哈，这个直接带入公式计算即可：

对于期权来说，因为期权的价值=intrinsic value + time value，并且在到期之前time value都是大于等于0的，所以期权的价值都是大于intrinsic value的，这是期权的下限。

而对于看涨期权来说，long方就是约定未来以X的价格来购买标的资产的权利，假设现在市场上的价格是10块钱，那我是不可能以超过10块钱的价格来购买看涨期权的，因为这样的话还不如直接在市场上直接买，所以这就决定了看涨期权的价格上限是不能超过 St的。

这个讲解同学可以听基础班M8Arbitrage and Replication这节课开头部分，老师有很详细的一个讲解哈。

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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 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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有点迷惑还希望细解答一下