哪里看出来用成本？

NO.PZ2023040401000098

问题如下：

According to put–call–forward parity, the difference between the price of a put and the price of a call is most likely equal to the difference between:

选项：

forward price and spot price discounted at the risk-free rate.

spot price and exercise price discounted at the risk-free rate.

exercise price and forward price discounted at the risk-free rate.

解释：

Put-call-forward parity can be written as:

p₀ – c₀ = [X – F₀(T)]/(1 + r)^T

This means that the difference between the price of a put and the price of a call is equal to the difference between exercise price and forward price discounted at the risk-free rate.

A is incorrect. Neither put–call parity nor put–call–forward parity support this interpretation.

B is incorrect. Neither put–call parity nor put–call–forward parity support this interpretation.

老师解析时说要算成本，为什么？题目哪里看得出？

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1 个答案

李坏_品职助教 · 2025年01月26日

嗨，努力学习的PZer你好：

老师的意思是，为了保持“put–call–forward parity”等式左侧和右侧的一致性，左侧和右侧都要从成本的角度进行计算。

从构造资产组合的成本的角度去考虑问题，比如你花费p元买入了看跌期权（put option），又以c元的价格卖出看涨期权（call option），那么这个资产组合的成本为p - c，这个就是等式的左侧成本。

为了保持一致，等式右侧也要从成本来考虑，买入无风险债券（到期收回的面值为X，当前的买入成本为X/(1+r)^T），并且做空forward，成本为-F(T)/(1+r)^T，所以等式右侧的资产组合成本 = X/(1+r)^T - F(T)/(1+r)^T。

左侧的成本 = 右侧的成本，即可组成put–call–forward parity公式。

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