investing proceeds in call option

问题如下：

You realize that the six-month put option on CWI shares is overpriced relative to the no-arbitrage price from Question 2. Which of the following statements best describes the steps you would take to earn a riskless arbitrage profit under this scenario?

选项：

A.Sell the six-month put option and sell CWI short, investing the proceeds in a call option and a risk-free bond.

B.Sell the six-month put option, buy a call option, and borrow at the risk-free rate to buy CWI shares.

C.Sell the six-month put option, buy a call option, enter a forward purchase of CWI, and invest in a risk-free bond.

解释：

The correct answer is A. Since the put option is overpriced, we would sell it to earn the difference between the price at which it is sold and the no-arbitrage price. The put–call parity relationship, from Equation 1, is

S₀ + p₀ = c₀ + X(1 + r)^–T.

We can rearrange this to demonstrate that the put option value is equivalent to a long call option, a long risk-free bond, and a short position in CWI shares:

p₀ = c₀ + X(1 + r)^–T – S₀.

Answer A reflects this long risk-free bond and short CWI combination, which has a payoff of X-S_T at expiration matching that of the put payoff, whereas Answer B involves a long cash position in CWI and Answer C involves a long synthetic (forward purchase) position in CWI stock.