From my understanding the solution should be C. After buying the undervalued call option, the trader should sell the replicating portfolio i.e short sell the stock through lending. Im unsure why they chose A, unless the question stem saying “hedge it with replicating trades” means that they’ll replicate the call option payoffs, which doesn’t make sense to do as a hedge.
If someone can explain I’ll appreciate it. Thanks
You can construct a portfolio c-hS which will have the same value whether the stock goes up or down, so that
c^{+}-hS^{+}=c^{-}-hS^{-} which gives h=\frac{c^{+}-c^{-}}{S^{+}-S^{-}}.
This is the value of h in A) and C) but not B).
They tell you the option is undervalued by the market, so you can make free money.
If the option were fairly priced, then the price would be hS+\textrm{PV}(c^{-}-hS^{-}) as they say
My answer wouldn’t be any of them.
I would short sell h units of the underlying and BORROW \textrm{PV}(c^{-}-hS^{-}).
That would give you the premium hS+\textrm{PV}(c^{-}-hS^{-}) of a fairly priced option.
The option is undervalued, so the premium would be less than this, so you pocket the difference.
After one time period, you get the option payoff, close out the short and repay the loan.
You already have cash from the short sale. Why would you borrow more? That’ll cost you interest.
Lend what you have.
Looks like they blew it.
I think we’re solving slightly different problems.
I misunderstood the question and assumed we needed to buy the option which is why I borrowed money.
Thank you for the confirmation. I was beginning to doubt my comprehension of this topic
