Risk-free investment strategy for european call and put option

Question

I have some trouble solving the following question:

We have an european call and put option (with the same maturity date $T$ en strike $E=10$). The stock price now is $S=11$ and we use a continuous compound interest of $r=0.06$. Determine, using the put-call parity, an investment strategy to accomplish a risk-free profit based on the arbitrage principle if both options have value $V=2.5$

I cannot figure out how to approach this problem. The put-call parity alone does not seem to solve this problem. Help is very much appreciated.

Answer 1

The left hand side $(C-P)$ of the put-call partity equation provides the same pay-off as the right hand side $(S-K\times e^{-rT})$. Determine (by filling in the numbers) which part of the equation is relative cheap e.g. $(C-P) < (S-K\times e^{-rT})$. If this is the case, sell the $(S-K\times e^{-rT})$ and use the funds from selling to buy $(C-P)$. The pay-off from $C-P$ can be used to settle $(S-K\times e^{-rT})$ at maturity, the profit from initial selling and buying is the profit.