# Risk-free investment strategy for european call and put option

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.

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## 1 Answer

The left hand side (C-P) of the put-call partity equation provides the same pay-off as the right hand side (S-K*e^(-rT)). Determine (by filling in the numbers) which part of the equation is relative cheap e.g. (C-P) < (S-K*e^(-rT)). If this is the case, sell the (S-K*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*e^(-rT)) at maturity, the profit from initial selling and buying is the profit.

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