Question

The price of a call option with a strike of $100 is $10. The price of a put option with a strike of $100 is $15. Interest rates are 0 and the current price of the underlying is $105. Can you make an arbitrage profit? If so how? Describe the trade and your pay offs in detail

Answer 1

As the interest rate is 0, the price of the call option should be =(105-100)=$5 but here the price $10 and it is overpriced

The price of put option should be =(105-100)=$5 but here the price is $15 and it is overpriced.

So, you need to short both call and put option. As you are shorting call, you need to take long position in spot underlying security and you are also shorting put. Hence, you also need to short in future/forward market to hedge the short put position (You can not take short position in spot market as you already taken long position to hedge short call).

Hence, your total payoff would be= Profit from call+ Profit from put

=(10-5)+(15-5)=$15