Problem:
A European put option on St. Paul Insurance (SPC) with a strike price of $40 and 1 year to expiration is trading at a price of $2. A European call option on SPC with a strike price of 40 and 1 year to expiration is trading at a price of $15. The risk-free interest rate is 5.129329% per year, compounded continuously (the present value of risk-free dollar to be received in one year is $0.95). If that the market price of SPC's stock is $50 per share, determine whether there is an opportunity to make a risk-free profit.
[Hint: If the prices above are not consistent with put-call parity, sell the overpriced security and hedge by purchasing the low-price substitute.]