Problem: A European call option and put option on a stock both have a strike price of $30 and an expiration date in three months. Both sell for $5. The risk-free interest rate is 6% per annum, the current stock price is $28 and a $1 dividend is expected in 2 months. Identify the arbitrage opportunity open to the trader.
Q1: To do this, take one of the option prices as correct and invoke the appropriate put-call parity to determine the arbitrage-free price of the other option.
Q2: Is the arbitrage-free price less than, greater than, or equal to the market price?
Q3: What strategy would lock in the gain from the apparent mispricing? What are your net profits in 2 months and at the expiration?