Problem 4. Consider an option on a stock when the stock price is $41, the strike price is $40, the risk-free rate is 6%, the volatility is 35%, and the time to maturity is 1 year. Assume that a dividend of $0.50 is expected after six months. 1. Use DerivaGem to value the option assuming it is a European call. 2. Use DerivaGem to value the option assuming it is a European put. 3. Verify that put-call parity holds. 4. Explore using DerivaGem what happens to the price of the options as the time to maturity becomes very large. For this purpose assume there are no dividends. Explain the results you get.