Suppose that you have an American call option on a dividend-paying stock. The stock price is $50, the time to maturity is 6 months, the risk-free interest rate is 8%, the option exercise price is $55, and the volatility is 25%. Dividends of $1.50 are expected in 4 months and in 10 months. a) Show whether it is optimal to exercise the option before maturity. Calculate the price of the option. ( 6 marks) b) While the volatility is provided in this problem, in many real life scenarios you would have to estimate it yourself. Explain how you can estimate the volatility parameter used in the Black-Scholes model using a self-made example. ( 3 marks)