The S&P 500 index price is currently standing at 4,000. Its volatility is 20% per annum, the risk-free interest rate is 5% per annum, and the dividend yield on the S&P 500 index is 3% both continuously compounded. Consider a long put option on S&P 500 index, expiring in six months, with a strike of 3,600. 1) When will the option be exercised? If the option is European, what is its Black/Scholes price of the put index option? 2) Use a two-step binomial tree to calculate the value of the European put options on the S&P 500 index. What positions in the index are necessary to dynamically hedge the European put option? 3) If the option is American, based on the two-step binomial tree, is it optimal to exercise the option earlier? Provide two reasons for the early exercise.