a. The S&P 500 index is currently priced at $4,000. The index will either increase or decrease by 5% each month (so next month the index will be worth either $4,200 or $3,800 and in two months the index will be worth either $4,410, $3,990, or $3,610. The probability of the index increasing each month is 70%, and the probability of the index decreasing is 30%. The current risk-free rate is 0% per year, compounded continuously. Use the binomial model to calculate the current price of a European put option with a strike of $4,200 that expires in two months