Would the price of the put option be higher, lower, or the same as the answer you obtained in part (a) if the probabilities of the index rising and falling were 60% and 40%, respectively (instead of 70% and 30%, respectively)? Assume the current index price, the risk-free rate, and the strike price are unchanged. [No need for any calculations here. A brief explanation will suffice.) (4 points) 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. (12 points) Payoff of 4200 put option 4410 0.7 U200 0-3 3990 = 4200-3990 = 210 $400 ) 3800 0.3 3610 = 4200-3610 590 Price of European put option 210 (03X0-7+ 0.7X0.3) B 590 (0:3X03) 210 X 0.42 +590x 0.09 $141.30