Hi, please help me with these questions. Thank you in advance!

1. The following binomial tree for the stock price has some missing prices. Please fill in the (relevant) missing prices. Assume that interest rates are zero. Stock Tree n=1 n=2 n=3 n=4 2. Suppose you were using the tree in (11 above to price a strangle of strikes 100 and 101. Fill in the values in the binomial tree below to estimate of the price of the strangle. 3. Consider the following tree for a 1-year European put. The stock price is today is 100 and the strike is 99. European Put Tree n=1 n=2 n=3 n= a. Interest rates in the economy are 5%. What would be the price of the American put? b. After the financial crisis, we observed negative interest rates. Suppose, the interest rate is -5% (negative 5%). (L) Would the European put price be higher or lower than the European put in (a) above? (ii.} Is the American put more or less valuable than the European put? * **Formula: T = time to maturity in years N = number of steps in the binomial tree t = time between each step in the binomial tree = T/N u = exp(volatility x sqrt(t)) d = 1/u R = exp(r t) q = (R-d)/(u-d) Note: exp(r t) = erxt