a three binomial tree BT3 is defined by the following parameter vector: (s₀, r, d, u, n)= (34, 0.2, 0.91, 1.07, 3)

r = risk-free interest rate = 0.2%. if this interest rate violates the no-arbitrage condition, divide by factor 2 and document this step.

a) calculate the risk-neautral probability of a downward movement

b) calculate the payoff profile of a european put option with the exercise price, K=34.50.

c) Price the European put option of b)

d) what is the value of the Put option, if the stock realised an downward movement from t=1 to t=1

e) Price an American Put option with exercise price, K=35.00

f) reconsider subquestion d) and argue with risk neutral probabilities if the price would be expected to increase or decrease in this situation