Consider a European put option on a non-dividend-paying stock $50, the strike price is $50, the risk-free rate is 4% per annum, the volatility is 35% per annum, and the time to maturity is 1 year. (Answer questions 3-7) 3. What is the percentage up movement for a two-step binomial tree? A. 28.08% B. 78.08% C. 128.08% D. 178.08% 4. What is the risk-neutral probability of a down movement for a two-step binomial tree? A. 0.4788 B. 0.8512 C. 0.1488 D. 0.5212 5. What is the value of this European put option using a two-step binomial tree? A. 9.972 B. 5.094 C. 7.521 D. 8.146 6. If the put option is American, all the other information remains the same, would it ever be optimal to exercise it early at any of the nodes on the two-step binomial tree? (The notations for the nodes are the same as discussed in the lecture notes)

Consider a European put option on a non-dividend-paying stock we polatility is 35% per $50 the strike price is $50, the risk-free rate is 4% per annum, the vor. $50, the strike price is $50, the risk-free rate is 4% per annum, the annum, and the time to maturity is 1 year. (Answer questions 37 ) 3. What is the percentage up movement for a two-step binomial tree? A. 28.08% B. 78.08% C. 128.08% D. 178.08% 4. What is the risk-neutral probability of a down movement for a two-step binomial tree? A. 0.4788 B. 0.8512 C. 0.1488 D. 0.5212 5. What is the value of this European put option using a two-step binomial tree? A. 9.972 B. 5.094 C. 7.521 D. 8.146 6. If the put option is American, all the other information remains the same, would it ever be optimal to exercise it early at any of the nodes on the two-step binomial tree? (The