The one-month interest rate is 4% and the two-months interest rate is 4.1%. We know that one month from now the one-month interest rate will be either 3.5% or 4.5%. All rates are annual. All bonds have a face value of $100. Question 1 [2 points] Compute the current price P(0, 2) of the two-month bond. Question 2 [4 points] Compute the two possible prices, P1(1, 2) and P2(1, 2), that the one-month bond will take, one month from now. Question 3 [2 points] Explain in a few words the relationship between P(0, 2), P1(1, 2) and P2(1, 2). (Hint: one month from now, the two-months bond will be a one-month bond.) Question 4 [4 points] Deduce from the previous questions the risk neutral probability in our model. Question 5 [3 points] Compute the current price of an interest rate derivative that pays $1 in one month if the one-month interest rate is 4.5% and $0.5 in one month if the one-month interest rate is 3.5%

Exercise 5 [15 points] The one-month interest rate is 4% and the two-months interest rate is 4.1%. We know that one month from now the one-month interest rate will be either 3.5% or 4.5%. All rates are annual. All bonds have a face value of $100. Question 1 (2 points] Compute the current price P(0, 2) of the two-month bond. Question 2 (4 points] Compute the two possible prices, P1(1, 2) and P2(1, 2), that the one-month bond will take, one month from now. Question 3 (2 points] Explain in a few words the relationship between P(0,2), P1(1, 2) and P2(1,2). (Hint: one month from now, the two-months bond will be a one-month bond.) Question 4 (4 points] Deduce from the previous questions the risk neutral probability in our model. Question 5 [3 points] Compute the current price of an interest rate derivative that pays $1 in one month if the one-month interest rate is 4.5% and $0.5 in one month if the one-month interest rate is 3.5%