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Exercise 1[15 points] We consider a two-period binomial tree to model interest rates. The time step dt is 1 year. We know that ro - 1%, u - 1.1 and d = 1/u. Let p represent the probability of an upward movement. We assume p - 0.5 (Black-Derman-Toy). Coupons are annual. We adopt the following notations for bond prices in the tree: t=1 t-2 Puu(2,2) Pu. (1,2) P(0,2) Pud (2, 2) Pa(1,2) Pad (2, 2) . Question 1 3 points): What is the price at ? = 0 of a two year 5% bond with a face value of $1000 ? Detail your answer by giving all the values inside the tree. . Question 2 [4 points]: What is the price at t = 0 of a two year zero coupon bond with a face value of $1000 ? Detail your answer by giving all the values inside the tree. . Question 3 4 pointa): Find the price at t = 0 of a put option on the bond of Question 2, with maturity 7 = 1 and strike K = $990. . Question 4 [4 points]: Find the price of a floorlet on the bond of Question 2, with maturity 7 -1 and floor rate K, = 1%. We recall that the payoff for this security is P(1, 2) X (K, - r).Max has a lot of data from stochastic process: (17 = 0.983}t_1 + (it 0.1.63-1 where 5t N N (0, 0'2) are Gaussian white noise. He tests for a unit root and mistakenly decides that the stochastic process is integrated of order 1. He then differences the data to obtain yt = A3: . A} Write out the ARMA model for 3,1,; . [2 points] B) If you were to t an ARMA model to 3;; ,what would the order of the AR and MA components be? [2 points] C) Is it; causal? [1 point] D) Is the ARMA model for y: stationary? [1 point] E} Is the ARMA model for y: invertible? [2 points] F] Knowing the ARMA model for yt = Amt , would you expect the ACF for y; , to cut off abruptly after 2 lags? Explain why. [1 point] G} Knowing the ARMA model for yt = Amt , would you expect the PACF for gt , to cut off abruptly after 1 lag? Explain why. [1 point] 1. Answer all questions: (a) ASHEEKA LTD. has annual turnover of