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I Consider a compound put option On a put OptiO (put on a put) which gives the right to sell at time T1 > 0 a put optiOn for a price K1. The underlying put option is written on a stock with strike price K2 and maturity T2 > T1. The simplest model for pricing a compOund put option is a two-step binomial tree model with time steps T1 and T2. Use a two-step binomial tree model to compute today's (t = 0) arbitrage-free price of a put on a put with T1 = 1 and T2 = 2 (measured in years). The current stock price is 80 = $50 and over each of the next two One-year periods it is expected to go up by 20% or down by 20%. The strike price of the put option on the stock (with maturity T2 = 2) is K; = $52, and the strike price of the compound put option 0n the put option (with maturity T1 = 1) is K1 = $5. Assume that the risk-free interest rate is 5% per annum. 2. A stock price is currently selling at $100. Over each of the next two 6-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate for each of these six months is 8%. (a) Using a two-step tree, compute the parameters K and 0 of the payoff function f(ST, K) = 0(ST - K)? that define the financial derivative d with initial cost do = $3.5 at time 0. [1.75 marks]. (b) If the derivative is American-style, should it be exercised early? [1.75 marks]. (c) Do the payoffs of this derivative share the insurance properties of call and put options? Explain your answer. [0.5 marks]. (d) Under which conditions on the terminal stock price will this financial derivative be a good investment strategy? [0.5 marks].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)