Question 5 [29 points]. Consider the riskeneutml HoLee model for continuously compounded rates for t = 0. 1. 2 and a step size of A = 0.25 year (today is denoted by time 0): m = 0.03 n = To + 0.01 + 0.02 5; r1 + 0.015 +0.02 s; T2 where, under the riskrneutral measure: the shocks 5: (t = 1.2). which are independent and identically distributed: are given by +1 with probability 0.5 71 with probability 0.5 1. [5 points] What is the price of a Qemonth nonecallable bond with principal 100 and an annual coupon rate of 8%? (To be precise= the coupons are paid at times t : 1. 2. 3, quarterly; while the principal repayment is at time t = 3). 2. [8 points] Now suppose that the above bond is callable. What is the value of the callable bond? 'What is the value of the implicit call option? In which nodes will the bond be called (assume no call option initially)? 3. [6 points] Compute the initial price of a 6month Asian interest rate call option with a strike of 'T'K = 0.04 and a notional amount of N = 100. That is. the payoff of this rn+r1+m 3 4. [2 points] 'What is the spot rate duration of the Asian option at t = 0? option is given by N x mad 1'33 0) and is paid at t = 2. 5. [8 points] Consider a @nionth Eurodollar futures. The underlying nal cash payment is: 6month LIBORX N. N = 100 is the contract size. The rates given in the Ho Lee interest rate tree= {rm}. are continuously compounded; whereas the LIBOR rate with a given maturity is in the Eurodollar futures is instead linearly compounded} i.e., L-IBOH(k.j) : i x (ermxe' 1). In the example. the 5month Eurodollar futures has I; = 0.5. Compute the futures price. (Hint: you may want- to use the convergence property and the law of iterated expectations of futures.)