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Problem 1: Consider a financial model where one can borrow and lend money at year i and up to year i +1 at the interest rate R(i,i + 1). That is, $x at time i becomes $x(1 + R(i,i + 1)) at time i + 1. The values Ri, i + 1) are potentially random and not known until year i. Consider a float note which has notional N = $1000, maturity T = 20 years, and, in addition to the notional payment at maturity, pays a coupon yearly. The value of the coupon paid at time i +1 is computed at time i and is given by N.R(i,i+1). That means that the float note has a cash-flow that pays N Ri - 1, i) at years i = 1, 2, ...,19, while at year i = 20, the float note pays N R(19, 20) + N. Compute Vo, the arbitrage-free price of the note at time zero. HINT: Start by thinking about a replicating strategy that starts with N in the bank. At year i = 1, the account has accrued interest and is valued at N:(1+R(0,1)). Now change up your strategy at year 1- take N R(0,1) out of the bank (in order to replicate the float note pay-off at i = 1), and keep the remaining N in the bank and hold until the next year. Problem 2: A textile company in North Carolina requires N = 500,000 lbs of cotton for its production after 2 months. It has 2 choices: Choice 1. Purchase the cotton now at the spot price S(0) = 45 cents per pound and store it for T = 2 months at annualized monthly storage cost q(12) = 1 cent per pound. In other words, at the end of each month the company will have to pay q(12)/12 cents per pound of stored cotton. Choice 2. Use put and call options on cotton with delivery T = 2 months to acquire N pounds of cotton at time T. The current value of the strike where the prices of put and call options coincide is K = 46 cents per pound. Compute the costs (at initial time) of both strategies and make your recommendation assuming that the annualized monthly interest rate r(12) = 12% (interest per month is r(12)/12 = 1%)

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