Consider a financial model where one can borrow and lend money at year i and up...

 

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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, Sx at time i becomes $x(1 + R(i, i + 1)) at time i + 1. The values R(i, 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 R(i-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. 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, Sx at time i becomes $x(1 + R(i, i + 1)) at time i + 1. The values R(i, 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 R(i-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.

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ANS WER The arbit rage free price of the note at time zero is P 0 N R 0 1 N R 1 2 N R 18 19 N R 19 2... View the full answer