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# John Hull Question 7.23

#### San955

##### New Member
Hi, I have been trying to solve exercise 7.23 from John Hull, edition 10th, but somehow the solution for valuation in terms of bonds and in terms of FRAs is not the same! In John Hull solution only the valuation in terms of FRAs is given which I have the same, but the ones in bonds is not correct. Do you have a solution of this problem?

Problem 7.23: In an interest rate swap, a financial institution has agreed to pay 3.6% per annum and to receive three-month LIBOR in return on a notional principal of $100 million with payments being exchanged every three months. The swap has a remaining life of 14 months. Three-month forward LIBOR for all maturities is currently 4% per annum. The three-month LIBOR rate one month ago was 3.2% per annum. OIS rates for all maturities are currently 3.8% with continuous compounding. All other rates are compounded quarterly. What is the value of the swap? Solution: We can value the swap as a series of forward rate agreements. The value in$ millions is:

(0.8 – 0.9)e^-0.038×2/12 + (1.0 – 0.9)e^-0.038×5/12 + (1.0 – 0.9)e^-0.038×8/12 + (1.0 – 0.9)e^-0.038×11/12 + (1.0 – 0.9)e^-0.038×14/12 = 0.289

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#### ericavv

##### New Member
Were you able to solve this problem?

Hi, I have been trying to solve exercise 7.23 from John Hull, edition 10th, but somehow the solution for valuation in terms of bonds and in terms of FRAs is not the same! In John Hull solution only the valuation in terms of FRAs is given which I have the same, but the ones in bonds is not correct. Do you have a solution of this problem?

Problem 7.23: In an interest rate swap, a financial institution has agreed to pay 3.6% per annum and to receive three-month LIBOR in return on a notional principal of $100 million with payments being exchanged every three months. The swap has a remaining life of 14 months. Three-month forward LIBOR for all maturities is currently 4% per annum. The three-month LIBOR rate one month ago was 3.2% per annum. OIS rates for all maturities are currently 3.8% with continuous compounding. All other rates are compounded quarterly. What is the value of the swap? Solution: We can value the swap as a series of forward rate agreements. The value in$ millions is:

(0.8 – 0.9)e^-0.038×2/12 + (1.0 – 0.9)e^-0.038×5/12 + (1.0 – 0.9)e^-0.038×8/12 + (1.0 – 0.9)e^-0.038×11/12 + (1.0 – 0.9)e^-0.038×14/12 = 0.289