6. Bootstrapping - IBOR Forward Rates (Medium-Hard, 25 points) You observe the following LIBOR rates, all quoted per annum with semiannual compounding: Maturity Years) LIDOR 0.5 3.0% 103.59 You also observe the following LIBOR fixed-for-floating swap rates, where floating payments are based on the 6-month LIBOR, payments are made every 6 months, and swap rate is quoted per annum with semiannual compounding Swap Expiration (years) Swap Rate 3.8% 3.9% (a) (3 points) Compute the 6-month to 12-month LIBOR forward rate using the two LIBOR rates. Express your answer as an annual rate with semiannual compounding, (b) (8 points) Assuming both swaps are priced using LIBOR-based discounting, compute the 12- to 18-month and 18-to 24-month LIBOR forward rates. Also express these as annual rates with semiannual compounding. Hint: remember that with LIBOR-based discounting, the LIBOR swap rate should be the coupon rate of a bond that sells at par. Hint 2: Be careful that you get the discounting right. Everything is quoted as an annual rate with semiannual compounding, so don't just plug your interest rates into e You paid attention in class, and remember that IBORs have some credit risk: there is always the risk that a AA-rated financial institution defaults over a longer time horizon. But, you still want to compute the LIBOR forward rates in order to value an existing swap. You remember that OIS rates have less credit risk, and are therefore more appropriate for discounting Rather than making you compute them all, suppose the OIS zero rates expressed annually with continuous compounding are: Maturity (years) 0.5 1.0 1.5 OIS Zero 2.8% 3.3% 3.6% 3.6% (c) (12 points) Compute the 12- to 18-month and 18-to 21-month LIBOR forward rates as suming OIS discounting. Warning: Example 7.5 in the textbook is filled with typos! You should feel free to look there to help you, but some of the numbers are off by powers of ten (d) (2 points) Comment on the results. In particular, are the answers in (b) and (c) quite similar or very different? 6. Bootstrapping - IBOR Forward Rates (Medium-Hard, 25 points) You observe the following LIBOR rates, all quoted per annum with semiannual compounding: Maturity Years) LIDOR 0.5 3.0% 103.59 You also observe the following LIBOR fixed-for-floating swap rates, where floating payments are based on the 6-month LIBOR, payments are made every 6 months, and swap rate is quoted per annum with semiannual compounding Swap Expiration (years) Swap Rate 3.8% 3.9% (a) (3 points) Compute the 6-month to 12-month LIBOR forward rate using the two LIBOR rates. Express your answer as an annual rate with semiannual compounding, (b) (8 points) Assuming both swaps are priced using LIBOR-based discounting, compute the 12- to 18-month and 18-to 24-month LIBOR forward rates. Also express these as annual rates with semiannual compounding. Hint: remember that with LIBOR-based discounting, the LIBOR swap rate should be the coupon rate of a bond that sells at par. Hint 2: Be careful that you get the discounting right. Everything is quoted as an annual rate with semiannual compounding, so don't just plug your interest rates into e You paid attention in class, and remember that IBORs have some credit risk: there is always the risk that a AA-rated financial institution defaults over a longer time horizon. But, you still want to compute the LIBOR forward rates in order to value an existing swap. You remember that OIS rates have less credit risk, and are therefore more appropriate for discounting Rather than making you compute them all, suppose the OIS zero rates expressed annually with continuous compounding are: Maturity (years) 0.5 1.0 1.5 OIS Zero 2.8% 3.3% 3.6% 3.6% (c) (12 points) Compute the 12- to 18-month and 18-to 21-month LIBOR forward rates as suming OIS discounting. Warning: Example 7.5 in the textbook is filled with typos! You should feel free to look there to help you, but some of the numbers are off by powers of ten (d) (2 points) Comment on the results. In particular, are the answers in (b) and (c) quite similar or very different