3. Boostrapping -IBOR Zero Rates (Medium, 20 points) Unlike problem 2., now suppose you are modern...

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3. Boostrapping -IBOR Zero Rates (Medium, 20 points) Unlike problem 2., now suppose you are modern and are using OIS discounting. That is, discount rates are calculated using OIS rates. From the OIS swap market, you observe the following swap rates. For this problem, assume OIS swaps have semiannual payments (payments every six months), and that swap rates are quoted per annum with semiannual compounding. Swap Expiration (years) OIS Swap Rate 0.5 1.0 1.5 2.0% 2.5% 3.0% For LIBOR, suppose you observe a 6-month LIBOR zero rate of 2.5% and a 1-year LIBOR zero rate of 3.0%. Both are quoted per annum with continuous compounding. Finally, you observe the swap rate of 3.5% on a LIBOR swap with an expiration date of 1.5 years and semiannual payments of, where this 3.5% swap rate is quoted per annum with semiannual compounding. Assume that this swap makes semiannual payments. (a) (10 points) Calculate the OIS zero rates. Express your answers per annum with continuous compounding. Summarize your answer in a table that looks like the following one, and round your numbers to 4 decimal places/5 significant digits (x.xxxx%). Maturity OIS Zero Rate 0.5 1.0 1.5 Hints: The 6-month zero rate should be very simple to compute. For the 1-year and 1.5- year zero rates, remember that we are using OIS discounting, so you can use the simpler method of bootstrapping out zero rates. (b) (10 points) Calculate the 18-month LIBOR zero rate. Express your answer per annum with continuous compounding. Summarize your answer in a table that looks like: Hints: Remember we are using OIS discounting, so use your answers from part (a) for discounting. Also, remember the general strategy. We know the 18-month LIBOR swap has zero value, so we can use this to find the 12- to 18-month LIBOR forward rate. Warning: Example 7.5 in the textbook may be helpful, but it 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. 3. Boostrapping -IBOR Zero Rates (Medium, 20 points) Unlike problem 2., now suppose you are modern and are using OIS discounting. That is, discount rates are calculated using OIS rates. From the OIS swap market, you observe the following swap rates. For this problem, assume OIS swaps have semiannual payments (payments every six months), and that swap rates are quoted per annum with semiannual compounding. Swap Expiration (years) OIS Swap Rate 0.5 1.0 1.5 2.0% 2.5% 3.0% For LIBOR, suppose you observe a 6-month LIBOR zero rate of 2.5% and a 1-year LIBOR zero rate of 3.0%. Both are quoted per annum with continuous compounding. Finally, you observe the swap rate of 3.5% on a LIBOR swap with an expiration date of 1.5 years and semiannual payments of, where this 3.5% swap rate is quoted per annum with semiannual compounding. Assume that this swap makes semiannual payments. (a) (10 points) Calculate the OIS zero rates. Express your answers per annum with continuous compounding. Summarize your answer in a table that looks like the following one, and round your numbers to 4 decimal places/5 significant digits (x.xxxx%). Maturity OIS Zero Rate 0.5 1.0 1.5 Hints: The 6-month zero rate should be very simple to compute. For the 1-year and 1.5- year zero rates, remember that we are using OIS discounting, so you can use the simpler method of bootstrapping out zero rates. (b) (10 points) Calculate the 18-month LIBOR zero rate. Express your answer per annum with continuous compounding. Summarize your answer in a table that looks like: Hints: Remember we are using OIS discounting, so use your answers from part (a) for discounting. Also, remember the general strategy. We know the 18-month LIBOR swap has zero value, so we can use this to find the 12- to 18-month LIBOR forward rate. Warning: Example 7.5 in the textbook may be helpful, but it 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.

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Answer a To calculate the OIS zero rates we can use the bootstrapping method The formula for calcula... View the full answer