A financial institution has entered into a swap where it agreed to receive quarterly payments at a rate of 4% per annum and pay the SOFR three- month reference rate on a notional principal of $100 million. The swap now has a remaining life of 12 months. Assume the risk - free rates with continuous compounding (calculated from SOFR) for 2 month, 5 months, 8 months, and 11 months are 1.7%, 2.5%, 3.6%, and 3.8%, respectively. Assume also that the continuously compounded risk - free rate observed for the last two months is 2.5%. Estimate the value of the swap.

A financial institution has entered into a swap where it agreed to receive quarterly payments at a rate of 4% per annum and pay the SOFR three- month reference rate on a notional principal of $100 million. The swap now has a remaining life of 12 months. Assume the risk - free rates with continuous compounding (calculated from SOFR) for 2 month, 5 months, 8 months, and 11 months are 1.7%, 2.5%, 3.6%, and 3.8%, respectively. Assume also that the continuously compounded risk - free rate observed for the last two months is 2.5%. Estimate the value of the swap.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Use the following information for questions 12-15: Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and to receive the 3-month LIBOR in return on a notional principal of $50 million with payments exchanged every 3 months. The swap has a remaining life of 14 months. The current rate being swapped for 3- month LIBOR is 11.8% per annum for all maturities. The 3-month LIBOR rate 1 month ago was 12% per annum. All rates are compounded quarterly.
Suppose that a bank has agreed to the following terms of an interest rate swap: - The notional principal is CAD 300 million and the remaining life of the swap is 11 months. - The bank pays 8% per annum, and receives three-month LIBOR. - Payments are exchanged every three months. - The swap (fixed) rate is 11% per annum for all maturities. - The three-month LIBOR rate a month ago was 12.5% per annum. All rates are compounded quarterly. Estimate the value of the swap using a) a bond-price valuation method, and b) a FRAS-based method?
An interest rate swap has three years of remaining life. Payments are exchanged annually. Interest at 3% is paid and 12-month LIBOR is received. An exchange of payments has just taken place. The one-year, two-year, and three-year LIBOR/swap zero rates are 2%, 3%, and 4% with continuous compounding. What is the value of the swap as a percentage of the principal when LIBOR discounting is used assuming that the principal is $100? (Note: You are expected to use continuous compounding/discounting. If you use discrete discounting the answer will be close) a. None of the other answers provided is correct. b. 2.88% c. 1.05% d. 0.00% e. 1.00%
Consider a one-year interest rate swap with semi-annual payments, based on 30/360 day count convention. The term structure of LIBOR spot rates is given as follows: 6-month LIBOR at 7.2%, and 12-month LIBOR at 8.0%. What is the annualized fixed rate on the swap? A. 7.42%. B. 7.93% C. 7.84%. D. 7.56%.
A $100,000 interest rate swap has a remaining life of 10 months. Under the terms of the swap, six-month LIBOR is exchanged for 4% per annum (compounded semi-annually). Six-month LIBOR forward rates for all maturities are 3.3% (compounded semi-annually). The six-month LIBOR rate was 2.6% two months ago. The risk free rate is 2.7% (cont. comp) for all maturities. What is the value of the swap to the party paying floating? (Required precision: 0.01 +/- 1)
An interest rate swap has three years of remaining life. Payments are exchanged annually. Interest at 2% is paid and 12-month LIBOR is received. A exchange of payments has just taken place. The one-year, two-year and three- year LIBOR/swap zero rates are 2%, 3% and 4%. All rates an annually compounded. What is the value of the swap as a percentage of the principal when LIBOR discounting * is used
A semi-annual pay interest rate swap where the fixed rate is 5.00% (with semi-annual compounding) has a remaining life of nine months. The six-month LIBOR rate observed three months ago was 4.85% with semi-annual compounding. Today’s three and nine month LIBOR rates are 5.3% and 5.8% (continuously compounded) respectively. From this it can be calculated that the forward LIBOR rate for the period between three- and nine-months is 6.14% with semi-annual compounding. If the swap has a principal value of $15,000,000, what is the value of the swap to the party receiving a fixed rate of interest? Assume OIS rates are the same as LIBOR rates.
A semi-annual pay interest rate swap where the fixed rate is 5.00% (with semi-annual compounding) has a remaining life of nine months. The six-month LIBOR rate observed three months ago was 4.85% with semi-annual compounding. Today’s three and nine month LIBOR rates are 5.3% and 5.8% (continuously compounded) respectively. From this it can be calculated that the forward LIBOR rate for the period between three- and nine-months is 6.14% with semi-annual compounding. If the swap has a principal value of $15,000,000, what is the value of the swap to the party receiving a fixed rate of interest? Assume OIS rates are the same as LIBOR rates. Please show how you get the floating payments
An interest rate swap has three years of remaining life. Payments are exchanged annually. Interest at 2% is paid and 12-month LIBOR is received. An exchange of payments has just taken place. The one-year, two-year and three-year LIBOR/swap zero rates are 2%, 3% and 5%. All rates are annually compounded. What is the value of the swap as a percentage of the $100 principal value?
An interest rate swap has three years of remaining life. Payments are exchanged annually. Interest at 5% is paid and 12-month LIBOR is received. An exchange of payments has just taken place. The one-year, two-year and three-year LIBOR/swap zero rates are 4%, 5% and 6%. All rates are annually compounded. What is the value of the swap as a percentage of the principal ($100) when OIS and LIBOR rates are the same? (
Suppose that some time ago a financial institution entered into a swap where it agreed to make semiannual payments at a rate of 3.5% per annum and receive LIBOR on a notional principal of $300 million. The swap now has a remaining life of 1.15 years. Payments will therefore be made 0.15, 0.65, and 1.15 years from today. The risk-free rates with continuous compounding for maturities of 0.15, 0.65, and 1.15 years are 2.8%, 3.2%, and 3.4%, respectively. We suppose that the forward LIBOR rates for the 0.15-to- 0.65 year and the 0.65-to-1.15 year periods are 3.4% and 3.7%, respectively, with semiannual compounding. The LIBOR rate applicable to the exchange in 0.15 years was determined 0.35 years ago. Suppose it is 2.9% with semiannual compounding. What is the floating cash flow at time 1.15 (in $ millions)?
An interest rate swap has three years of remaining life. Payments are exchanged annually. Interest at 3% is paid and 12-month LIBOR is received. An exchange of payments has just taken place. The one-year, two-year and three-year LIBOR/swap zero rates are 2%, 3% and 4%. All rates an annually compounded. What is the value of the swap as a percentage of the principal when OIS and LIBOR rates are the same how much?

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