Financial Engineering – IC302
Autumn Term 2020/1
Seminar 3: Swaps Questions
1. Suppose that it is September and you are receiving fixed in a one-year swap denominated in USD. Floating payments in the swap are made quarterly and the 3- month USD LIBOR rate for the next floating payment (to be made in December) has already been fixed. You decide to hedge the swap by trading in CME Eurodollar futures contracts.
(a) Should you go long or short the futures contracts?
(b) In which futures expiry months are you most likely to trade?
2. Why is the expected loss to a bank from counterparty default in a plain vanilla fixed- for-floating swap less than the expected loss from default on a loan to the counterparty with the same principal amount?
3. Under LIBOR discounting, if the one-year discount factor based on market swap rates is 0.980392, the two-year discount factor is 0.942319, and the three-year swap rate is 4%, what is the three-year discount factor?
4. Based on the discount factors you calculated in the previous question, what is the projected forward LIBOR for the period between two years and three years from now under LIBOR discounting?
5. Use the Excel workbook Swap Valuation – OIS Discounting to answer this question.
Set up the Excel workbook Swap Valuation – OIS Discounting to reflect the following initial market conditions:
Year
Swap Rate
OIS Rate
1
1%
0.5%
2
2%
1.5%
3
3%
2.5%
4
4%
3.5%
(a) Use the Excel workbook to show that the mark-to-market value of a newly initiated 4-year swap with notional amount $10 million in which we pay fixed at a rate equal to the market 4-year swap rate is zero.
[Hint: After entering the interest rate data in the table above, make sure that the ‘Shift swap curve’ and ‘Shift OIS curve’ values in cells B12 and B28, respectively, are set equal to zero; that the ‘First LIBOR’ value in cell H20 is set equal to the 1-year swap rate; and that the ‘Swap rate’ value in cell H21 is set equal to the current market 4-year swap rate.]
(b) Use the Excel workbook to calculate the mark-to-market value a 4-year swap in which we pay fixed at 3.00% in these same market conditions. What explanation can you offer for this result?
(c) Suppose that the swap in part (b) is our only derivative position with that counterparty. What is our credit risk exposure to the counterparty? What would our credit exposure be if we were the payer rather than receiver of fixed in the swap?
(d) Use the Excel workbook to estimate the DV01 of the swap in part (b) for a one-basis-point shift in the swap curve.
[Hint: You can shift the swap curve by entering an appropriate value in cell B12.]
(e) Restore the ‘Shift swap curve’ value in cell B12 to zero. What is the DV01 of the swap in part (b) for a one-basis-point in the OIS curve that leaves the market swap rates unchanged? Why is this different from the DV01 for a shift in the swap curve that you found in part (d)?