BUS333
Week 7 (Tutorial 6) – Swaps –Valuation and Off-market pricing
, Problem 7.10.
A financial institution has entered into an interest rate swap with company X. The total cost of default is therefore the cost of
Under the terms of the swap, it receives 4% per annum and pays six-month LIBOR following cash flows:
on a principal of $10 million for five years. Payments are made every six months.
Suppose that company X defaults on the sixth payment date (end of year 3) when
the six-month forward LIBOR rates for all maturities are 2% per annum. What is
the loss to the financial institution? Assume that six-month LIBOR was 3% per
3 year: $50,000
annum halfway through year 3 and that at the time of default all OIS rates are
1.8% per annum. OIS rates are expressed with continuous compounding; other 3.5 year: $100,000
rates are expressed with semiannual compounding. 4 year: $100,000
4.5 year: $100,000
5 year: $100,000
At the end of year 3 the financial institution was due to receive
$200,000 (=0.5×4% of $10 million) and pay $150,000
(=0.5×3% of $10 million). The immediate loss is therefore Discounting these cash flows to year 3 at 1.8%
$50,000. annum, we obtain the cost of the default as $4
To value the remaining swap we assume that LIBOR forward
rates are realized. All forward rates are 2% per annum.
Loss = $50, 000 + $100, 000(e −0.018×0.5 + e −0.018×1.0 + e −0.0
The remaining cash flows are therefore valued on the =$50, 000 + $100, 000 × 3.911203
assumption that the floating payment is 0.5×0.02×10,000,000 = = $441,120
$100,000.
The fixed payment is $200,000 and the net payment that would
be received is 200,000−100,000=$100,000.
Week 7 (Tutorial 6) – Swaps –Valuation and Off-market pricing
, Problem 7.10.
A financial institution has entered into an interest rate swap with company X. The total cost of default is therefore the cost of
Under the terms of the swap, it receives 4% per annum and pays six-month LIBOR following cash flows:
on a principal of $10 million for five years. Payments are made every six months.
Suppose that company X defaults on the sixth payment date (end of year 3) when
the six-month forward LIBOR rates for all maturities are 2% per annum. What is
the loss to the financial institution? Assume that six-month LIBOR was 3% per
3 year: $50,000
annum halfway through year 3 and that at the time of default all OIS rates are
1.8% per annum. OIS rates are expressed with continuous compounding; other 3.5 year: $100,000
rates are expressed with semiannual compounding. 4 year: $100,000
4.5 year: $100,000
5 year: $100,000
At the end of year 3 the financial institution was due to receive
$200,000 (=0.5×4% of $10 million) and pay $150,000
(=0.5×3% of $10 million). The immediate loss is therefore Discounting these cash flows to year 3 at 1.8%
$50,000. annum, we obtain the cost of the default as $4
To value the remaining swap we assume that LIBOR forward
rates are realized. All forward rates are 2% per annum.
Loss = $50, 000 + $100, 000(e −0.018×0.5 + e −0.018×1.0 + e −0.0
The remaining cash flows are therefore valued on the =$50, 000 + $100, 000 × 3.911203
assumption that the floating payment is 0.5×0.02×10,000,000 = = $441,120
$100,000.
The fixed payment is $200,000 and the net payment that would
be received is 200,000−100,000=$100,000.
