Citi Bank

What is Interest Rate Swap

- Bilateral agreement between two parties to exchange periodic interest payments over a period of time.

- Interest payments, which are calculated based on nominal principal amount, are nettled.

- Principal is not exchanged.

- One party will pay a predetermined fixed interest rate and the other party will pay a re-settable (‘floating’) interest rate

- Usually indexed on LIBOR (London Interbank Offer Rate) but can also be SIBOR, AUD BBSW, HKD HIBOR, Prime etc.

- Currency of the two sets of interest payments are the same

Interest Rate Swaps

The parties must agree on the following:

- The swap's nominal amount : This amount is generally not exchanged, but cash flows (payments) are calculated against it.

- The swap’s maturity: number of years the agreement is binding.

- The relevant interest rate index: While the fixed coupon is set at the beginning, the floating payment is tied to some agreed-upon index. Often this is 3 or 6-month LIBOR but many other possibilities exist.

- Payment (or “re-set”) dates: How Frequency of exchange of the payments

Swap Pricing : Discounted Cashflows

- A swap is constituent of the sum of individual cashflows.

- The fundamental of swap pricing is to find out the present values (PV) of these cash flows.

- Equating the present values of the amounts of the payments and receipts.

Calculation of Swap Rate

- Interest rate swaps are priced so that on the trade date, both sides of the transaction have equivalent NPVs.

- The fixed rate payer is expected to pay the same amount as the floating rate payer over the life of the swap, given the prevailing rate environment (where today’s forward curve lies).

- On the trade date, swaps can be thought as an exchange of a fixed rate bond, for a floating rate bond.

Discount Factor

- To calculate the present value, the appropriate discount factor that should be applied must be determined.

- Discount factors are extracted from market rates using “Bootstrapping”.

Calculating the 2- and 3-year Swap Rates

	1 year	2 year	3 year
Zero Rate	5.75%	6.10%	6.25%
Discount Factors	0.94563	0.88832	0.83372
Swap Rate	5.75%	-	-

What coupon would make a coupon bond trade for par today?
2 Year: 100 = C2/(1.0575) + (100+C2)/(1.0610)²
3 Year: 100 = .94563(C3) + .88832(C3) + .83372(100+C3)

Comparing the Swap Rates With the Forward Rates

	1 year	2 year	3 year
Zero Rate	5.75%	6.10%	6.25%
Discount Factors (DFs)	0.94563	0.88832	0.83372
Discount Factors (DFs)	5.75%	-	-

Present value of 3-year swap cashflows: (Assume $100 notional): DFs x Coupon = (0.94563 + 0.88832 + 0.83372) x $6.23 = $16.63
Present value of 3-year floating cashflows:: .94563 (FR0X1) + .88832 (FR1X2) + .83371 (FR2X3) = $16.63
The present values of the expected cashflows equal, thus we know the swap rate is accurate.

Completed Rate Table:

	1 year	2 year	3 year
Zero Rate	5.75%	6.10%	6.25%
Discount Factors (DFs)	0.94563	0.88832	0.83372
Forward Rate (FR)	5.75%	6.45%	6.55%
Swap Rate	5.75%	6.09%	6.23%

Equivalence of Swap Rates

Assume a $100, 3-year investment:
· 3-year Zero Rate:
$100(1.0625)3 = $119.95
· 3-year Forward Rate: $100(1.0575)(1.0645)(1.0655) = $119.94
· 3-year Swap Rate:
$6.23*(1.0645) = $6.6356
($6.63 + $6.23)(1.0655) = $13.7121
$13.71 + $106.23 = $119.95

※ User Profile

- A company with a floating-rate debt, who is concerned about the prospect of rising interest rates, might pay fixed on an interest rate swap to lock-in a known interest rate cost.

- An investor or financial institution with fixed-rate assets and floating-rate liabilities might enter into a swap to fix its net interest margin