Interest Rate Swap Valuation
Say that the city of Arkham has issued fixed-rate bonds to pay for a new infrastructure investment. Then, as rates across the world had dropped, city officials entered into a receive-fixed, pay-floating seven-year interest rate swap on notional value of CLP 10,000,000 because the officials believed that rates would continue to decline.
Now, two years later, the Arkham officials want to determine the value of that swap. What security would help determine that value?
Bingo!
Actually, no.
At each reset point, how will the floating values compare?
No.
The floating rates are reset at certain periods, so the new swap payments aren't higher.
No.
The floating rates are reset at certain periods, so the original swap payments aren't higher.
Exactly!
The floating rate payments are equal, so the valuation is simply the difference in the fixed rates.
The value of a fixed-rate swap at some future point in time _t_ is simply the sum of the present value of the difference in fixed swap rates times the stated notional value.
$$\displaystyle V_{swap} = NA \times (FS_0 - FS_t) \times \sum^{n}_{i=1} PV_i $$
With this equation, it's important to remember that _FS_0 is the fixed rate established at the start of the swap, and it goes to the party receiving fixed. Recall also that swaps are netted out for a single payer.
Say that the equation yields a negative value. Who pays?
No.
You got it!
If the equation yields a negative, that means that the receive-fixed, pay-floating holder has lost money and will be required to pay. But the receive-floating, pay-fixed holder receives the funds and has benefited. This also means that the floating rate increased over the time period.
Also, note that the equation values a swap on the payment date. If a swap is being valued between payment dates, some adjustments are necessary.
To sum it up:
[[summary]]
You'd need to find the value of an offsetting contract, just as with the forward contract valuation, so an offsetting contract for receive fixed, pay floating, is receive floating, pay fixed.
Receive floating, pay fixed
Receive fixed, pay floating
The new swap payments are higher
The swap floating payments are equal
The original swap payments are higher
Pay fixed
Pay floating
Continue
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