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## Wednesday, January 5, 2011

### IRS pricing <- forward <- spot rate

I don't think this needs a real trading system. low volume, simple math

Pricing a swap is all about predicting actual floating payments or future libor[4] rates or forward rates at each quarterly reset date.

[4] For muni, libor is replaced by the SIFMA muni swap index

http://www.bionicturtle.com/learn/article/forward_rates_and_spot_rates/ illustrates derivation of a single forward rate from a series of spot rates. "forward rate is a prediction about future spot rates."

Given
1) all the spot rates of ED deposits (not futures)
2) market (forward) rates of ED futures,
those future libor rates on each quarterly reset date are solvable. This is the basis of floating payment estimation.

In fact, "expected" 3m libor rate on each quarter boundary date (IMM date) is published in eurodollar futures  market[1]. Therefore the derivation is IRS pricing <- forward rates <- ED CD rates + ED futures rates. Note the floating leg comprises periods (aka coupon period). Pay at end of period but payment amount reset at onset of period. See also post on discount curve.

[1] ED futrures rates are very different from the deposit rates announced by BBA. There's no "market" for deposit rate.

What If I am convinced 3m USD libor will hit 120 bps/yr on 1/1/2020 but the derived libor is 200 bps/yr? How do i lock in the 1.2%? Well, the relevant eurodollar futures contract is trading at 98. I would buy it and hope it becomes 99.

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