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## Thursday, May 9, 2013

### IRS valuation, again

When I see "value of a swap" I first remind myself this is about the value of a series of cash flows, like the combined value of "out \$19, in \$13, out \$2, in \$5 ...". This value could be positive or negative. Next I ask myself "value of the cash flows to side 1 or 2"? [1]

A) First, you are always one of A) fixed-receiver or B) float-receiver. I feel for a beginner like me, better focus on one side. [[Hull]] example focuses on the fixed receiver. If IRS is important to your job, you will see both sides so many times and they will become quick and intuitive. From now on, Let's focus on the fixed receiver.

B) The "position" on our book is valued as a series of cash flows including Inflow and outflow. The valuation calc basically
1) predict the size of each inflow and outflow at each future payment date [1]
2) discounts the net Inflow to PV like \$81, -\$12, -\$25, \$52..
3) add up the PV to a single dollar amount like \$99

If total inflow PV is positive, then the position is like an asset (as of today). Devil is in the details. For now, step back from the gory details and notice the few important details --

Q: key question (per Kuznetsov) is how to estimate today the rate [1] to be announced in 3 months (by the BBA). It's not fixed on sign-up but "floating" like the future temperature in Dublin 3 months in the future. How is it estimated?
A: basically use the IR numbers known today to back out (RN?) the 3x9 fwd rate "6M rate 3M forward". I guess this is like the UIP (not the CIP) -- treating the RN expected spot rate as the natural expected spot rate. See http://en.wikipedia.org/wiki/Forward_rate_agreement

Note the very first payment date is fixed, not some "unknown future temperature". See [[Hull]].

Q: what kinda input data are needed to produce the soft market data which are needed for IRS valuation?
A: Lin Yu pointed out the key soft market data is the libor/swap curve, which often uses Libor, ED Futures , Swap rates from the market. But that's a bit involved. For now, let's look at the simple calc in [[Hull]]
A: Libor deposit rates. (A bit tricky!) If valuation-date is denoted T, and the payment dates are T+3M, T+9M .. then we need rate for a loan from T to T+3M.
** I'd say from Libor deposit rates T to T+...., we could estimate all the floating payment.
** note ED future rates are not used in this simple calc.

[1] A minor point -- if the value of the cash flows nets to positive for one side, it must be negative for the opposite side.