# value of a floating payer swaption

The London Interbank Offered Rate (LIBOR) yield curve is: • 180-days: 5.2%. • 360-days: 5.4%. What is the value of a LIBOR-based payer swaption (expiring today) on a \$10 million 1-year 4.8% swap? A) \$50,712. B) −\$50,712. C) \$0. Your answer: A was correct! i know how to solve this problem but what is the significance of the expiration date? how would this problem change if the expiry was 6 months from now?

i would think that instead of the 0.024 (.974659 + .948767) + .948767 = 0.994929 you had taken 1 - .994929 = .005071 x 10mm = 50,707.76 (or whatever rounding you do) so 6 months, i would think you’d just have 1.024(.97659) = .998051 subtract from 1 = .001949 x 10mm = 19,491 or so as the value? someone correct me if i went off of the tracks, but i would think that that shorter expiration would drop the px of your swaption here.

I get \$52k, I am assuming that the value of the swaption is the value in difference in swap rates. So the new swap rate is [(1-.948767) / (.97469 + .948767)] * 2 = 0.05327 so (.05327 - .048) * 10,000,000 = \$52,730 What am I doing wrong that I dont get the \$50,712?

they give you the fixed rate as 4.8%- you don’t have to make that calc you did above. fixed rate is the 4.8, so payments semi-annually are 0.024. says expiring today, so makes it easy- floating side = 1. you just have to get the fixed side (see above for my discount rates)

Isn’t there a problem here? Looking at the rates at expiration - I can see the rate is more than the 4.8% fixed rate. so wouldn’t the payer swaption get a big fat 0? I remember this was a question both of us (Banni, you and I) had gotten wrong the same day in QBank – and you had posted it on AF. Subsequently - Schweser seems to have updated the answer.

you’re paying the fixed 4.8, you’re receiving the libor side (which looks higher from the 5 and change rates)- this one looks like the payer swaption would be worth \$\$. whether schweser changed it or maybe it’s one of their questions where one q is a receiver, another q is a payer (but exact same info, they’re lazy like that)… not sure but i vaguely do remember getting something like this wrong b/c the answer should’ve been zero. but the bigger point- pay the fixed 4.8, get back over 5… that has value, no?

CPK- just bumped the original one, was a receiver not payer. sorry to have taken pleasure a few months ago in your wrong answer. i think i can still count on my hands the # of times you’ve guessed wrong ever. it’s rare, you’re going to destroy this test. this one looks kosher to me- payer.

cool… thanks for resolving that issue. I find I do make some silly stupid mistakes…