# Swaption freeze

When i see questions like this I freeze up and I don’t know where to start. Can anybody help? What do I do first? 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 percent swap? A) \$0. B) \$50,712. C) \$25,356. D) \$50,712.

D. If it’s correct I’ll tell you why,

Are D and B supposed to be the same answer

He probably forgot a negative sign on one of them.

whoops my bad B is negative -50712

Yes D is the answer please tell me why and, for the love of all that is holy, HOW

Why are B&D the same? I’m guessing you forgot the negative. Either way, its the positive 50 some thousand, although for some reason, I got 56,926. Basically a swaption, like any option is just worth the PV of the difference between the expected spot and the exercise. In this case, since your at maturity, its the difference between the spot and the exercise. Since it’s payer, you’re paying 4.8% and recieving the higher libor amount. I used the one year as this is a one year swap, although I could be wrong in that. Anyhow, if anyone can address why I got 57k instead of 51, that’d be a big help. My calculation looked like this: 10,000,000*[(.054-.048)/1.054]

I got close to what you got Swan. Basically the differnce is .6% of the 10M, so its 60,000 discounted back, which you would have to have a real high interest rate to discount it all the way back to 51k.

i’m sure there’s a WAY easier way to do it, but fixed side: 240k/1 +(.052x180/360) + 10,240,000/1.054 = 9,949,288.148. 10 mil minus that = the 50,711.85196

Wouldn’t we need to have specified bi-annual payments based on 180 day libor to use that approach.

That’s right Black but I assumed it was bi-annual payments and got to the same answer bannisja did.

i think yes- i guess i took liberties seeing it gave me a 180 day rate! if annual it would’ve just been the 10,480,000/1.054 = 9,943,074 pay, get 10 mil since we’re on reset day, so it’d be 56,925.99.

and one thing- even if by some sad, sad tragedy i don’t make it to L3 this year, i can say that i am a lot better at swaps now than i was a few months ago! i don’t even fear them on tests anymore for the most part. time series item sets… that’s another story. i just got a latte. i’m in for the evening session!

Find the fixed cost of the using the current LIBOR structure 2.66 x 2 = 5.32% So the first fixed payment would be 10M X 2.66% = 266,000 Using the 4.8% , the fixed payment would be 10M x (.0488(180/360)) = 240,000 Difference is \$26,000 x sum of PV factors on LIBOR structure (1.9235) = 50,000 I’d select D.

ALWAYS start with a TIMELINE. you can enter this swap by paying the 4.8% and receiving an equivalent fix payment of 5.32% based on LIBOR. 180-days: 5.2%…discount factor…0.97466 360-days: 5.4%…discount factor…0.94877 thus the swap coupon is 0.0266365 or 5.32% p.a. #1. you receive x-----------------------180days-----------------------------------360days PV?------------------266365.38---------------------------------266365.38+10Mio -----<0.97466 -------------------------------------------------<0.94877---------- #2. you pay (exercise rate = 4.8%) x-----------------------180days-----------------------------------360days PV?--------------------240000-------------------------------------240000+10Mio -----<0.97466 -------------------------------------------------<0.94877---------- whether you net the PMTs or subtract the PVs is up to you. I did: (266365-240000) * (0.97466+0.94877) = 50,711 so ans D.

damn… you guys are fast…

That’s exactly what my gf complains about barthezz

It’s because nobody else made a nice diagram like you. Thanks for that though, I’ll be saving this post. Makes it much more clear now!!

It is pretty, that’s definitely refrigerator material.

i can say the only reason i know swaptations is because of this board.