 # Swaption freeze

lol mcpass,… my gf wonders what is wrong with me, since i’m better than usual… i guess counting sheep or thinking about IPS and willingness vs. ability to take risk is the same…

tooo…much…info.

Wow, I stepped away for dinner and now I see all these responses…now I have to go through them all and hope that one of you cracked the thick layer of fat in the my head that prevents knowledge from getting in

I’m not getting this exactly. I just did a question about swaption payoff. I took the rate as of expiration minus the contract rate multiplied by the contract value. I then took that number and multiplied it by the sum of the discount factors. Why does that not work here?

barthezz Wrote: ------------------------------------------------------- > 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. Barthezz, can you tell me how you got this 5.32% number?

(1-0.94877) / (0.97466+0.94877) * 2 = 5,32%

(1-.94877)/(.94877+.97466)*(360/180) Basically that (1-Zn)/Z1+Z2…) formula This is the price of a what a swap would be worth at initiation.

Overall idea is this: You know that you can enter the swap as the fixed rate PAYER at 4.8 and the fixed rate one the underlying swap is 5.32 (what you would REC). So at every payment date of the swap you are going to get paid more than you have to pay out. Now discount the difference of each payment to the present value to get what this whole thing is worth today.

(.0532-.048)(.5)(10,000,000) = 26,000 26,000*(.97466+.94877) = 50,010 I guess thats close enough.

Thanks all. This is the explanation THEY gave, which helps also: (they didn’t get to a 5.32% number, which is why I asked. Determine the discount factors. 180 day: 1 / [1 + (0.052 × (180 / 360))] = 0.974659 360 day: 1 / [1 + (0.054 × (360 / 360))] = 0.948767 Then, plug as follows: (1 − 0.9487666) / (0.974659 + 0.9487667) = 0.026637 The value of the receiver swaption is the savings between the exercise rate and the market rate: (0.026637 − 0.024) × (0.97465887 + 0.9487666) × 10,000,000 = \$50,712.

Smarshy, I think it is really important that you understand the concept here so you can apply it to questions you get on this topic in the future. When you are long a payer swaption you have the RIGHT to enter into a swap as the fixed rate payer. Swaptions are always defined by the fixed rate. So the long in a receiver swaptions REC fixed rate payments and the long in a PAYER swaptions pay the fixed rate. For exam purposes these will always be european options. So at expiration of the swaption you have the RIGHT to enter a swap as the fixed rate payer. This will only have value if the MARKET rates for fixed rates are higher than the rate in the swaption. In this case you have the right to enter a swap as a fixed rate payer at 4.8%. At the exact same time though you could go the the MARKET and enter into the opposite side of a swap with the same duration (floating rates will cancel). In this case, you are going to enter into a swap as the fixed rate RECEIVER at 5.32%. When you do this you are going to lock in a profit. The profit is going to be the difference between what you REC minus what you PAY at each date. In our example it will be 26,000 on each payment date. So what are these 26,000 dollar payments worth to you today? Discount them back to todays value and you have your value today, which is the 50K number we arrived at. I hope I am not talking down to you, but in your orginal post it appeared that you were having trouble with the overall idea here.

Just to make sure I get this. If you are long a swaption (payer or reciever) you can never have a negative value other than the premium you paid to enter into the contract correct?

correct. You are long the option. You already paid up the premium to get the option, there is no possible negative value.

Niblita75 Wrote: ------------------------------------------------------- > Just to make sure I get this. If you are long a > swaption (payer or reciever) you can never have a > negative value other than the premium you paid to > enter into the contract correct? Yeah the option would just expire worthless. I can’t think of an example with a negative value.

Didn’t that question just have a negative as an answer or do you mean in general you can’t think of a time when it would be negative?

I guess theoretically it could have a negative value if the fixed rate on a market swap was lower than the fixed rate on the swaption. But if that were the case you would never exercise the option. Do you think I am missing something Nib?

That was one of the answer choices, but that could never be the answer. You can automatically rule that, and zero out. You know its not worthless because the swap rate is less that the current rate, thus making the value of the swaption positive, now you just have to figure out if its the 25k number or the 50k number.

I agree with you there. So come answer time if we are long a swaption we can disregard any negative answer.

You really could just eyeball this example by taking the differences in the two rates to figure out the payments (26K). Since there are two you know it could not be as low as 25K even when discounted to the present.

^^Exactly