It is important to note that a swaption contract specifies a fixed rate. Whether you want to be the payer or the receiver, this is your reference rate. Let’s say this rate is 4%.
On expiration, suppose the LIBOR rates dictate a fixed swap rate of 3.5%. If you had a payer swaption ( to pay 4%) you would pass this opportunity and let the option expire, because you can make a better swap agreement using the market rates.
If you had a receiver swap, you would exercise the swaption and make an agreement to receive 4% fixed.
If you remember, at inception a swap has no value. In this case it has a value, because you have an advantage of (4-3.5=0.5%) against other market participants. That’s what we value.
This mean ther is only one formula for swaptions, which essentially uses the absolute value difference between the fixed rates of the contract and the market. You just have to make sure it has intrinsic value (i.e. can be exercised) rather than value something worth zero…
At inception the contract is created using market rates, which are transparent and fair. So no party has an outright advantage at t=0. Only time will tell who was right who was wrong.
Every predetermined period (quarter, semester etc) the contract is marked to market to see who was right (who won) and who was wrong (who lost). The loser pays the difference. Towards the end of the contract the cash flow periods (quarters, semester etc) become less and less and hence the loser has more chances to make to the finish before becoming bankrupt…
Why is the midpoint the most dangerous in terms of counterparty risk? Because by that time the picture becomes more clear who is winning and chances are trends will continue. In the beginning when the two parties came together they had pretty good financial positions (due diligence was done) so it was assumed credit risk is small (otherwise call off the deal, right?). Towards the end we said dust is clearing and the loser is making it to the finish, so the greatest uncertainty is in the midpoint.
Currency swap is different. There is a large cash flow towards the end (the exchange of notional) that is why the last period is the most crucial one.
Also, for #4 and #5 regarding the foreign currency. I just tried this out and it worked. For anyone using this, it is the value of the foreign leg IN the domestic currency.
For example, you start off with $20 million and you apply the FX at inception to get to the foreign currency. Then you calculate the fixed or floating payment in that foreign currency. Then you apply the Current FX rate to get back to your payment in domestic currency.
Essentially, formula #4 and #5 does all of it for you and you just need to multiply this with the NOTIONAL $