I am told there are no closed form solutions for American swaptions, and my books don't contradict that. Does anyone have any references that give any reasonable approximation for these? Closed form only, no trees or MC or anything else. So that is looks like a Black style equation. Thanks.

SanFranCA2002,There ain't no closed-form solution for American swaptions.

If the American swaption you are trying to model is exercised, when does the underlying swap start? At the time of exercise or at the end of the option contract period? A general property of American options is that they will have the same price as otherwise identical European options if the underlying asset pays no cash flow before the expiry of the option. If the underlying swap starts on the final expiry date of the swaption (or later), then the American exercise feature has no additional value.There are a couple of analytic approximations for American option values, the best known being the Barone-Adesi/Whaley model and the Ho/Stapleton/Subrahmanyam model. The Whaley model requires one to solve for a critical underlying price using a Newton Raphson or similar scheme and loses accuracy for option maturities greater than a couple of months. The HSS model is more robust but requires you to solve the cumulative bivariate normal.

American swaptions are very different from American options on equities.Consider a 10NC3 payer struck at 5%. If one exercises at year 3, one gets a 7 year swap; if one exercises at year 3.1, one gets a 6.9 year swap, ..., if one exercises in year 9.9 one gets a 0.1 year swap.The equivalent deal in the equity world would be an American option that could be exercised at any time up to time T, but if one exercise at time tEx, one would only get (1 - tEx/T) of the asset and pay (1 - tEx/T) of the strikeYou can make up TOY models of American swaptions that have similarity solutions, but they are far from the truth.

American swaptions seems to be complicated to value. "Luckely" most swaptions are European style, and all the smart traders (+ one stupid =me) on wall street are now adopting (or at least trying) the SABR model by Pat Hagan, Kumar D., Lesniewski A. and Woodward D. "Managing Smile Riks" (Wilmott Mag Issue 1). I believed there was two main types of American swaptions, trombone and wasting swaptions.A) Wasting swaption: the type Pat is mentioning, that I assume is the most common form of American swaption. Wasting swaptions are popular for hedging bonds. I think the American swaption market stared partly as demand for arbitraging the option in callable bonds (?). B) Trombone swaption: a type where the underlying swap always has fixed tenor, just like the slide of a trombone. For example a 6m into 5 year, then you can exercise the option anytime over next 6 months, but always into a 5 year swap (with start spot from option expiration and expiry 5 years later). I was reading about this variant long time ago, but not sure if trombone swaptions trade much, personally I have never done this variant. Third one naturally has Bermudan style swaptions where you only can exercise on several fixed dates, can be wasting or trombone.Pat what would be most difficult to value? Wasting or Trombone swaption? or do they fall in same category when it comes to valuation model?

"Wasting" Bermudans are by far the most common ... they are the swap equivalent of callable bonds. A typical deal would be a 10NC3 at 6% ... This is a 10Y swap that can be cancelled on any pay date starting in year 3.We would be paying 6% semiannually ($3 or so every 6m), and in return we would be receiving a floating leg of 3m Libor. Starting in year 3, we can say "the next payment is our last one" with n days notice (typically 5 business days). In any case, the deal stops afte 10 years.These arise for 2 reasons: a) corporations (Fannie Mae!) issues callable bonds, and wish to receive floating (So we pay them 6%, they pay us floating, and they pay their customers 6%, ...)Alternatively, corporations can get a bit of extra coupon off a Bermudan since we will pay more if we can call the deal, than if we can't (Ie, they have sold us the Bermudan call option in return for extra coupons)These are usually priced as the value of the full 10 year swap, plus the Bermudan option to enter the opposite swap. So in the above example, we would have the value of the 10y payer swap, plus the Bermudan option (3 into 7, 3.5 into 6.5, ...) for entering into a receiver struck at 6%.Americans (or Bermudans which are exercised more frequently than once per period) are a pain because on cancellation, one has to catch up on all the accruals."Wasting" or "trombone" (normal and fixed tenor) Bermudans are valued by exactly the same code; the only real differnce are the instruments used to calibrate the model: for trombone one uses, say the 3 into 7, the 3.5 into 7, the 4 into 7, ... while for the usuall Bermudans, one calibrates the model to the 3 into 7, 3.5 into 6.5, etc. for obvious reasons.

what is the best way to price "Trombone" American Swaption?

I am trying to figure out the LS LSMethod, but for a simple put option I can understand the method.But I was trying to figure out how to use it on a structure as follows:you have a swap between floating libor and another floating payment that is dependent on another rate (eg 10yrs rate). Lets say for simplicity, you have to pay 80% of 10 yrs rate and you receive 1 yrs rate.Each your however, you can choose whether you want to end this agreement or continue.I am really confused how one should interpret the LS method. In the put-option example, you look the nodes where the option has intrinsic value. How should one take this into account? I am hoping to find some insight here, I would be forever greatful, or at least 10 years or so

QuoteOriginally posted by: pleoniI am trying to figure out the LS LSMethod, but for a simple put option I can understand the method.But I was trying to figure out how to use it on a structure as follows:you have a swap between floating libor and another floating payment that is dependent on another rate (eg 10yrs rate). Lets say for simplicity, you have to pay 80% of 10 yrs rate and you receive 1 yrs rate.Each your however, you can choose whether you want to end this agreement or continue.I am really confused how one should interpret the LS method. In the put-option example, you look the nodes where the option has intrinsic value. How should one take this into account? I am hoping to find some insight here, I would be forever greatful, or at least 10 years or so :-)take a look at thisV

out of curiosity, what's the standard form of an American zero coupon bond ?

"Americans (or Bermudans which are exercised more frequently than once per period) are a pain because on cancellation, one has to catch up on all the accruals." from PatPat, would you please show some detail how you deal with the American Swaption? How to handel the accrual? Many thanks

Sorry for bringing this old topic live again, but could anybody give me some directions on valuing "wasting" swaption that Pat mentioned above? I am new to this, so anything that is considered useful will be highly appreciated.Thanks.