I am working on pricing Bermudan swaptions using longstaff-schwartz method. Have some trouble in deciding the basis functions for regression. Anybody have experience on that? More specificly, can we just use the forward swap values, (maybe a quadratic function). would that be enough.Also, according to several papers, it takes more than 10,000 MC paths for it to be effective. it's a nightmare in terms of memory consumption etc. Any thoughts, tips on that?Thanks a lot

You may want to read this. 10,000 paths sounds about right and, properly coded, should take you a few seconds to run.

QuoteOriginally posted by: foraviewI am working on pricing Bermudan swaptions using longstaff-schwartz method. Have some trouble in deciding the basis functions for regression. Anybody have experience on that? More specificly, can we just use the forward swap values, (maybe a quadratic function). would that be enough.Also, according to several papers, it takes more than 10,000 MC paths for it to be effective. it's a nightmare in terms of memory consumption etc. Any thoughts, tips on that?Thanks a loti did some tests last year on the LS method. I found that it was decent but not great. The price tended to be quite affected by the choice of regression functions. I'd recommend using European swaptions. Also, how good it looks varies a lot with hwo complicated the market data. i.e. with flat vols and flat yield curve it looks a lot better than with curved vols, realistic market curve and many factors

European swaptions are the worst choice for in terms of complexity. This is real market data and humped vol term structure. on top of that, calculate forward european swaptions at each exercise dates is really not something I enjoy doing. How tough is that?Thanks

if you use a swap rate market model it's trivial

QuoteOriginally posted by: mjQuoteOriginally posted by: foraviewI am working on pricing Bermudan swaptions using longstaff-schwartz method. Have some trouble in deciding the basis functions for regression. Anybody have experience on that? More specificly, can we just use the forward swap values, (maybe a quadratic function). would that be enough.Also, according to several papers, it takes more than 10,000 MC paths for it to be effective. it's a nightmare in terms of memory consumption etc. Any thoughts, tips on that?Thanks a loti did some tests last year on the LS method. I found that it was decent but not great. The price tended to be quite affected by the choice of regression functions. I'd recommend using European swaptions. Also, how good it looks varies a lot with hwo complicated the market data. i.e. with flat vols and flat yield curve it looks a lot better than with curved vols, realistic market curve and many factorsIt it really true that choice of basis functions greatly affects the LS method. Several time it took me very serious experimentation to figure out some appropriate basis functions for complex derivatives other than bermudan swaptions.For the bermudan swaptions in multi-factor models, I would suggest a trick based on approach by Leif Andersen in his paper. He used the value of largest swap( by value) that is a component of Bermudan swaption for the decision of optimal exercise of the bermudan . I suggest that you use this value as a basis function in your regression. This really helps a lot and gives quite accurate results without having to calculate swaptions which actually are expensive to calculate for every path. Similar trick sometimes hold for more complex derivatives as well.You can download Andersen's paper from SSRN. A copy can be found on my web page. LIBOR MARKET MODEL WEBBest regards,Ahsan Amin

I have to price Bermudan Swaptions in the LM Model using MC (by Longstaff-Schwartz or Andersen) .When simulating the LM model, i can choose to simulate it under the spot measure or the terminal measure .What i'd like to known is : Is one choice of measure is preferable compared to the other & why?

QuoteOriginally posted by: mji did some tests last year on the LS method. I found that it was decent but not great. The price tended to be quite affected by the choice of regression functions. I'd recommend using European swaptions. Also, how good it looks varies a lot with hwo complicated the market data. i.e. with flat vols and flat yield curve it looks a lot better than with curved vols, realistic market curve and many factorsThe LS pricing of Bermudan options is actually very good. Have not noticed any of these phenomena. I don't recommend using European swaptions. There is only one choice of regression functions that makes sense. Using the spot measure is convenient.

QuoteOriginally posted by: elanThe LS pricing of Bermudan options is actually very good. Have not noticed any of these phenomena. I don't recommend using European swaptions. There is only one choice of regression functions that makes sense. Using the spot measure is convenient.Sorry Elan, could you tell me a little more on why the spot measure is more convenient (than the terminal) ?Concerning the variable of regression , one often find in the litterature the money market account (ie numeraire) and the value of the underlying swap. If i were to do the simulation under the terminal measure , would the terminal bond (ie numeraire) and the value of the underlying swap be an appropriate choice ?