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pcaspers
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Posts: 30
Joined: June 6th, 2005, 9:49 am
Location: Germany

Put-Call-Bermudan

April 3rd, 2016, 6:58 pm

Actually I did not really notice up to ten minutes ago, but from the plain pricing I had the condition in my code that only ITM paths are taken into account in the regression. This seems to break the new call pricing, in cases where the new call is deep ITM, the put OTM, and the put continuation value estimation has a big positive value although it should be negative (due to say a parabola only calibrated to the ITM points) so that the newcall price "call exercise + put continuation value" is totally wrong. Which is no problem for the put alone.
 
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Billy7
Posts: 262
Joined: March 30th, 2016, 2:12 pm

Put-Call-Bermudan

April 3rd, 2016, 7:22 pm

Great! All in line now. A few more powers of x and we'd be even closer but that's not important.I guess that wasn't straightforward to find. I also remember encountering some case when I was generally testing L-S, where both ITM and OTM paths were needed for correct valuation, but can't remember what option it was now... QuoteOriginally posted by: pcaspersHere are my updated results (16384 calibration paths, 65536 pricing paths, both MT, basis 1,x,x^2), they look better.Dividend = 0.06 Put = 0.371782 NewCall = 0.369788Dividend = 0.05 Put = 0.35782 NewCall = 0.356191Dividend = 0.04 Put = 0.344102 NewCall = 0.343301Dividend = 0.03 Put = 0.330794 NewCall = 0.332443Dividend = 0.02 Put = 0.317876 NewCall = 0.331628Dividend = 0.01 Put = 0.305251 NewCall = 0.346086Dividend = 0.00 Put = 0.293179 NewCall = 0.372513Dividend = -0.01 Put = 0.281477 NewCall = 0.406653Dividend = -0.02 Put = 0.270207 NewCall = 0.445153Dividend = -0.03 Put = 0.259406 NewCall = 0.49431Dividend = -0.04 Put = 0.24886 NewCall = 0.540387Dividend = -0.05 Put = 0.238844 NewCall = 0.589479Dividend = -0.06 Put = 0.229278 NewCall = 0.64232
Last edited by Billy7 on April 2nd, 2016, 10:00 pm, edited 1 time in total.
 
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pcaspers
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Posts: 30
Joined: June 6th, 2005, 9:49 am
Location: Germany

Put-Call-Bermudan

April 4th, 2016, 6:41 am

Yes, thanks a lot again. I can rerun with more paths, Sobol sequences + Brownian bridges, a richer basis, but as you say, it won't be very insightful. Concerning the regression I am even thinking if it might be useful to have two regions with a separate calibration. But for the time being the global one taking all paths looks good enough. :-)
 
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Billy7
Posts: 262
Joined: March 30th, 2016, 2:12 pm

Put-Call-Bermudan

April 4th, 2016, 9:28 am

QuoteOriginally posted by: pcaspersYes, thanks a lot again. I can rerun with more paths, Sobol sequences + Brownian bridges, a richer basis, but as you say, it won't be very insightful. You're very welcome. It was enjoyable and good practice to try and solve a problem together here with different people contributing, looking at it from different angles, using different methods, as Paul also said.QuoteOriginally posted by: pcaspersConcerning the regression I am even thinking if it might be useful to have two regions with a separate calibration. But for the time being the global one taking all paths looks good enough. :-) Yes, could be interesting as well, though you're right that it may not be necessary. If you do try it though, you have my PDE results (which are for the American/Bermudan generated put like in your case) which should be "exact" to all digits shown, so you could check any relative accuracy gain of the two-region regression, at least for the equity case.
Last edited by Billy7 on April 3rd, 2016, 10:00 pm, edited 1 time in total.
 
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pcaspers
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Posts: 30
Joined: June 6th, 2005, 9:49 am
Location: Germany

Put-Call-Bermudan

April 4th, 2016, 12:04 pm

that's great, thanks Billy7, I will look at it when there is some free time again for it