Hi wilmotters,I'm trying to make sense of the "this is so simple you should always try it" Richardson extrapolation as described in Paul Wilmott's book on page 1443. As an example Paul calculates prices for an option with 3 different methods:Analytical BSM gives 13.269Expl. Finite difference with 20 asset steps gives 13.183 (error = 0.202)Expl. Finite difference with 30 asset steps gives 13.275 (error = 0.286)Paul then applies Richardson extrapolation using the previous two finite difference results (with 20 steps, and with 30 steps) and gets a new result of 13.275 (error = 0.006). I have tried (and failed) to reproduce this result. Could one of you guys show me how I arrive at this price of 13.275? I tried to plug the values into the various formulae but I never get the right result. Surely it must be easy, but it's driving me insane ;-)Thanks much!A

Well, you've got the numbers wrong to start with!Expl. Finite difference with 20 asset steps gives 13.067 (error = 0.202)Expl. Finite difference with 30 asset steps gives 13.183 (error = 0.286)etc.P

QuoteOriginally posted by: PaulWell, you've got the numbers wrong to start with!Expl. Finite difference with 20 asset steps gives 13.067 (error = 0.202)Expl. Finite difference with 30 asset steps gives 13.183 (error = 0.286)etc.PI'm stupid -- I posted the wrong numbers here, but I used the right ones when trying to calculate 13.275. Could you kindly tell me how to arrive at this number? I am really stuck here.Here are the correct numbers from p.1244 again.BSM: 13.269, no errorFD,20 steps: 13.067, error=0.202FD,30 steps: 13.183, error=0.086Richardson: 13.275, error=0.006Thanks much!

Here is what I tried...which corresponds with the exact BSM value. However, how can I use these number to end at 13.275, the "Richardson Extrapolation"?

QuoteOriginally posted by: ASchmidtHere is what I tried...which corresponds with the exact BSM value. However, how can I use these number to end at 13.275, the "Richardson Extrapolation"?Well, first up, you could quit smoking....

QuoteOriginally posted by: TraderJoeQuoteOriginally posted by: ASchmidtHere is what I tried...which corresponds with the exact BSM value. However, how can I use these number to end at 13.275, the "Richardson Extrapolation"?Well, first up, you could quit smoking....Help me solve my (apparently quite stupid) question, and I'll quit tomorrow.

How does the error in the explicit method vary with number of asset steps? You need to weight each estimate by that dependence. Now read that page again and come back with the results!P

Solution:where 10=200/20 (Smax divided by 20 steps) and 6.667=200/30 (Smax devided by 30 steps).In hindsight it really wasn't that hard o_O...My problem was that I interpreted the deltaS^2 as the error. (Why? I don't know... but next time it guess I should begin reading at the beginning of the chapter, not the end...)

Go to page 1215:dS = 2 * Strike / NASSo, back to page 1244:ds1 = 2*100/20ds2 = 2*100/30 And:((ds2^2) 13.067 - (ds1^2) 13.183)/((ds2^2) - (ds1^2))13.2758Now quit smoking !

Although I missed your answer by 3 min, the quit smoking part is still valid.

Man! That was close! ;-)And, as for the quit smoking part, you'll want to send your request here.

QuoteOriginally posted by: MCarreiraAlthough I missed your answer by 3 min, the quit smoking part is still valid.smoke is not only bad for lungs

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: MCarreiraAlthough I missed your answer by 3 min, the quit smoking part is still valid.smoke is not only bad for lungsSee, I really wanted to quit, but you guys are just too slow. Now I have to continue smoking and die.And you (especially Paul and TraderJoe) share the guilt.