Posted by
cheng li on
Nov 14, 2014; 1:12pm
URL: http://quantlib.414.s1.nabble.com/Grids-shift-trick-to-improve-the-convergence-speed-PDE-method-tp16025p16030.html
Hi Spanderen,
The numerical result says there is no much difference between these 2
methods for vanilla option:
The parameters are same as my previous example
Grids Shift Grids + Damping Damping
10 4.049015807 4.023573966
20 3.888731876 3.883259801
30 3.859347301 3.860949207
40 3.853164351 3.853494439
50 3.850117743 3.850127399
60 3.848403455 3.848320323
70 3.847346072 3.847233176
80 3.846453732 3.846532679
90 3.846028584 3.84605574
100 3.845716741 3.845717576
110 3.845481428 3.845467956
120 3.845299598 3.845277305
130 3.845111453 3.845129343
140 3.845005422 3.845012225
150 3.844918509 3.84491863
160 3.844846402 3.844841907
170 3.844785935 3.844778105
180 3.844717978 3.844724605
190 3.844676773 3.844679439
200 3.844641179 3.844641171
210 3.844307792 3.844307792
Regards,
Cheng
-----邮件原件-----
发件人: Cheng Li [mailto:
[hidden email]]
发送时间: 2014年11月14日 20:09
收件人: 'Klaus Spanderen';
[hidden email]
主题: 答复: [Quantlib-dev] Grids shift trick to improve the convergence
speed PDE method
Hi Spanderen,
Let me do one for us. I'll come back to you when it is finished. IMO I think
the convergence speed won't improve as much as the case for digital since
there is no discontinuity in plain vanilla payoff.
BTW, I agree with you that this will change the default behavior if using my
implementation. That is the reason I sent this all the developers to see
other's opinion before raise a pull request in github.
Regards,
Cheng
-----邮件原件-----
发件人: Klaus Spanderen [mailto:
[hidden email]]
发送时间: 2014年11月14日 14:42
收件人:
[hidden email]
主题: Re: [Quantlib-dev] Grids shift trick to improve the convergence speed
PDE method
Hi
cool!
The results are looking promising. Do you get a similar improvement if you
apply the shift trick to plain vanilla option.
The only thing we might consider is that we change behavior if the shift
becomes the default.
regards
Klaus
On Wednesday, November 12, 2014 12:01:52 PM cheng li wrote:
> Hi Team,
>
>
>
> Current I am in an effort to improve the convergence speed of
> FdBlackScholesVanillaEngine to digital option. The background is as
follows:
>
>
>
> For digital option there is some discontinuity in the initial condition.
> Such discontinuity will cause the straight Crank-Nicolson method to
> show severe odd-even effect. In current implementation, the pricing
> engine will use several damping steps to suppress some effect. However
> as claimed in Interest Rate Modeling. Section 2.5 p60 in V1 by
> Anderson and Piterbarg, Damping steps is not adequate for such task.
> Referencing to Tavella and Randall's book, they suggest to shift the
> grids to let the discontinuity lies exactly half way between 2 grids.
> They claimed that this will greatly improve the convergence.
>
>
>
> I have completed such experimental implementation in QuantLib. Besides
> I do a comparison between "Grids Shift + Damping" and "Damping"
> methods. The result is promising. The convergence speed is greatly
> improved and is consistent with what Anderson and Piterbarg claimed.
> The result can be referred from the attached Shift_experiment.xlsx file.
>
>
>
> To replicate my result, you can replacing the original files in
> ql\methods\finitedifferences\meshers with the files I attached
> (concentrating1dmesher.hpp, concentrating1dmesher.cpp). And run the
> test program testPDEScheme.cpp
>
>
>
> The results is based on "Grids shift + 2 damping steps". Also you can
> run the test program without replacing the mesher file to see what is
> result of
> "2 damping steps". Besides I also run through the QuantLIb test suite.
> This change won't break any existing test case.
>
>
>
> Is anyone have some interest to have a look at this? I'd like to
> create a pull request for this change if no one is against it.
>
>
>
> Regards,
>
> Cheng
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