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by Dostoevsky
January 13th, 2015, 5:43 pm
Forum: Numerical Methods Forum
Topic: Sobol Sequences and Dimensionality
Replies: 2
Views: 5572

Sobol Sequences and Dimensionality

<t>> "I assume I need to be changing the direction numbers"I wouldn't play with changing or generation of the direction numbers. The direction numbers are the key to the efficiency of the Sobol' sequence generator. You can readI. Sobol', D. Asotsky, A. Kreinin, S. Kucherenko. Construction and Compar...
by Dostoevsky
October 27th, 2014, 3:12 pm
Forum: Technical Forum
Topic: Brownian Bridge
Replies: 22
Views: 154976

Brownian Bridge

QuoteOriginally posted by: TinManBear in mind too that you can't use Cholesky with SobolWhy is that ?
by Dostoevsky
October 27th, 2014, 9:00 am
Forum: Technical Forum
Topic: Sobol numbers from BRODA
Replies: 8
Views: 144992

Sobol numbers from BRODA

For statistical and other test of BRODA's and other Sobol' sequence generators you can read I. Sobol', D. Asotsky, A. Kreinin, S. Kucherenko. Construction and Comparison of High-Dimensional Sobol' Generators, 2011, Wilmott Journal, Nov, pp. 64-79
by Dostoevsky
October 26th, 2014, 10:11 am
Forum: Technical Forum
Topic: Sensitivity analysis in finance
Replies: 10
Views: 192298

Sensitivity analysis in finance

<t>..and two other papers on application of Global sensitivity analysis in finance:1. M. Bianchetti, S. Kucherenko, S. Scoleri, Better Pricing and Risk Management with High Dimensional Quasi Monte Carlo, WBS 10th Fixed Income Conference, Barcelona , September, 2014;2. Kucherenko S., Shah N. The Impo...
by Dostoevsky
October 26th, 2014, 9:54 am
Forum: Technical Forum
Topic: implementation of the SOBOL's sequences
Replies: 24
Views: 199280

implementation of the SOBOL's sequences

<t>A note of caution: the easiness of implementation doesn't imply efficiency: good Sobol' sequences are very difficult to construct. For comparison of various Sobol' sequence generators used in the industry read I. Sobol', D. Asotsky, A. Kreinin, S. Kucherenko. Construction and Comparison of High-D...
by Dostoevsky
October 16th, 2014, 4:53 pm
Forum: Numerical Methods Forum
Topic: I have a c code for Sobol sequence generation
Replies: 13
Views: 57098

I have a c code for Sobol sequence generation

<t>Quote Would be interesting to pin down exactly the cases where the brownian bridge discretisation works less well than the standard one (you claim cliquets?) as basically I've always found sobol unusable without bb. Also, have you tried the spectral construction of the wiener process? Should prob...
by Dostoevsky
October 15th, 2014, 8:37 am
Forum: Numerical Methods Forum
Topic: I have a c code for Sobol sequence generation
Replies: 13
Views: 57098

I have a c code for Sobol sequence generation

<t>Quotehave done any tests for the LMM? eg a TARN cf the examples in More Mathematical Finance.No, we haven't done such tests but we would like to do them. Would you be interested in doing them together ?With colleagues we've done recently a work ( Marco Bianchetti, Sergei Kucherenko, Stefano Scole...
by Dostoevsky
October 12th, 2014, 12:24 pm
Forum: Numerical Methods Forum
Topic: I have a c code for Sobol sequence generation
Replies: 13
Views: 57098

I have a c code for Sobol sequence generation

Difficult to tell why there is a saturation for many SobolSeq generators at low dimensions ( Dim = 8 ) at Fig. 1. I would be interested to see other similar comparisons with other discrepancy measures ( not just 0.0 anchored L2 discrepancy ).
by Dostoevsky
October 12th, 2014, 11:16 am
Forum: Numerical Methods Forum
Topic: High Dim Sobol
Replies: 10
Views: 58564

High Dim Sobol

<t>Currently, the Sobol' sequence generator with the highest dimension is BRODA's SobolSeq32000. It satisfy additional uniformity properties: Property A for all 32000 dimensions and Property A' for 5 adjacent dimensions. For comparison of various Sobol' sequence generators used in the industry read ...
by Dostoevsky
October 12th, 2014, 11:04 am
Forum: Numerical Methods Forum
Topic: I have a c code for Sobol sequence generation
Replies: 13
Views: 57098

I have a c code for Sobol sequence generation

<t>Quotei haven't done extensive tests but I reckon that JoeKuo D7 are the best. For comparison of various Sobol' sequence generators used in the industry ( including Joe&Kuo ) read I. Sobol', D. Asotsky, A. Kreinin, S. Kucherenko. Construction and Comparison of High-Dimensional Sobol' Generator...
by Dostoevsky
October 12th, 2014, 10:46 am
Forum: Numerical Methods Forum
Topic: Sobol Numbers
Replies: 3
Views: 22556

Sobol Numbers

<r>QuoteOriginally posted by: animeshsaxenaQuoteI am using the direction numbers given by this website <URL url="http://web.maths.unsw.edu.au/~fkuo/sobol/index.html">http://web.maths.unsw.edu.au/~fkuo/sobol/index.html</URL> I understand it's widely used so direction numbers are bound to be correct!F...
by Dostoevsky
October 12th, 2014, 9:44 am
Forum: Numerical Methods Forum
Topic: Quasi MC delusions and difficulties
Replies: 7
Views: 28678

Quasi MC delusions and difficulties

<t>QuoteOriginally posted by: quartzQuoteBesides that the sobol' direction numbers that have been used for a few years had some flows...Indeed, efficient direction numbers is the key to the perfomance of Sobol' sequence generators. For a comparison of various Sobol' sequence generators used in the i...
by Dostoevsky
May 28th, 2008, 9:36 am
Forum: Technical Forum
Topic: What variance reduction technique to choose?
Replies: 23
Views: 63680

What variance reduction technique to choose?

<t>QuoteWell, if I look at the results in the book of Jackel, it seems that beyond dimension 15 the difference between pseudo-random (Mersenne Twister) and Sobol numbers is negligible. So if you are building a model for multiple assets, the question is whether this is worth the trouble... Yes, it is...
by Dostoevsky
April 4th, 2008, 10:26 am
Forum: Technical Forum
Topic: What variance reduction technique to choose?
Replies: 23
Views: 63680

What variance reduction technique to choose?

QuoteI particularly am very interested in global optimization problem.Sobol' sequences can be efficiently used for solving global optimization problems. Read thesepapers for details
by Dostoevsky
April 3rd, 2008, 9:25 pm
Forum: Technical Forum
Topic: What variance reduction technique to choose?
Replies: 23
Views: 63680

What variance reduction technique to choose?

<t>Mersenne twister is just another random number generator. It gives a Monte Carlo convergence rate 1/sqrt(N), N is the number of sampled points or paths ).Sobol' sequence is the best ( in practice ) low-discrepancy sequence. It provides a rate of convergence 1/N ( for path dependent options it is ...
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