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There is a plethora of pseudo-random-generators out there. Some of them are definetly better and some of them severily underperform.

My standard tool is Mersenne Twister - when I need to generate some decent pseudo randoms.

Still I never actually explicitly tested how the random-generator-choice affects the prices of derivatives.

  • Are there any papers on this topic out there ?
  • Does a "gold-standard" exist ? (a standard generator that is very widespread in quant circles)
  • What are your personal experiences with the effects of generator-choice?
Probilitator
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  • I don't have an answer but: have you looked at quasi Monte Carlo? I think comparisons can be hard to make because of the influence of the seed on the generated sequence. – Bob Jansen Mar 26 '14 at 10:10
  • Yes I had a look at quasi Monte Carlo :) But I don't have a solid opinion whether it is a good or bad approach and when one should/can use quasi Monte Carlo instead of the normal one. – Probilitator Mar 26 '14 at 10:47
  • @BobJansen Perhaps just for educational/illustrational purposes one could perhaps consider a case where a random generator underporfmes in a way so that it is noticeable in the price? – Probilitator Mar 26 '14 at 11:25

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Mersenne Twister is currently the most used PRNG in the quant world. It was even incorporated in C++11 so it can be considered standard nowadays. Any PRNG with reasonable statistical quality shall perform well (equivalently) for pricing, so that differences relate more to convenience (speed, parallelizability etc..). If the statistical quality is poor then you shall avoid a PRNG in general, not just for pricing (so I won't point to comparison papers). However quality needed for pricing is lower than e.g. for cryptography (in that respect you could use e.g. AES as a slower reference to be sure your PRNG does not hide nasty surprises; conversely you couldn't use MT for crypto). I tend to use WELL because it's statitically better than MT, yet still fast enough.

As for statistical quality, one usually wants a PRNG to pass the DieHard and DieHarder test suites, that's usually more than enough.

Quasi MC is a more complex topic altogether where all you need is uniform distribution of the samples, not randomness. The analysis is totally different and somewhat more involved.

Quartz
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  • didn't know that MT has been incorporated into C++11. Also what is AES ? – Probilitator Mar 26 '14 at 10:50
  • With regard to quasi Monte-Carlo. Seeing how you seem quite knowledgeable in the topic. Any suggested reading with respect to pros and cons of Quasi-MC etc ? I must admit I do not know when it can be applied and when not - muy understanding of it is also still a bit fuzzy. – Probilitator Mar 26 '14 at 10:54
  • AES = Advanced Encryption Standard, it is used in cryptography and build to be very hard to predict. It uses entropy generated by different events at the OS level. This a smart way to achieve unpredictability but is very slow if you lead a lot of randomness.

    For an introduction to QMC methods you could look at Judd.

     – Bob Jansen Mar 26 '14 at 11:06
  • @Quartz could you elaborate on "reasonable statistical quality" - what tests should PRNGs pass to be eligible for pricing purposes ? – Probilitator Mar 26 '14 at 11:22
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    For qMC you can check the book from Lemieux, it also deals with various finance examples. Or the shorter introductions also by Lemieux&L'Ecuyer or by Larcher&Leobacher, or the chapter in Glasserman. Anyway it's quite a tricky topic, don't expect to use it as a black-box without surprises. – Quartz Mar 26 '14 at 14:03
  • @Quartz thank you for the warning. Does anyone know how to sample from AES ? I was also wandering why PRNG-choice is rarely mentioned in quant-finance-literature. This is what most of our results are based on but no one cares about the fundamentals ? – Probilitator Mar 27 '14 at 10:17
  • There's a lot of discussion about PRNGs in finace forums or some books, but given modern generators quality the issue is now kinda solved. Roughly said one samples from AES (or any other good hash function) by feeding in successive numbers, their encrypted values are then pseudorandom; check the so called "counter mode" of AES. – Quartz Mar 28 '14 at 09:55