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?
Answer
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.
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