- Traden4Alpha
**Posts:**23951**Joined:**

QuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaBut if you want samples drawn from NORMINV(f(rng)) to have the same moments as a regular normal distribution, then you'll need something a bit different. In fact, I suspect you will need a non-linear transform to get the 2nd the 4th moment to behave.that exactly what I was thinking!Nobody is talking about this choice.. Maybe because with 32 or 64 bit resolution this doesn't matter much (assuming you have at least the mean set at 0.5)Indeed! We are spoiled by precision. Yet might some TRNGs produce coarser outputs?Also, this transform might be useful for n-tree models.

- MiloRambaldi
**Posts:**273**Joined:**

QuoteOriginally posted by: outrunYou'll need an account in order to have write access. If you drop me an email at thijs@sitmo.com, then I can create an account. Also note that you need to make sure that you can release the code under the boost license (you mentioned something about "property of the IB that I work at"). OK. I will get started.I keep referring to code that has yet to be written. The code I have written is only available on the computers at work, and I do not have any remote network access. I am assuming that if I redo any of my work on my own time that its mine to release however I please. The particular code I was referring to for converting multiple seeds to MT states is only something like 20 lines.

QuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaBut if you want samples drawn from NORMINV(f(rng)) to have the same moments as a regular normal distribution, then you'll need something a bit different. In fact, I suspect you will need a non-linear transform to get the 2nd the 4th moment to behave.that exactly what I was thinking!Nobody is talking about this choice.. Maybe because with 32 or 64 bit resolution this doesn't matter much (assuming you have at least the mean set at 0.5)You raised a good point!And we should still care about it for QMC, where (e.g. in a large CreditVaR, but in general anyway) we might want to use just a few thousand samples per instrument. so sampling virtually only the most significant bits!

- MiloRambaldi
**Posts:**273**Joined:**

QuoteOriginally posted by: outrunQuoteOriginally posted by: MiloRambaldiI am assuming that if I redo any of my work on my own time that its mine to release however I please. read a bit about that, it's risky.. Here at the university we had some lawsuits. It's best to discuss it with your boss. It's either allowed, or not, and it better to know that before your start than afterwards.I see its not so straight forward. It would also not be so straightforward to know whether it is allowed or not (see some of my previous posts).However, I'm not really concerned. For one thing, this work does not involve new inventions. All of the algorithms/techniques are from publicly available literature. Secondly, I work in Canada where our laws are generally more liberal (i.e. fair) than the US. If you will accept my work, I have no hesitations going forward.

- Traden4Alpha
**Posts:**23951**Joined:**

QuoteOriginally posted by: outrunQuoteOriginally posted by: quartzQuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaBut if you want samples drawn from NORMINV(f(rng)) to have the same moments as a regular normal distribution, then you'll need something a bit different. In fact, I suspect you will need a non-linear transform to get the 2nd the 4th moment to behave.that exactly what I was thinking!Nobody is talking about this choice.. Maybe because with 32 or 64 bit resolution this doesn't matter much (assuming you have at least the mean set at 0.5)You raised a good point!And we should still care about it for QMC, where (e.g. in a large CreditVaR, but in general anyway) we might want to use just a few thousand samples per instrument. so sampling virtually only the most significant bits!Indeed,.. or just grid integration for low dimensional problems. For uniform distributions on [0,1], and N samples, we can see if we can define the mapping to [0,1] based on Simpson's, or Trapezoid etc Uniform grids or low discrepancy uniform sampling might miss or underrepresent the "most significant bits" of the system. That is, it might miss the bits in the tail where the pay-off function takes on extreme values.

- Traden4Alpha
**Posts:**23951**Joined:**

QuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: outrunQuoteOriginally posted by: quartzQuoteOriginally posted by: outrunQuoteOriginally posted by: Traden4AlphaBut if you want samples drawn from NORMINV(f(rng)) to have the same moments as a regular normal distribution, then you'll need something a bit different. In fact, I suspect you will need a non-linear transform to get the 2nd the 4th moment to behave.that exactly what I was thinking!Nobody is talking about this choice.. Maybe because with 32 or 64 bit resolution this doesn't matter much (assuming you have at least the mean set at 0.5)You raised a good point!And we should still care about it for QMC, where (e.g. in a large CreditVaR, but in general anyway) we might want to use just a few thousand samples per instrument. so sampling virtually only the most significant bits!Indeed,.. or just grid integration for low dimensional problems. For uniform distributions on [0,1], and N samples, we can see if we can define the mapping to [0,1] based on Simpson's, or Trapezoid etc Uniform grids or low discrepancy uniform sampling might miss or underrepresent the "most significant bits" of the system. That is, it might miss the bits in the tail where the pay-off function takes on extreme values.I think that a general issue, also for random sampling (except that you can't catch them on anything). I would say it depend of the ratio of probabilty decay vs payoff growth.Isn't this an orthogonal discussion that call for importance sampling and the likes?Whether this is orthogonal to the "Parallel RNG and distributed MC" discussion depends on how we decompose the system. If we view the job of the RNG and MC system to generate nice uniform samples and paths and relegate adjustment/weighting of the population of MC results in the pay-off's tails to some post process, then, yes, it's orthogonal. But if we want an RNG and MC process that samples in an application-specific, tail-dependent way to intelligently sample a nonlinear pay-off function, then this discussion is germane.For simplicity sake in version 1.0, I'd probably create a simple uniform sampler and defer weighting/tweaking of the MC results for later versions.

- Cuchulainn
**Posts:**62373**Joined:****Location:**Amsterdam-
**Contact:**

Thijs,Don't know if this is relevant but the transformation y = tanh(ax) ---> [0,1]. Tried it once with numerical quadrature. I remember posting it he once. See also this one as wellhttp://www.jstor.org/pss/2156486

Last edited by Cuchulainn on February 8th, 2012, 11:00 pm, edited 1 time in total.

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