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MCarreira
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March 31st, 2007, 4:57 pm

N,Let's say Abin Sur drops from space and gives you a power ring that produces "real" randomness, so you can rise above mankind as the RaNdom LanterN and laugh at their puny Mersenne twisters.But you decide to make money out of it, and you feed your ring's output to a MC engine.Unfortunately, your computer is not as powerful as you are, and works at the same speed as other computers. So your pricer will ask for let's say N=666666 random numbers as a reasonable compromise between accuracy and speed.Then what's the chance that your truly random numbers leave a specific part of the payoff unvisited ? Or the chance that you visit it too much ?Will true randomness betray you or be your friend ?Since it's a trash talk thread ... couldn't resist ! In Brazil we say "I may lose a friend but (would) not (miss) a joke".
Last edited by MCarreira on March 31st, 2007, 10:00 pm, edited 1 time in total.
 
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gardener3
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N's trash talk thread

March 31st, 2007, 6:57 pm

"We all know statistics is based on the normal distribution"No, this is clearly wrong. Statistics, doesn't even have to be based on probability theory, you can just count outcomes. "but financial timeseries have a Levy distribution"This is just an assumption as any. Can you prove it?
 
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PaperCut
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N's trash talk thread

March 31st, 2007, 11:23 pm

QuoteOriginally posted by: MCarreiraN,Let's say Abin Sur drops from space and gives you a power ring that produces "real" randomness, so you can rise above mankind as the RaNdom LanterN and laugh at their puny Mersenne twisters.But you decide to make money out of it, and you feed your ring's output to a MC engine.Unfortunately, your computer is not as powerful as you are, and works at the same speed as other computers. So your pricer will ask for let's say N=666666 random numbers as a reasonable compromise between accuracy and speed.Then what's the chance that your truly random numbers leave a specific part of the payoff unvisited ? Or the chance that you visit it too much ?Will true randomness betray you or be your friend ?Since it's a trash talk thread ... couldn't resist ! In Brazil we say "I may lose a friend but (would) not (miss) a joke".This post kicks ass.The RaNdom LanterN !! Awesome !!
 
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N
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N's trash talk thread

April 1st, 2007, 9:31 am

Then what's the chance that your truly random numbers leave a specific part of the payoff unvisited ? This isn't a joke at all. It's a good question. If the ring generates only truely random numbers, the chance of leaving a part of the payoff unvisited is 100% irrespective of the number of random numbers used. Payoff functions aren't trivial as your story may suggest.True randomness betrays all.
 
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N
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N's trash talk thread

April 1st, 2007, 11:52 am

QuoteOriginally posted by: outrunlow discrepancy sequences visit all regionsNow where did you get that very stupid idea? Low discrepancy numbers are quite limited in their application to integration and because of this are useless for finance applications. In other words, low discrepancy sequences help get the wrong answer faster!
 
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Traden4Alpha
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N's trash talk thread

April 1st, 2007, 12:11 pm

QuoteOriginally posted by: NThen what's the chance that your truly random numbers leave a specific part of the payoff unvisited ? If the ring generates only truely random numbers, the chance of leaving a part of the payoff unvisited is 100% irrespective of the number of random numbers used. Perhaps the best RNG would be a live market feed piped directly into the MC. That way, the MC would visit the same parts of the space that the market does.I wonder how many believers in EMH would do this?
 
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quartz
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April 1st, 2007, 1:44 pm

QuoteNow where did you get that very stupid idea? Low discrepancy numbers are quite limited in their application to integration and because of this are useless for finance applications. Please guys, why do you keep feeding him? This clearly could go on like this forever... as he seems "quite limited" in his application to topics expressable through an english alphabet. ED: repet.
Last edited by quartz on March 31st, 2007, 10:00 pm, edited 1 time in total.
 
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N
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N's trash talk thread

April 1st, 2007, 3:24 pm

QuoteOriginally posted by: quartzQuoteNow where did you get that very stupid idea? Low discrepancy numbers are quite limited in their application to integration and because of this are useless for finance applications. Please guys, why do you keep feeding him? This clearly could go on like this forever... as he seems "quite limited" in his application to topics expressable through an english alphabet. ED: repet.quartz,I bet you also believe in the second counting axiom (axiom of choice). Both low discripancy numbers and the second counting axiom only apply to the simplest manifolds (ie, translational groups and rotational groups, the ones with only abelian action).Can we move beyond undergrad math?Nedit: BTW Compound interest is an excellent of a translational group. Continuous compound interest is a translational Lie group with the algebra r*t. And yes, you can use sobel sequences on compound interest problems.
Last edited by N on March 31st, 2007, 10:00 pm, edited 1 time in total.
 
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MCarreira
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April 1st, 2007, 3:54 pm

quartz said:topics expressable through an english alphabetYou just put your finger on something here ... some threads remind me of Grant Morrison's "The Invisibles" ... remarkable characters, ideas impossible to express through the 26-letter alphabet, and the sense that the author is writing in a way (through his choice of images, metaphors and style) that makes sense only to him; so without having:(a) experienced what he has experienced and(b) attributed the same meanings to words and imagesone just feels dazzled and confused.N said:Then what's the chance that your truly random numbers leave a specific part of the payoff unvisited ? This isn't a joke at all. It's a good question. If the ring generates only truely random numbers, the chance of leaving a part of the payoff unvisited is 100% irrespective of the number of random numbers used. Payoff functions aren't trivial as your story may suggest.True randomness betrays all.I tried to wrap an idea on a joke; the idea was that true randomness happens, but when you are building a model of the world, you'll sometimes need to model randomness. Now, "model randomness" sounds ugly, but that's what you'll need to do if you want a model to work (if it works well or not it's another matter); you could model randomness in a gaussian way or not, you could buy RAND's "A Million Random Digits with 100,000 Normal Deviates", but you need to know what do you expect from your source of randomness and what do you expect from your model.If your goals are not that ambitious, and your model is really a toy model (we're not discussing physics here after all), some (pseudo/quasi-)randomness models may be more convenient to use than others.
 
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N
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April 2nd, 2007, 10:38 am

low discrepancy sequences are far superiors than true random sequences for integration. True, but low discrepancy sequences/RNGs are still limited to only trivial integration problems.
 
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N
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April 2nd, 2007, 1:14 pm

A simple example of non-trivial is a multi-valued payoff function. For example f(x)=tan(x) is okay, but f(x)=arctan(x) is not. Another example is when the random number generator output is orthogonal to what you're integrating.