mandelbrotian randomness in finance, examples of practical uses?

[eastbay]

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i'll answer the main question:

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what do you mean by mandelbrotian randomness

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i mean alternatives to stochastic models where the underlying assumptions are too stringently normal (even when jumps & other variations are introduced).

i am looking for a book i think i found in the book mandelbrot wrote on fractals in finance and that is on order being shipped to me.

the goal is to use power laws instead of the distributions where the probability of highly unlikely events decreases exponentially.

that is what i mean by mandelbrotian randomness.


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I think that is probably not the best description for the exceptionally general ideas you are talking about.

You might want to just say "non-Gaussian randomness" instead.

eastbay

[DcifrThs]

[ QUOTE ]
[ QUOTE ]
i'll answer the main question:

[ QUOTE ]
what do you mean by mandelbrotian randomness

[/ QUOTE ]

i mean alternatives to stochastic models where the underlying assumptions are too stringently normal (even when jumps & other variations are introduced).

i am looking for a book i think i found in the book mandelbrot wrote on fractals in finance and that is on order being shipped to me.

the goal is to use power laws instead of the distributions where the probability of highly unlikely events decreases exponentially.

that is what i mean by mandelbrotian randomness.


[/ QUOTE ]

I think that is probably not the best description for the exceptionally general ideas you are talking about.

You might want to just say "non-Gaussian randomness" instead.

eastbay

[/ QUOTE ]

fair. and thank you.

so i'm looking for non-gaussian randomness in asset pricing.

i assumed the most widely used at this point would likely be that of the famous mathematician benoit mandelbrot.

talk about stringent assumptions [img]/images/graemlins/tongue.gif[/img]

soooooo, back on track , does anybody know where i can find practical uses for non-gaussian randomness in terms of financial market analysis. this includes anything from portfolio construction to risk assessment.

Barron

[Jeff W]

Did you check SSRN?

[hawk59]

barron,

let me just say that from your posts it is pretty clear you are making the mistake of thinking that investing is supposed to be complicated and smart sounding, when it is really supposed to be very simple and straightforward

[DcifrThs]

[ QUOTE ]
barron,

let me just say that from your posts it is pretty clear you are making the mistake of thinking that investing is supposed to be complicated and smart sounding, when it is really supposed to be very simple and straightforward

[/ QUOTE ]

i think you are the better part of half right. for one, i tend to complicate things as that is just my nature.

investing may be "simple", but understanding where we are in the research behind it isn't. i'm not satisfied with my current level of knowledge (though i know enough to never have to learn more again should i choose not to. i.e. i can create passive porfolios and have a decent sense of where misvaluations are and can create an active portfolio that will, i hope, not blow up and seek to gain off of those misvaluations)

but, that isn't enough for me [img]/images/graemlins/frown.gif[/img]

i want to always be in the depths of finance. i want to understand everything that i can and, to that end, i'm applying to some of the top funds/banks in the world. knowing what is going on in the current scholarly research is helpful. understanding the practicality of it all and being able to form useful opinions is even better.

so i like to dig.

some of it may be useless to many of you but i enjoy it and want to learn. my language may not be as simple as possible but i try to be clear & correct as much as i can.

let me know if those rambling make any sense at all [img]/images/graemlins/confused.gif[/img]

thanks,
Barron

[DcifrThs]

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Did you check SSRN?

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ok, seriously... i need to ask you this question Jeff,


will you marry me?? THAT SITE RULES!

3 papers on finance by mandelbrot (multifractal model of asset returns, large deviations & the distribution of price changes, and multifractality of DM/USD exchange rates)

EDIT: also 2 papers by Taleb (we don't quite know what we are talkign about when we talk about volatility, and the illusions of dynamic replication) though i think i read one of them via his homepage

Barron

[Sniper]

Barron, can you explain why your time wouldn't be better spent looking for patterns of non-randomness, rather than randomness?

(Just to be clear, this is intended as a serious question)

ps... I was also hoping for a more detailed response to my last post, in this thread.

[DcifrThs]

[ QUOTE ]
Barron, can you explain why your time wouldn't be better spent looking for patterns of non-randomness, rather than randomness?

(Just to be clear, this is intended as a serious question)

ps... I was also hoping for a more detailed response to my last post, in this thread.



[/ QUOTE ]

i don't know what you mean by patterns of "non-randomness."

movements of asset/security prices are for the most part, random. improvements in modeling them have been made and one of the main ones in the past century was the creation of the B-S-M framework that does a good job of matching the results of models using stochastic variables to real world asset/security price moves (and thus valuation).

there are some setbacks with respect to using the models exclusively as has been noted in this thread.

the goal here is to understand the most current thoughts on the modeling of asset prices.

BM wrote a book that i ordered on the mathematical (& non-mathematical) treatment of scalable distributions in asset pricing (i.e. modeling the movement of asset prices through time). that should be a good start.

sorry i didn't give you a more complete answer last time. did i do better here?

if not, can you refine your question or point out where my answer is lacking?

thanks,
Barron

[edtost]

[ QUOTE ]

soooooo, back on track , does anybody know where i can find practical uses for non-gaussian randomness in terms of financial market analysis. this includes anything from portfolio construction to risk assessment.

Barron

[/ QUOTE ]

my first thought here would be things relating to risk assessment using copulas with non-gaussian (perhaps nonparametric) marginal distributions. i have no industry experience using such models, but can point to some books and papers for you to take a look at.

David Lando - "Credit Risk Modeling" (one short subsection, so I'll just list the papers he cites)
Gregory and Laurent 2003? "Basket default swaps, CDOs and factor copulas"
Li 2000 "On default correlation: a copula function approach"
Rogge and Schonbucher 2003? "Modeling dynamic portfilio credit risk"
Schubert and Schonbucher 2001 "Copula dependant default risk in intensity models"

Rene Carmona - "Statistical Analysis of Financial Data in S-Plus". I hate both him and this book, but it contains more of the type of thing you're asking about (I think) than any other reference I'm familiar with. He emphasizes the use of kernels and generalized pareto distributions. The writing is not as terse as either of the other two books I mention, and he seems to be more grounded in real-world applications than most academics.

also, the book "Financial Econometrics" by Gourieroux and Jasiac has a good section on management of extreme risks, describing methods for calculating VaR with semi- and non-parametric return distributions, creating VaR-efficient portfolios with such parameters, and proposing an alternative to standard CARA utility functions to use when doing such calculations.

[DcifrThs]

[ QUOTE ]
[ QUOTE ]

soooooo, back on track , does anybody know where i can find practical uses for non-gaussian randomness in terms of financial market analysis. this includes anything from portfolio construction to risk assessment.

Barron

[/ QUOTE ]

my first thought here would be things relating to risk assessment using copulas with non-gaussian (perhaps nonparametric) marginal distributions. i have no industry experience using such models, but can point to some books and papers for you to take a look at.

David Lando - "Credit Risk Modeling" (one short subsection, so I'll just list the papers he cites)
Gregory and Laurent 2003? "Basket default swaps, CDOs and factor copulas"
Li 2000 "On default correlation: a copula function approach"
Rogge and Schonbucher 2003? "Modeling dynamic portfilio credit risk"
Schubert and Schonbucher 2001 "Copula dependant default risk in intensity models"

Rene Carmona - "Statistical Analysis of Financial Data in S-Plus". I hate both him and this book, but it contains more of the type of thing you're asking about (I think) than any other reference I'm familiar with. He emphasizes the use of kernels and generalized pareto distributions. The writing is not as terse as either of the other two books I mention, and he seems to be more grounded in real-world applications than most academics.

also, the book "Financial Econometrics" by Gourieroux and Jasiac has a good section on management of extreme risks, describing methods for calculating VaR with semi- and non-parametric return distributions, creating VaR-efficient portfolios with such parameters, and proposing an alternative to standard CARA utility functions to use when doing such calculations.

[/ QUOTE ]

this is great and thanks for your input.

i want to get through one thing at a time though since i'm not as quick w/ math as i'd like to be.

i got both mandelbrot books i mentioend, one is all logic & expressive prose while the other is a technical treatment of his theories. i've finisehd the former and have started in on the latter.

i just wanted to update this thread with a note that this guy is a freaking genius and will definitely be remembered for centuries to come. i can't imagine how he came up w/ this stuff.

more importantly though, the precise application of his theories isn't complete yet, however, even in the current state, he can replicate real time price changes in wide ranges of markets/scenarios/environments for stress testing of portfolios. it is definitely worth reading the non-technical treatment for anybody (or even the first half of the technical book which isn't forbidding since he doesn't get into the math till page 107 or something).

his 'pictoral essays' on problems with the current model is obviously compelling.

i'm sure some of the guys you mentioned (edtoast) have likely created something similar by using pareto-esque distributions since those seem to be the original base from which mandelbrot came to his theories.

thanks again and i've saved your choices in my "to read" folder.

Barron