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Patrik
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Posted: 2004-04-01 01:27

I have been looking at the following article a bit, so far I think it seems to be interesting (even if I do not claim to understand every bit of it yet):

http://xxx.lanl.gov/PS_cache/cond-mat/pdf/0403/0403022.pdf

Anyone else have read it? Any thoughts or comments? I thought discussing articles like this one could be interesting topics here at NP.


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AVt


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Posted: 2004-06-13 22:32

As far as i can follow it that gives Student-t distributions for fixed times as RNDs (which would be enough for me for quick & dirty prices). What i can not see (as always i got lost in that things from physics): how it evolves through time (to give a term structure or complete vol surface). Do i see that right or has somebody played with it?

Axel


chiral3
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Posted: 2004-06-16 00:29

This is good Patrik, thank you for the reference.  I have not read it yet, but it is on my list. I mean we fidget around all these stable disrtibutions.  Look at

thing / [(1+X^2/n)^(n+1)/2] where thing = gamma functions (you know) and X is a stochastic process.

n=1, or n goes to inf are stable distributions, the latter of which is Gaussian.  In and of itself, it is just a Student's t-distribution.

Note to self: I'll get back after I read.


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Patrik
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Posted: 2004-06-16 11:24

C3,

I'm also a big fan of making personal lists of things that seem interesting and should get back to. I always seem to create longer lists than is processable though.. I'm also looking to read this stuff more carefully, and have been so since I started this thread..


Graeme


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Posted: 2004-06-16 11:36

A couple of days ago I got an email from a friend and ex-colleague who has recently emigrated to Australia. I'll cut and paste a piece of his email here:

"In particular, you should look at Eckhard Platen's "benchmarked" models. He has rejected risk-neutral pricing (empirically, you can demonstrate that no equivalent martingale measure exists - often badly so), and developed a pricing parardigm that relies completely on empirical data and the natural measure which one can derive from this (via market prices of risk). There are some very interesting things that fall out of this: the asset price dynamics naturally include stochastic volatility as an intrinsic feature (no need to model it separately); the volatility naturally ends up being inversely correlated with asset price returns; also, the asset price processes are essentially exponentiated Bessel processes... so you get fat tails and other stylized facts about asset prices for free. It's really very interesting - it's taken him over 10 years to develop the approach - and appears to be getting some attention from practitioners (these kinds of models have been very successfully employed for equity index and currency markets)."

I haven't had a look at this yet (been very busy the last couple of days, and going off line this afternoon for a few days) but this certainly looks very interesting. Anybody know about this stuff?


Graeme West

Johnny
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Posted: 2004-06-16 11:54

Anybody know about this stuff?

Sadly not! But I'd like to hear about it if/when you get a chance to wade through it.


chiral3
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Posted: 2004-06-17 01:56

Oh tay.  That was interesting.  They recovered many of the well known models and did a comparison to empirical data.  I suppose that this is fertile ground in finance, although Bouchaud is a smart guy.  I think it was Levy and Khintchine that classified stable distributions.  a=1/2, b=1 was Levy stable, a=1 was Lorentz and a=2 was Gaussian.  So most practitioners back into a=2, but an academic with a good understanding of limit theorems could blow the shit out of the field, esp when the academics also work on ML desks ;-)

Edit: Where the brock is bloodninja?


Nonius is Satoshi Nakamoto. 物の哀れ

kr
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Posted: 2004-06-17 03:39
for a non-physics guy, how do you solve the fast-diffusion eq'n?  all the skew stuff isn't too interesting to me, but I like the fast-diffusion piece and the natural appearance of student-t.

my bank got pwnd

Scotty


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Posted: 2004-06-18 07:35

Graeme

I've read some of the Benchmark stuff.  I understand it fits the data pretty well and in a form that requires fewer parameters.

Scott


“Whatever you do, or dream you can, begin it. Boldness has genius and power and magic in it.”

AVt


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Posted: 2004-06-20 21:09

I 'worked' through Bouchaud & Borland to implement it in rough form.

One has to jump around a bit in the paper to get everything together.

What i have left out are some limiting cases like q=1, q=3, alpha=1
(and r=0) as one would to have remove that singularities carefully.
At least i still have the impression, that for alpha=1 _and_ q=3 one
has a discontinuity and for q=2 and q=9/5 probably as well.

The single smiles look reasonable, short times give a 'V'-shape and
with increasing times they flatten out - even the minima of the smiles
drift off. But the minima are not decreasing (ok, i have not done too
much examples), so they are visible for longer times. On p 25/26 they
suggest some corrections to that behaviour by varying the parameters
sigma and alpha.

The pricing formula (using some Pade approximate) is stated for small
variance vol^2 * time smaller than 1 and for large times strange things
may come out.

To summerize: it would make me happier to have the densities explicitly
at hand or some transform solution (both are over my head). For me it
is impossible to have a feeling whether the sometimes strange behaviour
(under time aspects) comes through the approximate solution or is part
of the method. I was too lazy to crosscheck with Borlands solution as
stated on p. 18 (519, i e alpha=1.

Find enclosed a Maple session as pdf (if someone wants the Maple sheet
just let me know). It contains some simple examples. If you find errors
please let me know.

Axel

Attached File: BouchaudBorland-quick&dirty.zip

 


eye51


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Posted: 2004-12-27 11:32
Has anybody tried to replicate the results presented in this paper ?

I find that the results of the general case for alpha=1 do not converge to the results of her previous paper, or fig. 7.

Have more people encountered this problem ? Or is it my mistake..

Peace means reloading your guns

quantie


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Posted: 2004-12-27 16:57

Has anyone looked at the skew-normal by P.azziani. ?

I have some very early results using it for some equity indices, I have got some good fits and seems like a naturaly way to characterize the skew.

 


AVt


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Posted: 2004-12-28 23:08

@eye
For me nothing changed against the stated, no i have not tried again (ok,
through mails Borland said to clear some points, but she did not; on the
other hand Bouchaud has considerable reputation, so it should be correct
and may be you ask him).

@quantie
sometimes a link is helpfull for others ...

Hm, just out of a mood: i hate all the sophisticated models, that do some
fit for static smiles or use historic returns without showing how to fit
the whole surface and - that's more important - how they perform, if the
spot moves and the market decides to set its own opinion on the smiles.
Actually i have not seen one satisfactory answer in public for stochastic
vola + jump for even 1 of the Q just stated (ok, may be i should try to
read and understand Cont & Tankov). Just a mood, but after having a really
good old Chambertin :-)


Path Integral


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Posted: 2004-12-29 00:43

Implementing this model is also on my list of things to do. Something I have been wondering about though, is how exotics prices compare to e.g. Heston, VG, or other Levy-type processes. Another point I have rtouble with is how to sell a model like this to traders or even worse: managers. One question that would arise: "How do I hedge the entropy index q?"

What I do like is the simplicity of the model.


quantie


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Posted: 2004-12-29 04:39
avt here it is

TicTacToe


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Posted: 2004-12-29 05:24
I got interested in the Borland-Bouchaud paper right the day it appeared on lanl because it was a follow-up of another one by Borland on her own (she got it published in PRL; a purely finance paper on Phys Rev Lett! Think about where physics is heading...)

Theoretically, Borland's idea was profoundly interesting to a rookie like me at the time. It was the first concrete dynamics I ran into that affords risk-neutral pricing. (Of course, by now, I already know a whole lot more about risk-neutral pricing and come to understand that Borland's idea didn't arise out of blue.)

Technically, there are three problems, however:

[1] In her PRL paper, Borland mistook something like replacing a term by average of something else (I have not retained the details, but her mistake is crystal clear in the paper). This "trick" made her option formula (parallel to Black-Scholes-Merton) analytically exact. Borland and Bouchaud then corrected the mistake. But her option formula is NO LONGER AN EXACT SOLUTION although they keep pretending it is.

[2] But the above point is minor. What is much more serious is that even with their corrected method (and the original Borland's "trick" itself), the discounted stock price is NOT a martingale. Because of that, most, if not all, subsequent results and conclusions in their paper are questionable. I implemented another method that respects the martingale condition and could not recover many of their results. For example, the power-law behavior of the volatility term structure (like t^-1/8 or something like that) is not reproducible and likely not correct. (Anyone who can reproduce their results, do kindly let me know, please.)

[3] I was about to communicate with them about the non-martingale violation but for some reason my hesitation remains. After all, it is fixable. However, I was struggling to understand the meaning of index q. How does it arise? What is its economical rationale? Unlike Engle's GARCH or Mandelbrot's multifractal, the Tsallis index q in finance is enigmatic to me. Does it deeply (or subtly) reflect human's behavior in trading stocks? I give up.

In all, Borland's idea is rather cute. It proposes a description of fat-tailedness for pdf of stock returns, although I personally wouldn't solely bet on it. But honestly, I was captured by Borland's insight after a while struggling to understand it. [By the way, the BS-like eqn is her paper is not the right way to present her theory, I believe. It was this equation that misled me the most, to the point I was going to give up her theory.]

AVt


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Posted: 2004-12-29 16:30
quantie, thx. As i do not want to hack this thread only for short (as i do not see
what his thing is worth): i think one always can produce skewed distributions by
rotating (what ever it should mean precisely) log of the pdf. And may be already
one of the more common asymmetric distribution will do as bad / as well here.

Alchemist


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Posted: 2016-05-21 03:03
Could you please repost this paper? I cannot access any longer?

Thank you,

Alchemist

HankScorpio


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Posted: 2016-05-21 04:37
LM_Ph_GTFY
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