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Alex,
well, the answer is yes, of course:) cauchy might be interesting because of two considerations.
1. cauchy is the result of taking one normal variable and dividing it by another normal variable.
cauchy = N1 / N2 where N1, and N2 are normal.
now if we look at the general market impact function which is also called supply/demand-to-price
transform it is also in the form of W/L where both W ( order size ) and L ( liquidity ) might be normally distributed.
ie the hypothesis is that the market impact function generates fat tails because it generates near cauchy like price
distribution as a result of ratio of two normally distributed vars...
however the distributions of W and L are questionable to be normal...
anybody ever looked at the distribution of cumulative order size vs cumulative liquidity, on L2 for instance?
the data is there and it could be done, in fact was probably done...
but i know i haven't :)
2. cauchy does generate fat tails and is leptokurtic, so is the paretians...
bilo.
ps. anybody ever ran fit tests on return data for a chauchy?
someone should write a paper on market impact, order size distribution and liquidity distribution,
take data from L2 which is widely available and do fit tests on it and prove the f..king point once and for all.
----- Original Message -----
From: Alex Matulich
To: omega-list@xxxxxxxxxx
Sent: Monday, September 16, 2002 10:38 AM
Subject: Re: Gauss vs. Cauchy
>question in return: why cauchy and what for?
I can hazard a guess. A cauchy distribution can be made to fit the
distribution of price movements better than a gaussian, especially if
you let the exponent have a fractional part. I did some experiments
with this in the past. As I recall the math was a bit less intractable
than for a paretian.
-Alex
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