concrete fluid burst model
June 7, 2015 by zulfahmed
Zulfikar Ahmed <wile.e.coyote.006@gmail.com>


12:12 PM (1 hour ago)




Sir,
Attached is a fluid burst model that is a real application and fractional Brownian motion used to model traffic in a connectionless network. They are quite detailed in their justification of their uses. Although I have been a bit vague in the past, as I delve back into the Whittle approximation and approximate likelihood estimation for fractional Brownian motions with the hydrodynamic model as inspiration for volatility, it seems reasonable to begin with one of these other models which need the selfsimilarity property of fractional Brownian motion.
This will take a bit of time for me to wrap my mind around, but in principle, volatility is bursty in behaviour as it is literally due to traffic of the collective emotions of the whole market.
In other words, if global volatility were the central observation of finance rather than being some ‘firm foundation’ on a volatile ocean for pricing models that forget that under the illusion of firmness based on a lull in some war where the schools of pirhannas and sharks will begin their bloody need for destruction of human life around the planet to become the kings and queens of the new world order to reset the Hell on Earth once more and so on…
Zulfikar Ahmed <wile.e.coyote.006@gmail.com>






Suppose H>0.5 and Z_t is a normalized fBM with Hurst parameter H. Then consider the model of traffic as
A_t = mt + sqrt(mt) Z_t
The sqrt(m) term is motivated by the traffic modelers by appeal to the superposition principle for sums of fractional Brownian motions of the same H but different mean rates average to mt + sqrt(mt)Z_t where m is the mean of the m_i. In the traffic model assuming bursts of traffic arrive with Poisson lambda with rate r with IID volume B_n, so the length of time is B_n/n. We can note that in the traffic model, time length of the burst is determined, which will differ from volatility.
In the case of volatility we can intuitively model it in terms of wealth strata and their activity. Of course the highest wealth strata in the west happen to also govern the markets so their activity is the most important because they are playing geopolitical risk just like their ancestors the global robber barons and imperialists on global operations for resource control. We do not have to model them as Poisson processes.
Zulfikar Ahmed <wile.e.coyote.006@gmail.com>


1:50 PM (0 minutes ago)




The system can be made stationary if and only if the expected bursts are finite for the traffic model, and is long memory when K_t the number of bursts has infinite variance. See snapshot. For the traffic model, the author considers the tails of the distributions F() the distribution for bursts and argues that the tail power law decay parameter sets the Hurst exponent.
This is a model that is quite useful as a basis for volatility that can be criticised for its simplicity etc. but it’s concrete. The order book of the market is often analysed by quants and obviously traffic model on a network, even an abstract network of the type that I have called a market network, regardless of how global strategic decisions are made in an entire strate of ultrawealth (not just in the west but moreso in China and elsewhere which do not even claim a Republic inheritance) family offices and the old British imperial officers and their men and women on boards of large oil and other multinationals who have never — following good advice from Machiavelli– separated power from war and reduced to rationality the strategic logic of locusts and viruses against an entire human race.
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