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## Probabilistic models of financial volatility are similar to internet scale-free networks but how different?

A wonderful paper of Patrick Wolfe talks about null models in the study of internet.  Recently we’ve shown that for financial volatility with 188 stocks from Standard & Poors 500 Index, the graph has 5921 edges on 188 nodes and a power law with $\alpha=4.027$.  So the volatility graph in this case is like the internet network graph in the power law behavior which Barbasi had named ‘scale-free’.  But graph theoretic modeling generally assumes that nodes are permanent.  This assumption is incorrect in finance since Taleb’s main argument in his crusades against standard models is that Black Swan is big and wipes out nodes.  So it is not enough for us to claim a real science of finance if we do not heed Taleb’s main warning to the world.  We need models of volatility with AIG surviving and even a giant slave-worker firm like Lehman Brothers that dealt in slaves from early nineteenth century cotton fields of the American south to disappear like the twin towers destroyed in a war that is global capitalism.

Graphs with a given degree sequence is called ‘micro-canonical’ when graphs are given a uniform probability based only on their degree sequence and the exponential distribution is called ‘canonical’ in statistical mechanics.  So the Wolfe apporach is based on a paradigm of active research interest.  This is Diaconis from 2011 in the screenshot.

This tells us not to worry too much about this degree sequence aspect since we’ll get plenty of good theory from activity by statisticians in this direction.  We should worry instead about ensuring that we have the NODE EXISTENCE problem resolved first and then piggyback off these people’s work to found a new science of finance.