[FRIAM] Agent-Based Modelling of a Blowback - How Terrorists are made

[mgd at santafe.edu]

Quoting Frank Wimberly <wimberly3 at earthlink.net>:

> What about the following issue:  I suspect that a simulation
> (agent-based or otherwise) of the "stock market" (e.g. the DJIA) could
> be developed which is statistically indistinguishable from the real
> thing.  That is, the moments, fat tails, etc. would not serve to allow a
> statistician to distinguish between the simulated signal and some, as
> yet unobserved, actual data.  Yet, such a simulation would have no
> predictive value except on some set of measure zero.  However similar to
> the real world the simulation is, it won't tell you the level of the
> DJIA next Tuesday.  

One way is to get NYSE and NASDAQ datasets and iterate the 30 DJIA order books 
forward in time from a long  period of real observed order flow.  For each 
trader on each stock you could fit or engineer an agent that reproduces that 
order flow to some degree of precision (based on the evolving orderbooks they 
had in front of the and perhaps based on estimates of their initial inventory 
(or at least aversions to large changes).  Now take all of the order books and 
iterate them forward in time with the synthetic agent rules until next 
Tuesday.  You'd have estimates of all the best prices on all of the stocks and 
thus the DJIA, given assumption that the behaviors at work in the data would 
continue to occur into the future.

One question is how intelligent do the agents have to be?  That simple agents 
who do little more than hide their inventory can do a good job of getting 
aggregate statistics of the market right suggest that internal dynamics of the 
markets are as important as real news.

http://www.santafe.edu/~jdf/papers/zero.pdf
http://www.santafe.edu/~jdf/papers/TheoryForLongMemory.pdf
http://www.santafe.edu/~jdf/papers/quantitativemodel.pdf