George Soros models

Question

Mr. Soros in his books talked about principles which are not used by today's financial mathematics — namely reflexivity of all actions on the market. Simply it can be given by following: expectations of traders are based on the news and historical prices. They trade based on their expectations and hence influence prices which then influence expectations on the next "turn". I have never met an implementation of these ideas in the scientific framework. Have you? If yes, please give me a reference.

Answer 1

Keynes introduced this idea in the notion of a Keynesian Beauty contest: http://en.wikipedia.org/wiki/Keynesian_beauty_contest

Anyone who uses a rolling window regression where the parameters and/or parameter estimates are re-fitted periodically are implicitly accounting for this reflexivity (i.e. the market's changing behavior as agents respond and adapt to each others actions)

With respect to a scientific-framework, agent-based modeling is something that fits the bill and also game theory: http://en.wikipedia.org/wiki/Agent-based_model

Answer 2

The answers above are good, but I suspect they will be unsatisfactory if you are looking for implementations that are successful in practice. The sort of bottom-up analysis championed by Soros is very difficult to carry out in a rigorous, quantitative manner. This is true very generally, not just in finance. There are certainly models of financial markets that explicitly consider beliefs and actions of individual market participants (see game theory), but these always rely on extreme oversimplifications of actual human cognition and behavior.

On the other hand, many seem to be able to develop a good intuitive sense for what sort of beliefs and biases are driving the behavior of financial market participants and exploit this knowledge. Soros is often counted among their ranks. Although this approach may be sophisticated, it is usually not considered quantitative. Soros often claims that he looks for a sort of "turning point" where market participants realize the flaws in their beliefs. This is in contrast with most quantitative models that implicitly assume that whatever structure is observed in the data will persist long enough for a profit to be extracted.

Answer 3

This paper by Filimonov and Sornette might be interesting or useful to you. I've only read about the first third, but I thought the model was pretty cool. The model for price changes is a self-exciting Poisson process: there is an exogenous factor modeling the "real" price changes, and then there is a feedback mechanism where the overall arrival rate is an exponentially weighted average of recent arrivals. The paper is available here. If you go through it all, would welcome your thoughts.

Answer 4

Sure it is used in non-linear dynamics. What is not used is that this non-linearity is caused by huge operators who cause the deviation from Normal Law delaying the reversion to the mean. This is just common sense and mathematically logics when you go straight to Normal Law premisces: all samples must have about the same weight and being independant. Clearly these premisces are hugely violated in Stock Market.

Answer 5

I havent seen much implementing reflexivity in practice in a comprehensive way. Of course there are small steps in that direction, but no general framework yet.

To comment on answers above: incorporating updates of information is not reflexivity; reflexivity is about taking into account the effect of your own actions while chosing them (jointly with those of other market participants, sure), that is ex ante, not ex post. Also momentum and mean reversion need not have anything to do with reflexivity.

Even the modeling of market impact in algo trading, which should be the application par excellance of reflexivity, is still done in a kind of traditional "blind" way: ex post statistics of impact are taken and then the forecasting model is used to optimize strategies... Reflexivity in algo trading would be best applied to avoiding stop loss crashes, which is currently not yet done afaik. But sure market impact modeling goes a little bit towards reflexivity in a short term sense.

Stochastic control is one area where some reflexivity is indeed present by definition. And sure game theory, but that's not used much in practice.

Something might also be found in the bubble dynamics literature, but I'm not familiar with it. Agent modeling is surely interesting per se, but in its current state is far from even scratching the surface of that topic, and the main research stream doesnt touch reflexivity at all.

More on control theory (w/o stochasticity) which is already pertinent (see also dynamic programming). It deals with the response dynamics of a system to different inputs and how to best plan strategies. E.g. it is used in engineering to study and prevent oscillations. Oscillations are the typical problem arising when no control techniques are used (as seen in economic cycles, bubbles etc...): a target is aimed at, a steering parameter is directed towards that but the actual response of the system is not linear so the steering needs to be corrected, but then the correction itself must be called back with time yet still the dynamics leads away in the other direction, so one has to steer again in the original direction, and so on in an endless cycle... E.g. in algo trading of course your target is the quoted price, but you must adjust it to take into account market impact, which however is not given but depends itself on the your target and strategy generating some circularity. Control theory iirc is applied in pricing of americans for the exercise strategy, and all similar problems, although it's overkill since there's much more to it. Here some examples in finance. (Definitely people at the FED should take a course in control theory, before they start messing that way with the world economy. What will happen with inflation is a classic case of control myopia where they're oversteering without noticing it before it's too late. Here some examples in economics.)