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I empirically studied
the cross-correlations of stock indices in a diverse set of 37 countries all
over the world. I found that the more globalized
is the economy of a given country, the stronger it is coupled to the world
stock index. |
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I came
up with a simple model of a limit-order driven market, where agents
with equal probability trade stock at the market price or place limit orders,
i.e. instructions to sell (buy) if stock price raises above (falls below)
a predetermined price level. In spite of a minimalistic nature of this model (no strategies, or trader psychology,
e.t.c.) it has a number of nontrivial features. They include fat tails in the distribution
of price fluctuations characterized by two power
law exponents, volatility clustering, and a nontrivial Hurst exponent of the price as a function of time. |
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Mark Mills and I studied
the empirical properties of real-life limit order books. This work used
the NASDAQ Level II dataset collected by my collaborator Mark Mills who
does day trading for living. |
| My collaborators (Yi-Cheng
Zhang and Matteo Marsili) and I explored
multiplicative nature of fluctuations in economics. Even the simplest multiplicative
stochastic process -- multiplicative random walk -- has some unexpected
features.
A multiplicative fluctuations in dynamically
managed portfolio give rise to non-universal power law distributions. |
This figure from my paper on globalization shows the distribution of eigenvalues of the cross-correlations matrix computed using daily changes in stock price indices in a diverse set of 37 countries. Colored curves are fits based on predictions of the Random Matrix Theory. Clearly three eigenvalues are the outliers and as such represent collective behavior of world's stock indices. The corresponding eigenvectors shown suggest that the largest eigenvalue is the true "world stock index", while the second is dominated by stocks of Asian countries, and the third - by American ones.
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