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Register a new userMarket dynamics after large financial crash
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The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional potential $U$ under the influence of the variable noise intensity, depending on the particle position $x$. Based on the empirical data the approximate estimation of the Kramers-Moyal coefficients $D_{1,2}$ allow to predicate quite definitely the behavior of the potential introduced by $D_1 = - partial U /partial x$ and the volatility $sim sqrt{D_2}$. It has been shown that the presented model describes well enough the best known empirical facts relative to the large financial crash of October 1987.
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We study the behavior of U.S. markets both before and after U.S. Federal Open Market Committee (FOMC) meetings, and show that the announcement of a U.S. Federal Reserve rate change causes a financial shock, where the dynamics after the announcement is described by an analogue of the Omori earthquake law. We quantify the rate n(t) of aftershocks following an interest rate change at time T, and find power-law decay which scales as n(t-T) (t-T)^-$Omega$, with $Omega$ positive. Surprisingly, we find that the same law describes the rate n(|t-T|) of pre-shocks before the interest rate change at time T. This is the first study to quantitatively relate the size of the market response to the news which caused the shock and to uncover the presence of quantifiable preshocks. We demonstrate that the news associated with interest rate change is responsible for causing both the anticipation before the announcement and the surprise after the announcement. We estimate the magnitude of financial news using the relative difference between the U. S. Treasury Bill and the Federal Funds Effective rate. Our results are consistent with the sign effect, in which bad news has a larger impact than good news. Furthermore, we observe significant volatility aftershocks, confirming a market underreaction that lasts at least 1 trading day.
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We then characterize the time-evolving relationships between the different assets by investigating the correlations between the asset price time series and principal components. Using this approach, we uncover notable changes that occurred in financial markets and identify the assets that were significantly affected by these changes. We show in particular that there was an increase in the strength of the relationships between several different markets following the 2007--2008 credit and liquidity crisis.
The stock market has been known to form homogeneous stock groups with a higher correlation among different stocks according to common economic factors that influence individual stocks. We investigate the role of common economic factors in the market in the formation of stock networks, using the arbitrage pricing model reflecting essential properties of common economic factors. We find that the degree of consistency between real and model stock networks increases as additional common economic factors are incorporated into our model. Furthermore, we find that individual stocks with a large number of links to other stocks in a network are more highly correlated with common economic factors than those with a small number of links. This suggests that common economic factors in the stock market can be understood in terms of deterministic factors.
This paper has been withdrawn by the authors.
We describe the impact of the intra-day activity pattern on the autocorrelation function estimator. We obtain an exact formula relating estimators of the autocorrelation functions of non-stationary process to its stationary counterpart. Hence, we proved that the day seasonality of inter-transaction times extends the memory of as well the process itself as its absolute value. That is, both processes relaxation to zero is longer.
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