Conditional dynamics driving financial markets

The possibility that price dynamics is affected by its distance from a moving average has been recently introduced as new statistical tool. The purpose is to identify the tendency of the price dynamics to be attractive or repulsive with respect to its own moving average. We consider a number of tests for various models which clarify the advantages and limitations of this new approach. The analysis leads to the identification of an effective potential with respect to the movin...

It is hypothesized that price charts can be empirically decomposed into two components as random and non random. The non random component, which can be treated as approximately regular behavior of the prices (trend) in an epoch, is a geometric line. Thus, the random component fluctuates around the non random component with various amplitudes. Moreover, the shape of a trend in an epoch may be different in another epoch. It is further hypothesized that statistical evidence can ...

A phenomenon of the financial log-periodicity is discussed and the characteristics that amplify its predictive potential are elaborated. The principal one is self-similarity that obeys across all the time scales. Furthermore the same preferred scaling factor appears to provide the most consistent description of the market dynamics on all these scales both in the bull as well as in the bear market phases and is common to all the major markets. These ingredients set very desira...

A methodology is developed to identify, as units of study, each decrease in the value of a stock from a given maximum price level. A critical level in the amount of price declines is found to separate a segment operating under a random walk from a segment operating under a power law. This level is interpreted as a point of phase transition into a self-organized system. Evidence of self-organization was found in all the stock market indices studied but in none of the control s...

Predicting absolute magnitude of fluctuations of price, even if their sign remains unknown, is important for risk analysis and for option prices. In the present work, we display our predictions about absolute magnitude of daily fluctuations of the Dow Jones Industrials Average (DJIA), utilizing the original theory of conservation of total energy, for the coming 500 days.

We propose a new method (implemented in an R-program) to simulate long-range daily stock-price data. The program reproduces various stylized facts much better than various parametric models from the extended GARCH-family. In particular, the empirically observed changes in unconditional variance are truthfully mirrored in the simulated data.

This paper presents an exclusive classification of the largest crashes in Dow Jones Industrial Average (DJIA), SP500 and NASDAQ in the past century. Crashes are objectively defined as the top-rank filtered drawdowns (loss from the last local maximum to the next local minimum disregarding noise fluctuations), where the size of the filter is determined by the historical volatility of the index. It is shown that {\it all} crashes can be linked to either an external shock, {\it e...

Drawdowns are essential aspects of risk assessment in investment management. They offer a more natural measure of real market risks than the variance or other cumulants of daily (or some other fixed time scale) distributions of returns. Here, we extend considerably our previous analysis by analyzing the major financial indices, the major currencies, gold, the twenty largest U.S. companies in terms of capitalisation as well as nine others chosen randomly. We find for the major...

We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, the kurtosis (a measure of volatility surprises) reaches a minimum at the open of the market, when the volatility is at its peak. We confirm that the dispersion ...

We respond to Sornette and Johansen's criticisms of our findings regarding log-periodic precursors to financial crashes. Included in this paper are discussions of the Sornette-Johansen theoretical paradigm, traditional methods of identifying log-periodic precursors, the behavior of the first differences of a log-periodic price series, and the distribution of drawdowns for a securities price.