Conditional dynamics driving financial markets

We call attention against what seems to a widely held misconception according to which large crashes are the largest events of distributions of price variations with fat tails. We demonstrate on the Dow Jones Industrial index that with high probability the three largest crashes in this century are outliers. This result supports suggestion that large crashes result from specific amplification processes that might lead to observable pre-cursory signatures.

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...

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...

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...

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.

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 ...

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.

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...

Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We introduce a Markov-switching modeling approach for price change, where the latent Markov process is the transition between spreads. We then use a finite Markov mixture of logit regressions on past squared returns to describe the dependence of the probab...

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.