Explaining What Leads Up to Stock Market Crashes: A Phase Transition Model and Scalability Dynamics

The long memory and the transaction cost in financial markets

“…In Fig. 1(b), any L I above eight days can obtain 19 a positive predicted return R H that is still significantly smaller than the one in emerging markets for the same investment 20 duration.…”

Adding Resilience to Financial Markets: Toward a Volatility-based, Power-Law Indicated, Resilience Initiation Point

“…We develop in greater detail a theory building on Sornette et al's empirical work (Yan, Woodard & Sornette, 2010) that underlies his and our use of log periodicity and H > ½ to indicate the positioning of our 'R1' tipping-point indicator. This allows us to identify the tipping point between the random trader behavior at what Yalamova and McKelvey (2009) call the Triple Point [where greed, risk, and noise are balanced à la Bachelier's random walk of stock markets (PhD dissertation in 1900) and Fama's EMH (1970)] and the beginning of herding-style trading-which dates back to Henri Poincaré (1914)-that instigates bubble-build-ups toward a market crash at the Critical Point.…”

“…Financial engineering resilience interventions have to be imposed as early as possible in the transition from random-walk-EMH (Bachelier, 1914;Fama, 1970) trader behavior at the Triple Point to bubble-build-ups based on trader herding behavior leading up to the Critical Point (i.e., stock market crash; Yalamova & McKelvey, 2009) as is possible, but not too early. The key question is: How appropriately early we can get resilience dynamics introduced to offset the various dynamics underlying the build-up toward the Critical Point?…”

“…To accomplish this, we draw on Minsky's "positive-feedback" theory about market bubbles and crashes (1982,1986), and suggest several additional "scale-free" causes of skew distributions, that when combined lead to the extreme outcomes of long-tailed Pareto distributions, as signified by power laws (PLs) (Newman, 2005). We draw on Bak's (1996) "self-organized criticality" theory signify increasing PL distributions of price (stock return) volatilities in market trading as general indicators of impending crashes, as traders move away from an efficient-market's Triple Point toward the Critical Point (Yalamova & McKelvey, 2009). We suggest ~40 formulaic resilience engineering interventions to be automatically imposed after the tipping point so as to thwart the market crash vulnerabilities of financial engineering…”

Phase-transition behavior in the emerging market: Evidence from the KOSPI200 futures market

“…They insist that mutual information concerning market crash events such as the sub-prime meltdown in 2007 undergoes a qualitative change. Yalamova and McKelvey (2009) introduce attempts to explain the phase-transition phenomenon as caused by nonlinear trader behavior, within the framework of scalefree theory. Besides these methods, one might use liquidity-related measures as subsidiary tools to analyze phase-transition behavior, in that the responses of different financial markets to the same size of external impact can be different, depending on their market liquidity; this is because liquid markets absorb external shocks more easily than illiquid markets.…”