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We study distributions which have both fractal and non-fractal scale regions by introducing a typical scale into a scale invariant system. As one of models in which distributions follow power law in the large scale region and deviate…

Statistical Mechanics · Physics 2008-12-18 Atushi Ishikawa , Tadao Suzuki

We present a self-consistent model for explosive financial bubbles, which combines a mean-reverting volatility process and a stochastic conditional return which reflects nonlinear positive feedbacks and continuous updates of the investors'…

Risk Management · Quantitative Finance 2014-08-26 L. Lin , Ren R. E , D. Sornette

The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel…

Statistical Finance · Quantitative Finance 2019-06-26 Josselin Garnier , Knut Solna

The bubble is a controversial and important issue. Many methods which based on the rational expectation have been proposed to detect the bubble. However, for some developing countries, epically China, the asset markets are so young that for…

Statistical Finance · Quantitative Finance 2016-10-25 Shu-Peng Chen , Ling-Yun He

We investigate the waiting-time distribution of the absolute return in the Korean stock-market index KOSPI. We define the waiting time as a time interval during which the normalized absolute return remains continuously below a threshold…

Physics and Society · Physics 2008-12-02 Jae Woo Lee , Kyoung Eun Lee , Per Arne Rikvold

The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise…

Statistical Finance · Quantitative Finance 2015-06-03 Vladimir Filimonov , Didier Sornette

We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity…

Statistical Finance · Quantitative Finance 2016-10-12 Mateusz Denys , Maciej Jagielski , Tomasz Gubiec , Ryszard Kutner , H. Eugene Stanley

We study the statistics of record-breaking events in daily stock prices of 366 stocks from the Standard and Poors 500 stock index. Both the record events in the daily stock prices themselves and the records in the daily returns are…

Statistical Finance · Quantitative Finance 2015-06-16 Gregor Wergen

We define a financial bubble as a period of unsustainable growth, when the price of an asset increases ever more quickly, in a series of accelerating phases of corrections and rebounds. More technically, during a bubble phase, the price…

Risk Management · Quantitative Finance 2014-04-09 Didier Sornette , Peter Cauwels

The sporadic large fluctuations are seen in the stock market due to changes in fundamental parameters, technical setups, and external factors. These large fluctuations are termed as Extreme Events (EE). The EEs may be positive or negative…

Statistical Finance · Quantitative Finance 2023-08-09 Anish Rai , Salam Rabindrajit Luwang , Md Nurujjaman , Chittaranjan Hens , Pratyay Kuila , Kanish Debnath

We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use…

Trading and Market Microstructure · Quantitative Finance 2010-02-09 Leilei Shi , Yiwen Wang , Ding Chen , Liyan Han , Yan Piao , Chengling Gou

In this study we examine the evolution of price, volume, and the bid-ask spread after extreme 15 minute intraday price changes on the NYSE and the NASDAQ. We find that due to strong behavioral trading there is an overreaction. Furthermore…

Statistical Mechanics · Physics 2009-11-10 A. G. Zawadowski , J. Kertesz , G. Andor

Universal power laws have been scrutinised in physics and beyond, and a long-standing debate exists in econophysics regarding the strict universality of the nonlinear price impact, commonly referred to as the square-root law (SRL). The SRL…

Trading and Market Microstructure · Quantitative Finance 2025-12-16 Yuki Sato , Kiyoshi Kanazawa

This study explores the time-varying structure of market efficiency in the prewar and wartime Japanese stock market using a new market capitalization-weighted stock price index, the equity performance index. We examine whether the adaptive…

Statistical Finance · Quantitative Finance 2024-05-17 Kenichi Hirayama , Akihiko Noda

We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette model of rational expectation bubbles. The model is based on a percolation…

Trading and Market Microstructure · Quantitative Finance 2016-09-21 Maximilian Seyrich , Didier Sornette

Leverage is strongly related to liquidity in a market and lack of liquidity is considered a cause and/or consequence of the recent financial crisis. A repurchase agreement is a financial instrument where a security is sold simultaneously…

General Finance · Quantitative Finance 2010-11-05 Wanfeng Yan , Ryan Woodard , Didier Sornette

Price gap, defined as the logarithmic price difference between the first two occupied price levels on the same side of a limit order book (LOB), is a key determinant of market depth, which is one of the dimensions of liquidity. However, the…

Trading and Market Microstructure · Quantitative Finance 2018-02-27 Gao-Feng Gu , Xiong Xiong , Yong-Jie Zhang , Wei Chen , Wei Zhang , Wei-Xing Zhou

The minute fluctuations of of S&P 500 and NASDAQ 100 indices display Boltzmann statistics over a wide range of positive as well as negative returns, thus allowing us to define a {\em market temperature} for either sign. With increasing time…

Physics and Society · Physics 2011-09-27 H. Kleinert , X. J. Chen

A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals…

Physics and Society · Physics 2008-12-02 Martin Schaden

We analyze the constituents stocks of the Dow Jones Industrial Average (DJIA30) and the Standard & Poor's 100 index (S&P100) of the NYSE stock exchange market. Surprisingly, we discover the data collapse of the histograms of the DJIA30…

Statistical Finance · Quantitative Finance 2009-03-13 Rui Gonçalves , Alberto Pinto