Consentaneous agent-based and stochastic model of the financial markets

We are looking for the agent-based treatment of the financial markets considering necessity to build bridges between microscopic, agent based, and macroscopic, phenomenological modeling. The acknowledgment that agent-based modeling framework, which may provide qualitative and quantitative understanding of the financial markets, is very ambiguous emphasizes the exceptional value of well defined analytically tractable agent systems. Herding as one of the behavior peculiarities considered in the behavioral finance is the main property of the agent interactions we deal with in this contribution. Looking for the consentaneous agent-based and macroscopic approach we combine two origins of the noise: exogenous one, related to the information flow, and endogenous one, arising form the complex stochastic dynamics of agents. As a result we propose a three state agent-based herding model of the financial markets. From this agent-based model we derive a set of stochastic differential equations, which describes underlying macroscopic dynamics of agent population and log price in the financial markets. The obtained solution is then subjected to the exogenous noise, which shapes instantaneous return fluctuations. We test both Gaussian and q-Gaussian noise as a source of the short term fluctuations. The resulting model of the return in the financial markets with the same set of parameters reproduces empirical probability and spectral densities of absolute return observed in New York, Warsaw and NASDAQ OMX Vilnius Stock Exchanges. Our result confirms the prevalent idea in behavioral finance that herding interactions may be dominant over agent rationality and contribute towards bubble formation.Comment: 17 pages, 6 figures, Gontis V, Kononovicius A (2014) Consentaneous Agent-Based and Stochastic Model of the Financial Markets. PLoS ONE 9(7): e102201. doi: 10.1371/journal.pone.010220

Cross-correlations between volume change and price change

In finance, one usually deals not with prices but with growth rates $R$, defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rate $\tilde R$, the difference in logarithm between two consecutive values of trading volume. To this end, we use several methods to analyze the properties of volume changes $|\tilde R|$, and their relationship to price changes $|R|$. We analyze $14,981$ daily recordings of the S\&P 500 index over the 59-year period 1950--2009, and find power-law {\it cross-correlations\/} between $|R|$ and $|\tilde R|$ using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these cross-correlations. Motivated by the relationship between $| R|$ and $|\tilde R|$, we estimate the tail exponent ${\tilde\alpha}$ of the probability density function $P(|\tilde R|) \sim |\tilde R|^{-1 -\tilde\alpha}$ for both the S\&P 500 index as well as the collection of 1819 constituents of the New York Stock Exchange Composite index on 17 July 2009. As a new method to estimate $\tilde\alpha$, we calculate the time intervals $\tau_q$ between events where $\tilde R>q$. We demonstrate that $\bar\tau_q$, the average of $\tau_q$, obeys $\bar \tau_q \sim q^{\tilde\alpha}$. We find $\tilde \alpha \approx 3$. Furthermore, by aggregating all $\tau_q$ values of 28 global financial indices, we also observe an approximate inverse cubic law.Comment: 7 pages, 5 figure

Non-extensive Behavior of a Stock Market Index at Microscopic Time Scales

This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when returns are measured over intervals less than one hour, the empirical distributions are well fitted by q-Gaussians with exponential damped tails. Scaling behavior is also observed for these microscopic time intervals. We find that the time evolution of the distributions is according to a super diffusive q-Gaussian stationary process within a nonlinear Fokker-Planck equation. This regime breaks down due to the exponential fall-off of the tails, which in turn, governs the transient dynamics to the long-term macroscopic Gaussian regime. Our results suggest that this modeling provides a framework for the description of the dynamics of stock markets intraday price fluctuations.Comment: 17 pages, 11 figures and 1 tabl

Time-Varying Risk Aversion and the Profitability of Carry Trades: Evidence from the Cross-Quantilogram

open access articleThis paper examines the predictive power of time-varying risk aversion over payoffs to the carry trade strategy via the cross-quantilogram methodology. Our analysis yields significant evidence of directional predictability from risk aversion to daily carry trade returns tracked by the Deutsche Bank G10 Currency Future Harvest Total Return Index. The predictive power of risk aversion is found to be stronger during periods of moderate to high risk aversion and largely concentrated on extreme fluctuations in carry trade returns. While large crashes in carry trade returns are associated with significant rises in investors’ risk aversion, we also found that booms in carry trade returns can be predicted at high quantiles of risk aversion. The results highlight the predictive role of extreme investor sentiment in currency markets and regime specific patterns in carry trade returns that can be captured via quantile-based predictive models

Dynamic scaling approach to study time series fluctuations

We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog of spatial variable. In this way we found that the fluctuations of many real-world time series satisfy the analog of the Family-Viscek dynamic scaling ansatz. This finding permits to use the powerful tools of kinetic roughening theory to classify, model, and forecast the fluctuations of real-world time series.Comment: 25 pages, 7 figures, 1 tabl