766 research outputs found
Ordering dynamics in the voter model with aging
The voter model with memory-dependent dynamics is theoretically and
numerically studied at the mean-field level. The `internal age', or time an
individual spends holding the same state, is added to the set of binary states
of the population, such that the probability of changing state (or activation
probability ) depends on this age. A closed set of integro-differential
equations describing the time evolution of the fraction of individuals with a
given state and age is derived, and from it analytical results are obtained
characterizing the behavior of the system close to the absorbing states. In
general, different age-dependent activation probabilities have different
effects on the dynamics. When the activation probability is an increasing
function of the age , the system reaches a steady state with coexistence of
opinions. In the case of aging, with being a decreasing function, either
the system reaches consensus or it gets trapped in a frozen state, depending on
the value of (zero or not) and the velocity of approaching
. Moreover, when the system reaches consensus, the time ordering of
the system can be exponential () or power-law like ().
Exact conditions for having one or another behavior, together with the
equations and explicit expressions for the exponents, are provided
Time-variation of higher moments in a financial market with heterogeneous agents: An analytical approach
A growing body of recent literature allows for heterogenous trading strategies and limited rationality of agents in behavioral models of financial markets. More and more, this literature has been concerned with the explanation of some of the stylized facts of financial markets. It now seems that some previously mysterious time-series characteristics like fat tails of returns and temporal dependence of volatility can be observed in many of these models as macroscopic patterns resulting from the interaction among different groups of speculative traders. However, most of the available evidence stems from simulation studies of relatively complicated models which do not allow for analytical solutions. In this paper, this line of research is supplemented by analytical solutions of a simple variant of the seminal herding model introduced by Kirman [1993]. Embedding the herding framework into a simple equilibrium asset pricing model, we are able to derive closed-form solutions for the time-variation of higher moments as well as related quantities of interest enabling us to spell out under what circumstances the model gives rise to realistic behavior of the resulting time series --
A noise trader model as a generator of apparent financial power laws and long memory
In various agent-based models the stylized facts of financial markets (unit-roots, fat tails and volatility clustering) have been shown to emerge from the interactions of agents. However, the complexity of these models often limits their analytical accessibility. In this paper we show that even a very simple model of a financial market with heterogeneous interacting agents is capable of reproducing these ubiquitous statistical properties. The simplicity of our approach permits to derive some analytical insights using concepts from statistical mechanics. In our model, traders are divided into two groups: fundamentalists and chartists, and their interactions are based on a variant of the herding mechanism introduced by Kirman [1993]. The statistical analysis of simulated data points toward long-term dependence in the auto-correlations of squared and absolute returns and hyperbolic decay in the tail of the distribution of raw returns, both with estimated decay parameters in the same range like those of empirical data. Theoretical analysis, however, excludes the possibility of ‘true’ scaling behavior because of the Markovian nature of the underlying process and the boundedness of returns. The model, therefore, only mimics power law behavior. Similarly as with the phenomenological volatility models analyzed in LeBaron [2001], the usual statistical tests are not able to distinguish between true or pseudo-scaling laws in the dynamics of our artificial market --Herd Behavior,Speculative Dynamics,Fat Tails,Volatility Clustering
A Note on institutional hierarchy and volatility in financial markets
From a statistical point of view, the prevalence of non-Gaussian distributions in nancial returns and their volatilities shows that the Central Limit Theorem (CLT) often does not apply in nancial markets. In this paper we take the position that the independence assumption of the CLT is violated by herding tendencies among market participants, and investigate whether a generic probabilistic herding model can reproduce non-Gaussian statistics in systems with a large number of agents. It is well-known that the presence of a herding mechanism in the model is not sucient for non-Gaussian properties, which crucially depend on the details of the communication network among agents. The main contribution of this paper is to show that certain hierarchical networks, which portray the institutional structure of fund investment, warrant non-Gaussian properties for any system size and even lead to an increase in system-wide volatility. Viewed from this perspective, the mere existence of nancial institutions with socially interacting managers contributes considerably to nancial volatility.Herding; financial volatility; networks; core-perifery
Searching out of Trading Noise: A Study of Intraday Transactions Cost
We attempt to identify in this paper the role of trading noise as a transactions cost to market participant in the sense of Stoll (2000), especially in the presence of trading concentration. Applying the measures of Hu (2006) and Kang and Yeo (2008), we analyze the noise proportion in intraday stock returns and its interaction with investor herding and search cost. Although this noise is high on individual orders and low on institutional orders, its behavior at market open is entirely different from the rest of the day. Noises for small cap stocks, unlike volatilities, are lower than those for large cap stocks. We also found that noise relates positively to trading volume, but inversely to holdings and turnover ratio of institutional investors. Responses from institutional and individuals are quite the opposite. The noise proportion generated by individual order rises with institutional turnover and search cost encountered, while that of institutional order behaves just oppositely. At market open, behaviors of noise from institutional and individual orders just switch mutually, and then switch back afterwards. Also, noise from high-cap stocks is actually more responsive than that from low-cap ones across investors. So trading noise is a specific transactions cost, prominent to only certain investors, at certain time and for certain stocks in the market, rather than a general market friction as argued in Stoll (2000). This transactions cost is inversely related to search costs encountered in trading, which depends on investor, trading hour of day and market capitalization of stocks.Noise, transaction cost, herding, search model, order book
A queueing theory description of fat-tailed price returns in imperfect financial markets
In a financial market, for agents with long investment horizons or at times
of severe market stress, it is often changes in the asset price that act as the
trigger for transactions or shifts in investment position. This suggests the
use of price thresholds to simulate agent behavior over much longer timescales
than are currently used in models of order-books.
We show that many phenomena, routinely ignored in efficient market theory,
can be systematically introduced into an otherwise efficient market, resulting
in models that robustly replicate the most important stylized facts.
We then demonstrate a close link between such threshold models and queueing
theory, with large price changes corresponding to the busy periods of a
single-server queue. The distribution of the busy periods is known to have
excess kurtosis and non-exponential decay under various assumptions on the
queue parameters. Such an approach may prove useful in the development of
mathematical models for rapid deleveraging and panics in financial markets, and
the stress-testing of financial institutions
Time-variation of higher moments in a financial market with heterogeneous agents: An analytical approach
A growing body of recent literature allows for heterogenous trading strategies and limited rationality of agents in behavioral models of financial markets. More and more, this literature has been concerned with the explanation of some of the stylized facts of financial markets. It now seems that some previously mysterious time-series characteristics like fat tails of returns and temporal dependence of volatility can be observed in many of these models as macroscopic patterns resulting from the assumed interaction of speculative traders. However, most of the available evidence stems from simulation studies of relatively complicated models which do not allow for analytical solutions. In this paper, this line of research is supplemented by analytical solutions of a simple variant of the seminal herding model introduced by Kirman (1993). Embedding the herding framework into a simple equilibrium asset pricing framework, we are able to derive closed-form solutions for the time-variation of higher moments as well as related quantities of interest enabling us to spell out under what circumstances the model gives rise to realistic behavior of the resulting time series. --
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