Date of Publication


Document Type

Master's Thesis

Degree Name

Master of Science in Physics

Subject Categories



College of Science



Thesis Advisor

Rene C. Batac

Defense Panel Chair

Robert C. Roleda

Defense Panel Member

Emmanuel T. Rodulfo
Reggie C. Pantig


The efficient market hypothesis (EMH) states that all markets are efficient. Efficiency is defined as the degree in which the market price fully reflects all information coming into the market. Empirical studies however have shown that real markets do not follow a martingale process and are therefore not efficient. As such, the fractal market hypothesis was introduced and it asserts that heterogeneity in investment horizons contribute to the inefficiency of markets. A market whose agents have varying investment horizons can be described as a complex system with agents heterogeneous in nature. Such systems can be modeled through agent-based models (ABMs). The ABM that this study will emphasize on is the Ising model of financial markets, formulated by Zhou and Sornette (2007). In the context of statistical physics,it is a mathematical model of ferromagnetism. However, in the context of financial markets, the model consists of sites on a lattice with values +1 for buying agent and -1 for selling agents. In this study, a modified version of the Ising model of financial markets was considered wherein the possibility of non-participants were incorporated. The study considered an Ising model of n2 agents on an n × n 2D square lattice where an agent i can either buy (si(t) = +1), sell (si(t) = −1), or not participate (si(t) = 0) at time step t according to a rule formulated by Zhou and Sornette (2007). The Ising model of financial markets with non-participants is specified by the parameter configuration (bmax, σmax,CV ) where bmax is a parameter associated with an agent’s idiosyncratic imitation tendency, σmax associated with an agent’s sensitivity to the news and CV is a common constant across all agents associated with private information. In addition to these parameter configurations, this study has considered varying percentages of non-participants in the market from 0% − 50% with a step of 10%. The study has considered over 7000 parameter configurations with non-participants and have found that the simulated markets exhibit fat tails in the distribution of large returns and volatility clustering. Additionally, it was found through a multiple regression analysis with the market efficiency, quantified through the spread in the generalized Hurst exponents ΔH obtained through the multifractal detrended fluctuation analysis, as the regressand and the Ising parameters bmax and σmax as the regressors that an increase in σmax leads to a decrease in ΔH and an increase in bmax leads to an increase in ΔH. These results imply that the more sensitive the agents are to the news, the more efficient the market, and that the more the agents imitate their neighbors, the less efficient the market. This study has also found, through the comparison of simulated Ising market returns to real market returns taken from eleven stock markets, that this study’s Ising model of financial markets with non-participants is not a good model to use for forecasting real market returns.

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371 leaves


Ising model; Time-series analysis; Multifractals; Financial institutions

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