System Dynamics Modeling Of Stylized Features Of Stock Markets
The common theme throughout the thesis is to explore the possibility of using a single framework, namely the systems theory framework, in modeling a few stylized features of a financial market. A systems theoretic model is developed, in this thesis in Chapter 3, for confidence bias of an individual. The effect of this bias on his investment decision is brought out explicitly. The phenomenon of excessive trading, arising due to overconfidence and optimism, has been explained. The concept of virtual capital, incorporating the ideas from prospect theory, is introduced. We have proposed a dynamical system framework to model limits to arbitrage and the herding behavior in financial markets in Chapter 4. The market evolves due to the participation of traders. It is instructive to look at the market as a system evolving from a set of initial conditions during every time interval. In the proposed model, herding is defined as a specific relation between the system responses. The proposed herding measure quantifies how far the individual is from clustering with others. It is also shown how this interpretation helps us to understand the effects of herding. There exists a risk when the market price variation, due to herding, is thought of as entirely due to the portfolio fundamentals. The generic dynamical system model that captures some aspects of the limits of arbitrage is also proposed wherein fundamental risk, noise trader risk, implementation risk, and model risk can be incorporated. The proposed model offers a single framework to study the Marginally Efficient Market and Synchronization Risk models. In Chapter 5, we have proposed a switching dynamical system with minority game rules incorporated within the framework. We have explored the possibility of developing a market model, in Chapter 6, in the same framework that has been used to develop models for arbitrage and herding. We have explored, in this thesis, the possibility of using a single framework to model stylized features of stock market. It will be a long way before a single model can capture all complex characteristic features of a stock market. We have attempted, in this thesis, to capture a few stylized features in a single framework, if not in a single model. Different models proposed for individual confidence bias, limits to arbitrage, herding, and switching model for incorporating minority games are all set up in system dynamics framework. This leads to a stage where one can explore incorporating other features, not addressed in this thesis, in system dynamics framework. If each feature is captured using a different framework like confidence bias as stochastic system, herding as pattern cluster, limits to arbitrage as rule-based agents, etc., it would be difficult to integrate them into a single framework. But, in the present work, we have captured the chosen stylized features using system dynamics framework though individual models differ from each other substantially. The challenges are many in creating a single framework. The vision of such framework may involve different components such as modeling decision making, considering risk profiles, devising investment strategies, etc. Stylized features would come as emergent properties of complex interactions among the components of the system. Emergence refers to the way in which multiplicity of simple interactions lead to complex behavior. Emergence of such features may include different time scales of causal relationships among components. System may have thresholds, determined by diversity of traders and nature of interactions, which is vital for features to become emergent. This can be seen in practice. Stock market regulates the relative prices of companies across the world. There is no single central agency to control the workings of the market. Traders have knowledge of only few companies within their portfolio, and to follow transaction rules. Trends and patterns are still emerging which are studied by technical analysts. Emergent properties are mostly signature of self-organizing complex system. Self-organization in complex system relies on four properties which are fundamental in system dynamics framework: positive feedback, negative feedback, multiple interactions, and balance among strategies. A complex adaptive stock market system which is self-organizing and exhibit stylized features as emergent property is a distant goal of system theorists around the world. The challenge does not end there. We have attempted to model and study the stylized features of a stock market in systems theory framework. The focus of our approach is to use the dynamical system modeling to study the features. We have not considered the investment aspects in a financial market. The investment models are very important in real life for individuals and policy-makers. Future extension of the ideas explored in this thesis could be along the lines of creating investment models for individuals and policy-makers. Creating such models using complex adaptive stock market system goes a long way in understanding a phenomenon that had started by Dutch East India Company issuing shares on Amsterdam Stock Exchange way back in 1602.
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