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| [blok00b] |
Hendrik J. Blok.
On the nature of the stock market: Simulations and experiments. PhD thesis, University of British Columbia, 2000. Available from http: |
Abstract
Over the last few years there has been a surge of activity within the physics community in the emerging field of Econophysics - the study of economic systems from a physicist's perspective. Physicists tend to take a different view than economists and other social scientists, being interested in such topics as phase transitions and fluctuations.In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Fluctuations are driven by a stochastic component in the agents' forecasts. As the scale of the fluctuations is varied a critical phase transition is discovered. Unfortunately, this model is unable to generate realistic market dynamics.
The second model discards the requirement of centralized trading. In this case the stochastic driving force is Gaussian-distributed "news events" which are public knowledge. Under variation of the control parameter the model exhibits two phase transitions: both a first- and a second-order (critical).
The decentralized model is able to capture many of the interesting properties observed in empirical markets such as fat tails in the distribution of returns, a brief memory in the return series, and long-range correlations in volatility. Significantly, these properties only emerge when the parameters are tuned such that the model spans the critical point. This suggests that real markets may operate at or near a critical point, but is unable to explain why this should be. This remains an interesting open question worth further investigation.
One of the main points of the thesis is that these empirical phenomena are not present in the stochastic driving force, but emerge endogenously from interactions between agents. Further, they emerge despite the simplicity of the modeled agents; suggesting complex market dynamics do not arise from the complexity of individual investors but simply from interactions between (even simple) investors.
Although the emphasis of this thesis is on the extent to which multi-agent models can produce complex dynamics, some attempt is also made to relate this work with empirical data. Firstly, the trading strategy applied by the agents in the second model is demonstrated to be adequate, if not optimal, and to have some surprising consequences.
Secondly, the claim put forth by Sornette et al. [sornette96] that large financial crashes may be heralded by accelerating precursory oscillations is also tested. It is shown that there is weak evidence for the existence of log-periodic precursors but the signal is probably too indistinct to allow for reliable predictions.
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| On the nature of the stock market: Simulations and experiments |
Individual sections
| Front matter | |
| Chapter 1 Introduction | |
| Chapter 2 Centralized Stock Exchange Model | |
| Chapter 3 Decentralized Stock Exchange Model | |
| Chapter 4 Analysis and results: Phase space | |
| Chapter 5 Analysis and results: Empirical results | |
| Chapter 6 Experiments with a hypothetical portfolio | |
| Chapter 7 Concluding remarks | |
| Bibliography | |
| Appendix A Discounted least-squares curve fitting | |
| Appendix B Sampling discrete processes | |
| Appendix C Long-range memory: The Hurst exponent |
BibTeX Entry
@PHDTHESIS{blok00b,
author = {Hendrik J. Blok},
year = 2000,
title = {{On} the nature of the stock market: {Simulations} and experiments},
note = {\url{http://rikblok.shorturl.com/lib/blok00b.html}},
school = {University of British Columbia},
keywords = {econophysics; financial markets; modeling; centralized stock
exchange model (CSEM); investment fraction; forecasting; risk
aversion; market clearing; decentralized stock exchange model
(DSEM); fixed investment strategy; Poisson processes; Bayesian
probability theory; phase transitions; critical points;
first-order phase transition; distribution of returns;
exponentially decaying power law; autocorrelation of returns;
efficient market hypothesis; news; clustered volatility;
distribution of wealth; hypothetical portfolio; minimum friction;
log-periodic precursors; discrete scale invariance; complex
critical exponents; discounted least-squares curve fitting;
sampling discrete processes; fat tails; Poisson Brownian motion;
Hurst exponent; fractional Brownian motion (fBm); fractional
Gaussian noise (fGn); dispersional analysis; scaled window
variance analysis; L\'evy flig}
}