Developing computerised agent-based models of the stock market

Abstract

This thesis, based on four research papers, develops three novel agent-based models with the aim of approximating stock markets with greater realism. Two methods are presented for examining parameter e ects on an agent based model. The rst is parameter variation Monte Carlo which we derive by applying the law of large numbers pointwise. The second method is to use (multivariate) regression using Maximum Likelihood estimation. These two methods are applied to the Santa-Fe model of LeBaron et al. (1999) which is shown to be a reasonable model. Subsequently, three new agentbased models of the stock market are developed which incorporate genetic learning. In the rst model, a multiple stock model of the stock market is developed, which signi cantly generalises the Santa-Fe model. By Monte Carlo simulations and estimation of a Dynamic Conditional Correlation (DCC) model, stock bubbles are shown to exist and the relationship between agent beliefs and stock mispricing, stock volatility and cross-correlations is studied. The model is shown to be reasonable regarding the impact of parameters on simulated prices. Subsequently, signi cant evidence is presented that various time unconditional and conditional kernel distributions of stock market returns are a mixture of distributions, including during important nancial economic periods such as the Great Depression, the Dot-Com bubble and the Great Recession. To explain these phenomena, mixture modelling is incorporated into the development of two agentbased mixture models. In the rst of these two new research papers, smart (algorithmic) traders and portfolio managers trade and invest in an equally weighted average of stocks that underlie an equity index such as the S&P 500, have consistent beliefs about stock market dynamics and learn over time. It is shown that the model can produce kernel distributions of stock market returns that are observed in the real-world. In the second of these two new research papers, smart (algorithmic) traders and portfolio managers trade and invest in the underlying equities that constitute an equity market index and optimise their holdings in their portfolio optimisation, have consistent beliefs about stock market dynamics and learn over time. It is shown, by Monte Carlo simulations, that the model can produce kernel distributions of aggregated stock market returns observed in the real-world. To compute optimal stock holdings of traders and investors, the law of iterated expectations and the expectation of a log mixed random variable is applied. The latter result is developed and is novel to the best of our knowledge. In total, eleven new theorems are developed and proved and 172800 Monte Carlo simulations are conducted. Page 1