Microscopic Simulations of the Complex Behavior of Financial Markets

• Understanding Stylized Facts in Stock Markets

  The complex dynamics of financial markets can be characterized by some stylized facts, which are common across many financial instruments, markets, and time horizons. Most of them are counter-intuitive and contrary to the expectations of traditional financial theories. These stylized facts (Fat tails in the distribution of return and volatility clustering) have been observed or discussed in many independent studies.
  In recent years, researchers have used microscopic simulation to explore complex economic dynamics from bottom up. With MS, we study a complex system by directly modeling its individual elements and their interactions. The macroscopic behavior of the system will eventually emerge from the micro-dynamics. MS has shown great potential for more realistically modeling complex dynamical systems in economics and finance. In addition, it facilitates the testing of existing economic or financial models and theories, and the development of new theories and models. At present, most research of MS in finance focuses on understanding the characteristics of financial markets. To achieve this objective, many MS models of financial markets have been developed during the last decade. However, researchers in the field have not yet reached an agreement on explaining the complex dynamics of financial markets. In addition, as recently pointed out by Cont, due to the complexity of the existing (agent-based) models, it is often not clear which aspects of the models are responsible for generating the stylized facts and whether all their ingredients are indeed required for explaining empirical observations. We have conducted a comparative study of different microsimulation methods. Details can be found in the following MSc thesis.
  Our general motivation is to develop a MS model with a simple structure that can reproduce the main stylized facts. More importantly, the causalities of the dynamics generated by the model can be clearly identified. In particular, we wish to confirm the main stylized facts within a parsimonious CA framework by dealing with local agent interactions and adopting simple rules for representing agents' behavior and a simple rule for price updating. Building on the previous work, we have constructed a novel CA model in order to achieve these objectives. In our simulations, we make sure that the model parameters have clear economic relevance or interpretations. For details see the following paper (G. Qiu; B.D. Kandhai and P.M.A. Sloot: Understanding the complex dynamics of stock markets through cellular automata, Phys Rev E., vol. 75, pp. 046116+11. 2007. (DOI: 10.1103/PhysRevE.75.046116)). In contrast to other microscopic simulation~(MS) models, our results suggest that it is not necessary to assume a certain network topology in which agents group together, e.g., a random graph or a percolation network. That is, long-range interactions can emerge from local interactions. Volatility clustering, which also leads to heavy tails, seems to be related to the combined effect of a fast and a slow process: the evolution of the influence of news and the evolution of agents' activity, respectively. In a general sense, these causes of heavy tails and volatility clustering appear to be common among some notable MS models that can confirm the main characteristics of financial markets.

• Understanding Volatility Smile in Option Markets

  It is well-known that the Black-Scholes model cannot account for the volatility smile observed in financial markets. To explain the deviations of option prices from the Black-Scholes formula, models based on processes other than the geometric Brownian motion, such as stochastic volatility and jump diffusion processes, have been proposed. While these models can include the smile-effect on the valuation of options to some extend, they do not explain the origin of the smile phenomenon.
  In this work, we aim to get a better understanding of volatility smile through microsimulation of option markets. Within our model, we adopt traders of only two types: speculators and arbitrageurs, and put and call options on only one underlying asset with different strikes. Speculators make decisions based on their expectations of the price of the underlying asset in the future. In addition, their expected prices are influenced by news over time. Arbitrageurs trade at different arbitrage opportunities such as violation of the put-call parity. Difference of liquidity between out-of-the-money options and in-the-money-options is also included in the model. Price changes of the options are proportional to their excess demands.
  Albeit its simplicity, our model can generate profiles of implied volatility similar to empirical observations. Our results suggest that the volatility smile is related to the combined effect of the typical behavior of different option traders, the difference in liquidity between options with different strikes, and the market mechanism of supply-demand balancing.