This dissertation is concerned with the application of Cellular Automata (CA) to financial models. Because of ever increasing computational power in storing and processing real-time multi-dimensional data from global financial markets, researchers and professionals discovered many interesting market characteristics, which challenge the basic assumptions of conventional models, including the Efficient Market Theory, the Geometric Brownian Motion, and the Black-Scholes Theory. In particular, these models fail to explain serious market anomalies, including sudden crashes. Thus, new effective methodologies to account for real markets' behavior are actively researched. The methodology described in this dissertation is based on Cellular Automata (CA).
CA-based models directly address the market micro-structure. The basic idea is to have a large group of interacted agents, and to specify individual evolution rules for the market participants to mimic various market trading mechanisms. Instead of relying on mathematical descriptions of market macro-behaviors, CA-based models generate market macro-behaviors from the aggregate behaviors of a large population of agents. This bottom-up idea provides a new perspective for explaining some market puzzles that cannot be resolved by conventional models.
The contributions lie in the following aspects: (1) A CA-based model is proposed and applied to derivatives pricing, price dynamics modeling and market microstructure. For each application, we obtain plausible explanations for key market characteristics. Theoretical works to connect our model with the conventional ones are provided. (2) In the derivatives pricing application, the CA-based model is proven to generalize the Black-Scholes theory and the Binomial Tree model. (3) In the application to price dynamics, the model provides analytical results and understanding of bubble formation and burst, mean-reverting price mechanism, and volatility anomalies. (4) A Brief discussion about asynchronous CA is given in the end concerning future research directions.
|School:||University of California, Riverside|
|School Location:||United States -- California|
|Source:||DAI-B 69/03, Dissertation Abstracts International|
|Subjects:||Finance, Electrical engineering, Artificial intelligence|
|Keywords:||Asynchronous trading, Cellular automata, Derivative pricing, Market microstructure, Stochastic volatility|
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