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Mathematical Finance

An Interactive Agent-Based Model

Po–Keng Cheng: Stony Brook

Location:  Hill 705
Date & time: Tuesday, 24 January 2017 at 11:45AM - 11:45AM

We develop and examine a simple heterogeneous agent model, where the distribution of returns generated from the model have stylized facts in financial markets, such as fat tails and volatility clustering. Our results indicate that the risk tolerance of fundamentalists and the relative funding rate of positive-feedback traders versus fundamentalists are key factors determining the path of price fluctuations. Fundamentalists are more able to dominate the market when they are more willing than positive-feedback traders to take risks. In addition, more crises occur as positive-feedback traders face higher funding costs compared to fundamentalists. Our model suggests that fundamentalists cause heavy tails, and positive-feedback traders cause the formation of speculative bubbles.

We introduce a heterogeneous agent mechanism extending from the model. We add one more key factor, length of evaluations on performances between strategies, which also have significant influence on price fluctuations. We also introduce Markov transition matrix, Perron-Frobenius transition matrix, and Inertia to investigate the transitions among states. Our results show the stickiness of states switching from one to another, and the longer length of evaluations on performances would generate more complex dynamic price fluctuations.

We then estimate key parameters in our model. Our empirical results indicates that traders’ attitudes towards risk vary across time and market. The generally low level of risk bearing by fundamentalists could explain the frequent occurrence of bubbles.

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Department of Mathematics

Department of Mathematics
Rutgers University
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