Modeling Information Theory Effects on Price Uncertainty Using Multiple Agents with Heterogeneous Volatility

Abstract

A multiple agent model is developed where traders must receive, process, and send communications to and from a distant market. This model highlights the importance that information theory’s communication constraints have on the level of price uncertainty each agent faces. The collective uncertainty of many such agents leads to the nontrivial structure of the implied volatility surface. This type of analysis helps to reconcile traditional financial theory such as the Black-Scholes model with the realities seen in the financial markets. Apparent anomalies such as non-constant volatility across strikes and times to expiration are intuitively generated. Additionally the relationships established offer novel applications outside the realm of existing theories about uncertainty in finance and economics.

Keywords: financial engineering, information theory, Black-Scholes, implied volatility, econophysics

JEL Classification: G1, G12, G14, D84