Stock Price Fluctuations in an Agent-Based Model with Market Liquidity

TL;DR

This paper develops an agent-based stock market model incorporating market liquidity and constraints, deriving a reflected SDE for stock prices and analyzing how constraints affect pricing.

Contribution

It introduces a novel continuous-time stock price model with constraints using oblique reflection in SDEs, extending previous models by including market frictions.

Findings

Constraints cause overpricing and underpricing effects.

The model captures market liquidity impacts on stock prices.

Reflected SDE accurately describes constrained agent behaviors.

Abstract

We study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via agents' excess demand functions, and the diffusion approximation approach is applied to characterize the continuous-time limit (as transaction intervals shorten) as a solution of the corresponding stochastic differential equation (SDE). In this paper we further make the assumption that some of the agents are bound by either short sale constraints or budget constraints. Then we show that the continuous-time process of the stock price can be derived from a certain SDE with oblique reflection. Moreover we find that the short sale (respectively, budget) constraint causes overpricing (respectively, underpricing).