A dynamical model of market under- and overreaction

Jorge R. Sobehart, Ricardo Farengo

Abstract

ABSTRACT

In this article we introduce a dynamical model of securities prices based on a particular notion of “irrational exuberance” and “market fear” generated by the under- or overreaction of market participants. The addition of a small amount of irrational behavior (behavioral noise) allows us to reproduce realistic distribution of price returns that would be absent in a perfectly rational world. Our model of asset dynamics is based on cognitive biases of market participants and their reaction to price momentum. The resulting price dynamics yields fat-tailed distributions of returns. When we apply our model to the pricing of option contracts we obtain implied volatility skews and smiles generated by the irrational behavior of market participants.