Option Pricing with Greed and Fear Factor: The Rational Finance Approach

Abstract

In this article, we explain main concepts of prospect theory and cumulative prospect theory within the rational dynamic asset pricing framework. We derive option pricing formulas when asset returns are altered by a generalized prospect theory value function or a modified Prelec’s weighting probability function. We introduce new parametric classes for prospect theory value functions and probability weighting functions consistent with rational dynamic pricing theory. After studying the behavioral finance notion of “greed and fear” from the perspective of rational dynamic asset pricing theory, we derive the corresponding option pricing formulas when asset returns follow continuous diffusions or discrete binomial trees. We define a mixed subordinated variance gamma process to model asset return and derive the corresponding option pricing formula. Finally, we apply the proposed probability weighting functions to study the greedy or fearful disposition of option traders when asset returns follow a mixed subordinated variance gamma process. The results indicate availability bias and diminishing sensitivity of option traders.