Option Pricing with Mixed Levy Subordinated Price Process and Implied Probability Weighting Function

TL;DR

This paper introduces a mixed Levy subordinated model to incorporate investor behavior into asset pricing, analyzing how greed and fear influence option traders' probability weighting and risk perception.

Contribution

It develops a novel mixed Levy subordinated model that integrates behavioral finance concepts into rational asset pricing theory.

Findings

Option traders overweight the probability of large losses.

Diminishing sensitivity affects the probability weighting function.

Model captures behavioral biases in option trading.

Abstract

It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this paper, we reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, we employ the method of subordination which has been proposed in the literature by including business (intrinsic, market) time. We define a mixed Levy subordinated model by adding a single subordinated Levy process to the well-known log-normal model, resulting in a new log-price process. We apply the proposed models to study the behavioral finance notion of "greed and fear" disposition from the perspective of rational dynamic asset pricing theory. The greedy or fearful disposition of option traders is studied using the shape of the probability weighting function. We then derive the implied probability weighting function for the fear and greed deposition of option traders in comparison to spot traders. Our result shows the diminishing sensitivity of option traders. Diminishing sensitivity results in option traders overweighting the probability of big losses in comparison to spot traders.