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

Abstract

It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this article, the authors reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, they employ the method of subordination that has been proposed in the literature by including business (intrinsic, market) time. They define a mixed Lévy subordinated model by adding a single subordinated Lévy process to the well-known log-normal model, resulting in a new log-price process. They 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. They then derive the implied probability weighting function for the fear and greed deposition of option traders in comparison to spot traders. Their 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.

TOPICS: Derivatives, options

Key Findings

• • Behavioral finance and rational finance are reconciled by using a mixed Lévy subordinated process.

• • The mixed Lévy subordinated process develops a more realistic asset pricing model by incorporating the behavior and sentiment of investors in the log-return pricing model.

• • The implied probability weighting function under the mixed Lévy subordinated process model indicates the diminishing sensitivity of option traders.