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 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 Lévy subordinated model by adding a single subordinated Lévy 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.

Deep variance gamma processes

“…In spite of their clear utility for cryptocurrency modeling, Lévy processes have only been recently explored (Philippas et al, 2019). Shirvani et al (2022) propose using a doubly subordinated normal inverse Gaussian Lévy process for daily Bitcoin return data. We push this idea further and show that deeper subordination using the DVG provides better fits of the small log‐returns, but also captures tail behavior better than the model of Shirvani et al (2022).…”

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

“…To quantify an option trader's fear and greed disposition, Shirvani et al (2019) introduced a new Lèvy process for asset returns in the form of a mixed geometric Brownian motion and subordinated Lèvy process. The mixed subordinated Lèvy process is designed to incorporate the views of investors into log return asset pricing models.…”

“…In the mixed subordinated Lèvy log-price process in Equation ( 46),  ≠ 0 is the volatility of the continuous dynamics of X, and s is the volatility of the pure jump of the subordinated process L V t . Shirvani et al (2019) used the mean-correction martingale measure 36 method to price options. By applying this method, the authors showed that the proposed pricing model is indeed arbitrage free.…”

Using Parallel Diesel Generator and Fuel Cell as an Islanded Microgrid

“…The mentioned issues have been considered in recent research in recent decades. But, other factors such as forecasting or numerical issues based on economic models need to be considered soon [3][4][5][6][7].…”