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

Abootaleb Shirvani, Yuan Hu, Svetlozar T. Rachev and Frank J. Fabozzi
The Journal of Derivatives Winter 2020, 28 (2) 47-58; DOI: https://doi.org/10.3905/jod.2020.1.102
Abootaleb Shirvani
is a PhD student in the Department of Mathematics and Statistics at Texas Tech University in Lubbock, TX
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Yuan Hu
is a PhD student in the Department of Mathematics and Statistics at Texas Tech University in Lubbock, TX
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Svetlozar T. Rachev
is a professor of quantitative finance in the Department of Mathematics and Statistics at Texas Tech University in Lubbock, TX
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Frank J. Fabozzi
is a professor of finance at EDHEC Business School in Nice, France
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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.

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The Journal of Derivatives: 28 (2)
The Journal of Derivatives
Vol. 28, Issue 2
Winter 2020
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Option Pricing with Mixed Lévy Subordinated Price Process and Implied Probability Weighting Function
Abootaleb Shirvani, Yuan Hu, Svetlozar T. Rachev, Frank J. Fabozzi
The Journal of Derivatives Nov 2020, 28 (2) 47-58; DOI: 10.3905/jod.2020.1.102

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Option Pricing with Mixed Lévy Subordinated Price Process and Implied Probability Weighting Function
Abootaleb Shirvani, Yuan Hu, Svetlozar T. Rachev, Frank J. Fabozzi
The Journal of Derivatives Nov 2020, 28 (2) 47-58; DOI: 10.3905/jod.2020.1.102
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  • Article
    • Abstract
    • OPTION PRICING FOR MIXED SUBORDINATED LÉVY PROCESS
    • OPTION PRICING FOR MIXED SUBORDINATED NORMAL INVERSE GAUSSIAN PROCESS
    • NUMERICAL EXAMPLE
    • IMPLIED PROBABILITY WEIGHTING FUNCTION
    • CONCLUSION
    • ADDITIONAL READING
    • ENDNOTES
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