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Application of Extended Normal Distribution in Option Price Sensitivities

Author

Listed:
  • Gangadhar Nayak

    (Department of Mathematics and Humanities, Odisha University of Technology and Research, Bhubaneswar 751029, India)

  • Subhranshu Sekhar Tripathy

    (School of Computer Engineering, KIIT Deemed to be University, Bhubaneswar 751024, India)

  • Agbotiname Lucky Imoize

    (Department of Electrical and Electronics Engineering, Faculty of Engineering, University of Lagos, Akoka, Lagos 100213, Nigeria)

  • Chun-Ta Li

    (Program of Artificial Intelligence and Information Security, Fu Jen Catholic University, New Taipei City 24205, Taiwan)

Abstract

Empirical evidence indicates that asset returns adhere to an extended normal distribution characterized by excessive kurtosis and non-zero skewness. Consequently, option prices derived from this distribution diverge from those predicted by the Black–Scholes model. Despite the significance of option price sensitivities for risk management in investment portfolios, the existing literature lacks a thorough exploration of these sensitivities within the context of the extended normal distribution. This article addresses this research gap by deriving the Greeks for options based on the extended normal distribution. The Greeks under consideration include Vega, Delta, Theta, Gamma, Rho, Vanna, Charm, and Vera, all of which are crucial for informed financial decision-making. Furthermore, this study provides a detailed analysis of how these option price sensitivities vary with different levels of kurtosis, offering valuable insights for various market applications. This contribution not only enhances the theoretical understanding of option pricing under non-standard distributions but also presents practical implications for portfolio risk management.

Suggested Citation

  • Gangadhar Nayak & Subhranshu Sekhar Tripathy & Agbotiname Lucky Imoize & Chun-Ta Li, 2024. "Application of Extended Normal Distribution in Option Price Sensitivities," Mathematics, MDPI, vol. 12(15), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2346-:d:1444050
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    References listed on IDEAS

    as
    1. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    2. repec:eme:mfppss:v:35:y:2009:i:5:p:427-438 is not listed on IDEAS
    3. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    4. Karagiorgis, Ariston & Drakos, Konstantinos, 2022. "The Skewness-Kurtosis plane for non-Gaussian systems: The case of hedge fund returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Hosam Ki & Byungwook Choi & Kook‐Hyun Chang & Miyoung Lee, 2005. "Option pricing under extended normal distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(9), pages 845-871, September.
    7. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    8. Kosowski, Robert & Neftci, Salih N., 2014. "Principles of Financial Engineering," Elsevier Monographs, Elsevier, edition 3, number 9780123869685.
    9. Richard Harris & C. Coskun Kucukozmen, 2001. "The empirical distribution of stock returns: evidence from an emerging European market," Applied Economics Letters, Taylor & Francis Journals, vol. 8(6), pages 367-371.
    10. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    11. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    12. MacBeth, James D & Merville, Larry J, 1980. "Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
    13. Bo Martin Bibby & Michael SÛrensen, 1996. "A hyperbolic diffusion model for stock prices (*)," Finance and Stochastics, Springer, vol. 1(1), pages 25-41.
    14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    15. Gurdip Bakshi & Charles Cao & Zhaodong (Ken) Zhong, 2021. "Assessing models of individual equity option prices," Review of Quantitative Finance and Accounting, Springer, vol. 57(1), pages 1-28, July.
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