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Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset

Author

Listed:
  • Youssef El-Khatib
  • Stéphane Goutte

    (VNU - Vietnam National University [Hanoï], Cemotev - Centre d'études sur la mondialisation, les conflits, les territoires et les vulnérabilités - UVSQ - Université de Versailles Saint-Quentin-en-Yvelines)

  • Zororo S Makumbe
  • Josep Vives

Abstract

In this paper a hybrid model is investigated to capture both financial behaviors of an asset: (i) the leverage effect and (ii) the stochastic volatility component. For this we consider a hybrid model that takes the strengths of the Heston and the CEV models. The pricing of European options is investigated both theoretically and empirically. A decomposition formula that allows to estimate the option price is obtained. Moreover, numerical simulations of the asset price are done to give a better and concrete vision of the adding of this approach. In addition, the price of a European call option under the hybrid model is computed using the Monte Carlo method and our formula. Illustrations and tables show the efficiency of the numerical method based on our approximate formula.

Suggested Citation

  • Youssef El-Khatib & Stéphane Goutte & Zororo S Makumbe & Josep Vives, 2021. "Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset," Working Papers halshs-03211698, HAL.
    • Handle: RePEc:hal:wpaper:halshs-03211698
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03211698
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    References listed on IDEAS

    as
    1. Raul Merino & Josep Vives, 2015. "About the decomposition of pricing formulas under stochastic volatility models," Papers 1503.08119, arXiv.org.
    2. Elisa Alòs & Rafael De Santiago & Josep Vives, 2015. "Calibration Of Stochastic Volatility Models Via Second-Order Approximation: The Heston Case," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-31.
    3. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    4. Sun-Yong Choi & Jean-Pierre Fouque & Jeong-Hoon Kim, 2013. "Option pricing under hybrid stochastic and local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1157-1165, July.
    5. Raúl Merino & Josep Vives, 2017. "Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications," International Journal of Stochastic Analysis, Hindawi, vol. 2017, pages 1-16, July.
    6. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    7. 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.
    8. Raúl Merino & Josep Vives, 2015. "A Generic Decomposition Formula for Pricing Vanilla Options under Stochastic Volatility Models," International Journal of Stochastic Analysis, Hindawi, vol. 2015, pages 1-11, June.
    9. 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.
    10. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
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    Cited by:

    1. El-Khatib, Youssef & Goutte, Stephane & Makumbe, Zororo S. & Vives, Josep, 2023. "A hybrid stochastic volatility model in a Lévy market," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 220-235.
    2. Xu, Lei & Ma, Xueke & Qu, Fang & Wang, Li, 2023. "Risk connectedness between crude oil, gold and exchange rates in China: Implications of the COVID-19 pandemic," Resources Policy, Elsevier, vol. 83(C).

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    Keywords

    Heston-CEV model; Stochastic volatility; European options; Monte Carlo method; Decomposition formula;
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