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

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  • El-Khatib, Youssef
  • Goutte, Stephane
  • Makumbe, Zororo S.
  • Vives, Josep

Abstract

In this paper we investigate, since both, the theoretical and the empirical point of view, the pricing of European call options under a hybrid CEV-Heston model. CEV-Heston model captures two typical behaviors of financial assets: (i) the leverage effect and (ii) the stochastic volatility. We prove theoretically that the CEV-Heston model covers the leverage-effect and show empirically the volatility clustering property. Then, we utilize a decomposition of the option price to get an approximate formula for European call options. The accuracy of this estimate is compared with the Monte Carlo method. The results show the efficiency of our approximate formula.

Suggested Citation

  • El-Khatib, Youssef & Goutte, Stephane & Makumbe, Zororo S. & Vives, Josep, 2022. "Approximate pricing formula to capture leverage effect and stochastic volatility of a financial asset," Finance Research Letters, Elsevier, vol. 44(C).
    • Handle: RePEc:eee:finlet:v:44:y:2022:i:c:s1544612321001537
    DOI: 10.1016/j.frl.2021.102072
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    References listed on IDEAS

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    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. 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).
    2. 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.

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