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Implied higher order moments in the Heston model: a case study of S &P500 index

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  • Farshid Mehrdoust

    (University of Guilan)

  • Idin Noorani

    (University of Guilan)

Abstract

This paper proposes a stochastic volatility model based on the Cox-Ingersoll-Ross process for stock market modeling. We derive a semi-analytical solution of the higher order moments for the compound returns based on the Heston model. Next, we derive a linear relationship between VIX index and variance process. Then, through it and actual data of the VIX index, the volatility process parameters are estimated. We also calibrate the option price obtained by the Heston model based on the S &P500 index option prices. An experimental study demonstrates the efficiency of the proposed method.

Suggested Citation

  • Farshid Mehrdoust & Idin Noorani, 2023. "Implied higher order moments in the Heston model: a case study of S &P500 index," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(2), pages 477-504, December.
    • Handle: RePEc:spr:decfin:v:46:y:2023:i:2:d:10.1007_s10203-023-00396-z
    DOI: 10.1007/s10203-023-00396-z
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