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

Farshid Mehrdoust () and Idin Noorani
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Farshid Mehrdoust: University of Guilan
Idin Noorani: University of Guilan

Decisions in Economics and Finance, 2023, vol. 46, issue 2, No 5, 477-504

Abstract: 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.

Keywords: Calibration; Heston model; Higher order moments; VIX index (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10203-023-00396-z

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