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Rescaling the double-mean-reverting 4/2 stochastic volatility model for derivative pricing

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Listed:
  • Cao, Jiling
  • Kim, Jeong-Hoon
  • Liu, Wenqiang
  • Zhang, Wenjun

Abstract

The popular 4/2 stochastic volatility model reveals important features of volatility but a closed-form formula for derivative prices is still lacking. This paper proposes a modified form of the 4/2 model into which two scale double-mean-reverting stochastic volatility is incorporated in order to remedy its shortcomings. We obtain a closed-form formula for the prices of European derivatives. The formula can be explicitly calculated by taking derivatives of the Black–Scholes prices and thus faster calibration of the 4/2 model becomes available. We also show that the rescaled 4/2 model is flexible enough to capture essential features (skew or smile) of market implied volatilities.

Suggested Citation

  • Cao, Jiling & Kim, Jeong-Hoon & Liu, Wenqiang & Zhang, Wenjun, 2023. "Rescaling the double-mean-reverting 4/2 stochastic volatility model for derivative pricing," Finance Research Letters, Elsevier, vol. 58(PB).
    • Handle: RePEc:eee:finlet:v:58:y:2023:i:pb:s1544612323007468
    DOI: 10.1016/j.frl.2023.104374
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    Keywords

    4/2 stochastic volatility; Double-mean-reversion; Closed-form formula; Derivative; Implied volatility;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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