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Hyperbolic normal stochastic volatility model

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  • Jaehyuk Choi
  • Chenru Liu
  • Byoung Ki Seo

Abstract

For option pricing models and heavy‐tailed distributions, this study proposes a continuous‐time stochastic volatility model based on an arithmetic Brownian motion: a one‐parameter extension of the normal stochastic alpha‐beta‐rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that our model has a closed‐form Monte Carlo simulation scheme and that the transition probability for one special case follows Johnson's SU distribution—a popular heavy‐tailed distribution originally proposed without stochastic process. It is argued that the SU distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.

Suggested Citation

  • Jaehyuk Choi & Chenru Liu & Byoung Ki Seo, 2019. "Hyperbolic normal stochastic volatility model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(2), pages 186-204, February.
    • Handle: RePEc:wly:jfutmk:v:39:y:2019:i:2:p:186-204
    DOI: 10.1002/fut.21967
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    Cited by:

    1. Jaehyuk Choi & Byoung Ki Seo, 2023. "Option pricing under the normal SABR model with Gaussian quadratures," Papers 2301.02797, arXiv.org.
    2. Choi, Jaehyuk & Kwok, Yue Kuen, 2024. "Simulation schemes for the Heston model with Poisson conditioning," European Journal of Operational Research, Elsevier, vol. 314(1), pages 363-376.
    3. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2021. "A Black-Scholes user's guide to the Bachelier model," Papers 2104.08686, arXiv.org, revised Feb 2022.
    4. Choi, Jaehyuk & Wu, Lixin, 2021. "The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    5. Jaehyuk Choi, 2024. "Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Lo\`eve expansions," Papers 2402.09243, arXiv.org.
    6. Jaehyuk Choi & Lilian Hu & Yue Kuen Kwok, 2024. "Efficient simulation of the SABR model," Papers 2408.01898, arXiv.org.
    7. Jaehyuk Choi & Minsuk Kwak & Chyng Wen Tee & Yumeng Wang, 2022. "A Black–Scholes user's guide to the Bachelier model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 959-980, May.
    8. Jaehyuk Choi & Lixin Wu, 2021. "A note on the option price and ‘Mass at zero in the uncorrelated SABR model and implied volatility asymptotics’," Quantitative Finance, Taylor & Francis Journals, vol. 21(7), pages 1083-1086, July.
    9. Jaehyuk Choi & Yue Kuen Kwok, 2023. "Simulation schemes for the Heston model with Poisson conditioning," Papers 2301.02800, arXiv.org, revised Nov 2023.

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