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Efficient and accurate simulation of the stochastic-alpha-beta-rho model

Author

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  • Choi, Jaehyuk
  • Hu, Lilian
  • Kwok, Yue Kuen

Abstract

We propose an efficient, accurate and reliable simulation scheme for the stochastic-alpha-beta-rho (SABR) model. The two challenges of the SABR simulation lie in sampling (i) integrated variance conditional on terminal volatility and (ii) terminal forward price conditional on terminal volatility and integrated variance. For the first sampling procedure, we sample the conditional integrated variance using the moment-matched shifted lognormal approximation. For the second sampling procedure, we approximate the conditional terminal forward price as a constant-elasticity-of-variance (CEV) distribution. Our CEV approximation preserves the martingale condition and precludes arbitrage, which is a key advantage over Islah’s approximation used in most SABR simulation schemes in the literature. We then adopt the exact sampling method of the CEV distribution based on the shifted-Poisson mixture Gamma random variable. Our enhanced procedures avoid the tedious Laplace inversion algorithm for sampling integrated variance and non-efficient inverse transform sampling of the forward price in some of the earlier simulation schemes. Numerical results demonstrate our simulation scheme to be highly efficient, accurate, and reliable.

Suggested Citation

  • Choi, Jaehyuk & Hu, Lilian & Kwok, Yue Kuen, 2026. "Efficient and accurate simulation of the stochastic-alpha-beta-rho model," European Journal of Operational Research, Elsevier, vol. 329(1), pages 166-179.
    • Handle: RePEc:eee:ejores:v:329:y:2026:i:1:p:166-179
    DOI: 10.1016/j.ejor.2025.09.027
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    References listed on IDEAS

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    1. 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).
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    4. Archil Gulisashvili & Blanka Horvath & Antoine Jacquier, 2018. "Mass at zero in the uncorrelated SABR model and implied volatility asymptotics," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1753-1765, October.
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    6. 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.
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