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

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...

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Vydáno v:European journal of operational research Ročník 329; číslo 1; s. 166 - 179
Hlavní autoři: Choi, Jaehyuk, Hu, Lilian, Kwok, Yue Kuen
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 16.02.2026
Témata:
Constant elasticity of variance process
SABR model
Shifted-Poisson-mixture Gamma distribution
Simulation
Constant elasticity of variance process
Simulation
SABR model
Shifted-Poisson-mixture Gamma distribution
ISSN:0377-2217
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Shrnutí: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. •We provide an efficient simulation scheme for the stochastic-alpha-beta-rho model.•The method eliminates the need for inverse transformations or root-finding.•It utilizes simple, commonly used random variables for implementation.•Our scheme achieves superior speed and accuracy compared to existing approaches.
ISSN:0377-2217
DOI:10.1016/j.ejor.2025.09.027