The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model

Jaehyuk Choi, Lixin Wu
11/29/2019
q-fin.MFq-fin.PR

Official code: quants-net/PyFENG (184 stars, GPL-2.0, last commit 2026-08-07). 1 more implementation below.

Abstract

This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error in a way similar to the control variate method because the CEV model is the zero vol-of-vol limit of the SABR model. Moreover, the CEV volatility approximation yields a finite value at a zero strike and thus conveniently leads to a small-time asymptotics for the mass at zero. The numerical results compare favorably with the BS volatility approximations in terms of the approximation accuracy, small-strike volatility asymptotics, and no-arbitrage region.

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Cite this paper

@article{choi2019equivalent,
  title  = {The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model},
  author = {Jaehyuk Choi and Lixin Wu},
  year   = {2019},
  eprint = {1911.13123},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1911.13123}
}

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