The Equivalent Constant-Elasticity-of-Variance (CEV) Volatility of the Stochastic-Alpha-Beta-Rho (SABR) Model

33 Pages Posted: 19 Dec 2019 Last revised: 8 Jun 2021

See all articles by Jaehyuk Choi

Jaehyuk Choi

Peking University HSBC Business School

Lixin Wu

Hong Kong University of Science & Technology - Department of Mathematics

Date Written: December 2, 2019

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.

Keywords: Stochastic Volatility, SABR Model, CEV Model

JEL Classification: C15, C52, G13

Suggested Citation

Choi, Jaehyuk and Wu, Lixin, The Equivalent Constant-Elasticity-of-Variance (CEV) Volatility of the Stochastic-Alpha-Beta-Rho (SABR) Model (December 2, 2019). Journal of Economic Dynamics and Control, Vol. 128, 104143, 2021, Available at SSRN: https://ssrn.com/abstract=3495464 or http://dx.doi.org/10.2139/ssrn.3495464

Jaehyuk Choi (Contact Author)

Peking University HSBC Business School ( email )

Shenzhen

HOME PAGE: http://jaehyukchoi.net/phbs_en

Lixin Wu

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong
2358-7435 (Phone)
2358-1643 (Fax)

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