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

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