Before revision:  Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent volatility under the constant-elasticity-of-variance (CEV) model, which is the limit of the SABR model when the volatility of volatility approaches 0. Numerical examples demonstrate the accuracy of the CEV volatility approximation for a wide range of parameters.
After revision:  Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent volatility under the 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 when the volatility of volatility approaches 0. Numerical examples demonstrate the accuracy of the CEV volatility approximation for a wide range of parameters.