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 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 use of CEV volatility has the effect of imposing an absorbing boundary condition at the origin and thus provides small-time asymptotics for the mass at zero. The numerical results compare favorably with the BS volatility approximations in terms of the approximation accuracy and no-arbitrage region