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

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 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. Moreover, in our approach, arbitrage occurs at a lower strike price than in existing BS-based approximations.