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

TL;DR

This paper derives new analytic approximations for the SABR model's equivalent CEV volatility, improving accuracy and small-strike behavior compared to traditional Black-Scholes-based methods.

Contribution

It introduces a novel CEV volatility approximation for SABR, reducing approximation error and enabling better small-time and zero-strike asymptotics.

Findings

CEV volatility approximation outperforms BS volatility in accuracy

Provides finite zero-strike volatility, aiding small-time asymptotics

Numerical results show improved approximation and no-arbitrage region

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.