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.

这项研究提出了随机α-β-rho（SABR）模型的新的解析近似。与现有研究关注等效的Black-Scholes（BS）波动率不同，我们代之以等效的恒定弹性方差（CEV）波动率。我们的方法以类似于控制变量方法的方式有效地降低了近似误差，因为CEV模型是SABR模型的零体积极限。此外，CEV波动率近似值在零打击时产生一个有限值，因此方便地导致质量为零时的小时间渐近性。数值结果在近似精度，小震荡波动渐近性和无套利区域方面，与BS波动率近似值相比具有优势。