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The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model
Journal of Economic Dynamics and Control ( IF 1.9 ) Pub Date : 2021-05-06 , DOI: 10.1016/j.jedc.2021.104143
Jaehyuk Choi , Lixin Wu

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.



中文翻译:

随机α-β-rho(SABR)模型的等效恒定弹性方差(CEV)波动率

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。

更新日期:2021-05-27
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