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 .
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 .
D
volatility under the
R
model, which is the
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
R
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
. 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