SABR Model
The SABR model [4] is a stochastic volatility (see Stochastic Volatility Models) model in which the forward asset price follows the dynamics in a forward measure 
:
The stochastic volatility at, is described by a geometric Brownian motion. The model depends on four parameters: α, ν, ρ, and β. By using singular perturbation techniques, Hagan et al. [4] obtained a closed-form formula for the implied volatility σBS(
, K), at the first-order in the maturity . Here, we display a corrected version of the formula [8]:
with
Though this formula is popular, volatility does not mean-revert ...
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