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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 images:

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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(images, K), at the first-order in the maturity images. Here, we display a corrected version of the formula [8]:

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with

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Though this formula is popular, volatility does not mean-revert ...

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