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memo

Calibration of the SABR Model in Illiquid Markets

Abstraction

5. The interpretaiton of parameters

5.1 The $\beta$ parameter.

5.2 The $\alpha$ parameter.

\[\begin{equation} \frac{ (1 - \beta)^{2} \tau }{ 24F^{2-2\beta} } \alpha^{3} + \frac{ \rho\beta\nu\tau }{ 4F^{1-\beta} } \alpha^{2} + \left( 1 + \frac{ 2 - 3\rho^{2} }{ 24 } \nu^{2} \tau \right) \alpha - \sigma_{\mathrm{atm}} F^{1-\beta} = 0 \end{equation}\]