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What is The Closed-Form Implied Volatility Estimator (As Defined by Hallerbach 2004) for A P...

What would be the equation for a put option? Thank you! $$\sigma\sqrt{T} = \frac{\sqrt{2\pi}}{2(S+X)}\Biggl[2C+X-S+\sqrt{(2C+X-S)^2-1.85\frac{(S+X)(X-S)^2}{\pi\sqrt{XS}}}\Biggl]$$ …
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