### A simple formula for calculating implied volatility?

• We all know if you back out of the Black Scholes option pricing model you can derive what the option is "implying" about the underlyings future expected volatility.

Is there a simple, closed form, formula deriving Implied Volatility (IV)? If so can you could you direct me to the equation?

Or is IV only numerically solved?

I found this one via Google: Implied Volatility Formula

yea, saw that one too. Newton method was used here. am I right? But how is IV calculated? Anyone here use a standard procedure?

Jaeckel has a paper for a more efficient method of backing out the implied vol here - it includes a link to the source code.

Please refer to this 2016-17 article by Jaeckel : https://jaeckel.000webhostapp.com/ImpliedNormalVolatility.pdf It has been mentioned above in a comment, but that link is broken

8 years ago

Brenner and Subrahmanyam (1988) provided a closed form estimate of IV, you can use it as the initial estimate:

$$\sigma \approx \sqrt{\cfrac{2\pi}{T}} . \cfrac{C}{S}$$

What are the definitions of T,C and S ? I'm guessing T is the Duration of the option-contract, C is the theoretical Call-value and S is the Strike-price, correct ?

No, S is the current price of the underlying. However the approximation by Brenner and Subrahmanyam works best for at the money options, hence the difference should be small in that case.

@Dominique (S = Spot price of the underlying, a.k.a. current price)

The formula is based on the ATM price under normal model approximation. See https://quant.stackexchange.com/a/1154/26559 for further detail.

Content dated before 7/24/2021 11:53 AM
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