### A simple formula for calculating implied volatility?

• jessica

8 years ago

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.

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