How to calculate Implied Volatility by hand?

The way I was taught was to brute force the IV using Black Shcholes using something like the Bisection method.

Its my understanding that there are no exact formulas that allow you to compute BS IV for all options, hence the need for something like Bisection or Newtons method.


http://en.wikipedia.org/wiki/Bisection_method

You write a computer program where you price the current option using some volatility guess.

Is the actual price higher or lower ? If higher, adjust your guesses up. If lower, adjust your guesses down. Keep going until the price from the option model is a close to the price currently being traded. That is your implied volatility.

"Financial Modeling" by Simon Beninga comes with working VBA code for computing IV if you want code samples.

Incidentally, Ivolatility takes this concept a bit futher.

Once you know how to compute implied volatility, you can compute a three dimensional "vol surface" that plots IVs for all options on a given instrument. X axis = strike, y = expiration, z = IV.

Ivolatility has a proprietary method where they condense IVs for all strikes/maturities into a single IV number which they call their index.


-Tony
 
Quote from sle:

At the money, you can approximate it as

Implied Vol = P / (0.4 F Sqrt(t) )

where P is price of option, F is forward price (for short dated stuff it's ok to use spot price), t is time to expiry in years.
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Attached is a paper "A New Formula for Computing Implied Volatility" describing, afaik, the most recent analytical IV approximation that works well regardless of moneyness.

The complete paper is a sure way to a quick headache so first look at top of page 11 where the resulting formula is mentioned to see if you could work with this.

BTW there are also some less complex (and less accurate) formulas mentioned in previous pages that may suffice for your purpose.
 

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Quote from nonprophet:

Attached is a paper "A New Formula for Computing Implied Volatility" describing, afaik, the most recent analytical IV approximation that works well regardless of moneyness.

The complete paper is a sure way to a quick headache so first look at top of page 11 where the resulting formula is mentioned to see if you could work with this.

BTW there are also some less complex (and less accurate) formulas mentioned in previous pages that may suffice for your purpose.
More...

I've just joined this board while researching the B&S VI formula and its improvements -- much to my liking I found this thread's exchanges enlightening, and thanks to all who've contributed to it.

I too admittedly lack in the equation department. I understand the basis of the theorm thanks to gummy's fantastic site, but I'm in no position to adapt it.

What I'd like to do (i'm a neo-turtle index futures trader solely) instead of relying on range exhaustion rallies, incremental changes in ATRs and trades from breakout to breakout, is monitor, by hand, being the classicist I am, IVs compared to possible mean reversions and ATRs to stay longer in trades. My hope is to transform turtle trading into reversal trading in my trading plan.

I can calculate the mean reversion to a percentage, but the forecasting and discounting with my pre-algebraic disposition leaves me at a distinct disadvantage, verily but unfortunately.

Would any of you be as kind as to help a fellow trader over this hurdle? I don't have any business trading options at this point, but helping me compute IVs strictly for equity markets would be a tremendous service should I gain the confidence to make the transition later on .

A many great thanks in advance.
 
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