how most people do to construct historical implied volatility? I could always get one ATM- Call and Put by Black-schole formula, but how to get the single value which can represent the implied volatility of a day? my underlying is index thanks
1) Determine wihich option quotes you are going to use for your calculations. Iterate the respective IV's from them. Average the calculated values. OR 2) Look at the pretty graphs of historical IV at IVolatility.com
From my limited experience, historical implied volatility is much less useful as a guide to volatility forecast than historical underlying price used as a guide to underlying price trend. More than often, it gives you false comfort.
There's really no right or wrong way to do this - everyone has their own ideas. If you're feeling energetic and really want to do a bang-up job on this, see how the VIX is calculated (CBOE website has details) and duplicate it. This is probably the most robust such calculation out there. If all you want is something good enough for government work, perhaps an average IV of the two closest strikes would work. It really depends on how much precision you need, and how much work you want to put into it. It also depends a lot on what you need it for, as that will determine what strikes need to be considered, whether the skew should be worked into it, etc.