Looking a bit more closely at PUT Implied Volatility for some instruments, specifically focusing on SPX and RUT initially; there appear to be well behaved characteristics that I find interesting. The standard technique for determining the Implied Volatility of a specific option is to use a good model, and iterate on the "volatility" input to the model with all the other "KNOWN" variables properly input, to determine the specific "volatility" input value that results in the option Price that agrees with the "actual" option price. I am using the Black & Scholes model, which seems ideal for this task. The technique above has a weakness in that the "actual" option price is only really appropriate the instant a trade occurs. Providers of Implied Volatility sometimes use the Mid price {(Bid + Ask)/2 } as the option price for determining IV, which is a close approximation. OptionVue provides access to Bid/Ask/and Mid price derived IV. This implies there may be increasing error in the Implied Volatility values for options which have no trades, or have not traded recently (bid and ask spreads widen) -- such as those further from ATM. For those of you that have interest, I am including a CSV file and a gnuplot .dem file which will plot a 3-D view of the bid/ask/mid IV derived for SPX Weeklies and monthlies (not the WED expirations) for the next 100 days at market close today. (remove the .txt extension necessary to permit the upload) Tweak the .dem file to display RUT options, which are also included in the .csv file. The Red dots are the Bid derived IV, the Black dots are the Mid derived IV and the Green dots are the Asked derived IV. Note that some ITM IV values are plotted with zero values: This implies the price of the option would infer a Negative IV value which is impossible, so truncated to zero. The X axis chosen is Moneyness, and the formula I used is provided. If the X axis is Strike or Delta (other common representation), the uniformity of the data is less apparent. I am curious if anyone notices an error or issue in what I am observing! It seems possible to produce more accurate IV values for options which may have no trades and larger bid/ask spreads by properly weighting the known data. Below is a graph of the Mid-price of today's closing SPX PUT IV with those with trades in green and no volume shown in RED. Below is screen shot of the graph with Bid/MID/Asked IV (SPX PUTs only).
So, option market makers value options on the basis of an IV, usually derived from the market and historical data.... They start with ATM IV and then plot across the strikes with some skew... giving them a theoretical value for each option. They quote around that value. They all kinda agree and then we see the quoted market. So why don't you just look at mid price and mid IV? Because that's what everyone else looks at... If someone is of with their pricing, they will be arbitraged or everyone decides that is the new theoretical price and quotes on the new mid IV. Also, I would not use deep ITM options for valuation, but instead use the OTM opposite, so instead of 1000 call (ITM) use the 1000 put. They will use the same IV for pricing since the are basically the same. OTM is always more actively traded. You can also take 6 strikes and plot you own IV curve using spline interpolation.