One approach to trading options is to look for pricing relationships between options that are out of whack, based on historical norms. The best way IMHO to compare the price of two options not at the same strike, or not with the same expiration date, is to compare their implied volatilities.
Wouldn't that be similar to comparing of the option's IV to the stock's historical volatility based on historical norms? This data ( option's IV and stock's historical volatility ) is easily available on the web.
No, completely different approach. In this approach you couldn't care less what the actual or historic volatility is. Doesn't matter a bit. You simply see that one option is overpriced relative to another option, giving you the opportunity to buy the underpriced option and sell the overpriced option. You are betting only that the normal pricing relationship between the two options - expressed as their IV relationship - will reestablish itself. In the meantime you will need to manage your position fairly delta, gamma and vega neutral - or else be right on the direction of the price of the underlying and of volatility.
I am not sure though how to establish the historical norm between volatilities of 2 option strikes in your approach? It would be difficult to make any profit if historically volatility of the first strike is higher than volatility of the second strike. No reversion to historical norm because that's their historical norm.
The way to compare historical IV with current IV is to normalize the volatility surface across strike, time and IV. Reference the work of Robert Tompkins. A normalized surface will look something like the attached spreadsheet.
You establish the historical norm of strike-to-strike volatility relationships in a particular contract - in other words, the historical norm of the skew - simply by observing it over a period of time. In index options - the SPY for example or options on the S&P500 futures - the IV of each strike is always lower than that of the strike below and higher than that of the strike above. So the lower the strike, the higher the IV. That relationship holds true day in and day out. You can go to the bank on it. Now imagine that in a moment of extreme bullishness there's a mad rush to buy OTM calls, causing the normal skew relationship to reverse. Suddenly the higher strikes are trading at higher IVs than the lower strikes. This violates historical norms, and is unlikely to last. So if you buy lower strikes and sell higher strikes - and manage the position more or less delta and gamma neutral until the normal skew reasserts itself - you would make money. The above is an extreme example for purposes of explanation only, so don't hold your breath waiting for it to happen. The index skews are actually quite rigid, and don't change much, even at market tops or bottoms. A more likely place to look for such anomalies is stocks that reflect natural resource values such as mining stocks, USO, GLD, etc., which can have fairly "pliable" skews.