This is a follow up question of this one.
My aim is to create the most realistic historical option prices possible with publicly available data. I want to do this for backtesting purposes.
The following paper gives a good master plan how to backtest option strategies with the standard Black Scholes formula. If you use the publicly available implied volatility indices (like VIX) for the vol parameter the results are pretty good for ATM options:
Problems arise when you want to backtest strategies with (deep) ITM or OTM options.