Did you ever check out how Sosnoff did the derivation quoted in the first article ? Could be worth to get an accurate point of view on who is a real trader with millions made on the markets and who is a ... tastytrader
https://en.wikipedia.org/wiki/Mark_Spitznagel...
Got it. My point was that call put parity hold for european style options. American style is something different. JackRab pointed out the fact that delta of a long call/short put may have a value beyond 100%, it's a reality and everyone can price it, knowing that interest rates are low nowadays...
2 different strikes => call/put parity => 2 equations with 2 unknowns. Feel free to ask for the details. In practice, you would do the same for every strike with a tight bid/ask spread you could find to get an accurate number. Really nothing new here.
I think a better way is to get implied riskfree rate and dividend rate from option prices.
That way you'll be sure to get the same implied volatility as it has been priced by the market.