Listen, I have no interest in an internet argument of any kind, but multiple times you've exposed a significant gap in your options knowledge...and you run an options advisory service! Put/call parity is chapter 1 or 2 in any basic options text. You come off as a little smug and dismissive, but I'm genuinely trying to help you/your service. Any of the books by Natenberg, Baird, Sinclair, Hull should cover the basics you're missing. For more on the math presented, An Introduction to the Mathematics of Financial Derivatives by Neftci should help (or at least I think it will from memory, it's been ages).