No, they are only the same price under very strict assumptions. The put-call parity says that buying a call and selling a put creates the same payoff structure as being long the stock itself. Depending on the strike, the put or the call could be ~100% of the value of the position. Only when you get near the price of the underlying do the put and call equal each other.

I think I do understand them, from a value-investor's perspective. If I buy an option, I actually intend to exercise it or hold it until expiration, not hedge with it.

If I bought a GameStop put today, for the pricing in my post above, it would be because I was willing to make a strong bet that GameStop's intrinsic value in November would remain below $60/share and that I was fairly sure the market would return to its senses by then. How the option-seller reaches her offering price is entirely irrelevant to me.

It is true that much of the pricing of options comes from volatility, but for me, as a buyer, it is perhaps irrelevant.

Thanks for your perspective, though. I'll read your link with interest.

What I mean is you cannot make directional predictions of a stock from option prices. The information just isn’t there. The same way you can’t use long dated futures. Because S&P 500 futures (during regular trading hours) will always be the current price, modified by the financing cost. There can never be a directional prediction, because all directional predictions get arbitraged away into the current price.

I've had more time to think about this now -- it would appear that directional prediction can be arbitraged away in a world where the future cannot be known. In general, however, through research, one can begin to divine a glimmer (or more) of the future direction of the underlying.

In that situation, someone with a reasonable guess at the future could absolutely murder uninformed arbitrageurs, right? It is my expectation that "correct" pricing of the options should fold in information about both the expected volatility and the direction of the underlying.

Ah. Understood. Thank you.