Quote from slickpick:
Let us for a second imagine a world where people only traded single equity options positions. If this were the case, one person wins and one person loses - zero sum game. The payoff function for a vanilla call is max(S-k,0) where S is the terminal value of the underlyer.
Now I can see where you're coming from when you introduce more positions, then we get payoffs where both parties can make money depending on how they hedge their positions. However, what you're saying is akin to that blackjack is not a zero sum game if you're winning on some sports bet elsewhere simultaneously.
If you break down the trades individually and assuming the market you're looking at is zero sum (equities are not), you should see that options are in fact a zero sum game!
+1
:eek: