Scenario: stock trading at 100 today, 80% chance it will trade at 110 tomorrow, 20% chance it will trade at 90 tomorrow
A new 100 strike call option on this stock is worth 8 today (assuming no discounting).
Assume you buy this call option. Now, you can hedge this option by selling 50 shares today, giving a payoff of -3 tomorrow. This is clearly a poor trade.
Logically, shouldn’t the payoff of the hedged position be zero in this scenario? What am I missing here?