I know that you can compute the P&L of a delta-hedged option by adding up alll the gamma profits - Delta-Hedged Option P&L = 0.5 * Sum (t = 0, t = T) [r(t) ^ 2 - Implied Vol ^ 2 * dt) * Gamma(t)A trader I work with gave me a theory that I can't prove or disprove. Any help would be appreciated. He says that if an option is fairly priced (at correct volatility) then its price and delta-hedging P&L should theoritically be zero (of course an individual option P&L is path-dependent, but in general its right). So my P&L from an option should simply be - Vega (at t = 0) * (Implied Vol - Realized Vol) What's incorrect about this expression?

QuoteWhat's incorrect about this expression?It is like saying: at this moment (t=0) the instantaneous velocity of my car is 50 km/h, therefore in an hour I will be exactly 50 km from where I am now.

Your trader is right(assuming perfect environment),but I believe the copyright still belongs to B&S