Saturday, January 10, 2015

options - What really is Gamma scalping?


How does Gamma scalping really work? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price V(t,S) at time t and the underlying stock price at S with no interest, the infinitesimal change of the overall portfolio p&l under delta hedging, assuming we have the model, volatility, etc., correct, is 0=dVVSdS=(Θ+12σ2S2Γ)dt. So the Gamma effect is cancelled by the Theta effect. Where does so called Gamma scalping profit come from?


Note: My condition implies that P&L[0,T]=T012Γ(t,St,σ2t,impl.)S2t(σ2t,real.σ2t,impl.)dt coming from the misspecification of volatility is 0.





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