delta-gamma approximation using Black-Scholes formula


I hope that is good place to ask. I’m writing my master’s thesis and found a problem. I want to compare estimation methods VaR: analytically and delta-gamma approximation. Assume the portfolio contains two options: long call and long put. My histograms for an analytical calculations and the delta-gamma approximation overlaps when in the D-G approximation I have for a call position Theta*t + Delta *deltaS - 0.5 * (deltaS)2*Gamma and for put position Theta*t - Delta *deltaS - 0.5 * (deltaS)2*Gamma (in the definition we have Theta*t + Delta *deltaS + 0.5 * (deltaS)2*Gamma). Otherwise the histogram produced by D-G is “truncate” on the right side. I know that for a long call delta>0 and gamma>0, for a long put delta<0 and gamma>0, but histograms are similar when I have "-Gamma’.

Beep beep boop boop.

Use link below if it’s an ODE or PDE.


@Patricia Backtest this model but you should probably pay for that.