Delta - Gamma approximation VaR using Black-Scholes formula

Patrycja

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May 9, 2018
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I don't know if this is right place, but I' ll try. In my master's thesis I want to compare VaR calculating using Black-Scholes formula and delta - gamma approximation. I wrote the simulation and have few problems.

Assume, the portfolio contains only 2 options: long call and long put. My histograms for an analytical calculations and the delta-gamma approximation overlaps when in D-G approximation I have

Theta*t + Delta *deltaS - 0.5 * (deltaS)2*Gamma

(in the definition there is "+"), otherwise the histogram produced by D-G is "truncate" on the right side. I fund properies for the long call and put, namely delta for a long call is positive, for a long put is negative, and gamma>0 for long option positions and this is Can anybody help me?

newplot (1).jpgnewplot.jpg
 
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