YouTube T4-04: Delta-gamma value at risk (VaR) with the Taylor Series Approximation

[Nicole Seaman]

The Taylor Series lets us approximate a smooth function with a polynomial. Here we apply it to both an option position (where the second term captures gamma) and a bond position (where the second term captures convexity)

David's XLS is here: https://trtl.bz/2rlVj7H

 

[anind1]

In the you tube video, Delta normal value at risk the VAR of a long call option for single risk factor of underlying stock price change has been calculated assuming delta to be constant. That means gamma has been assumed to be zero. Does this method have any practical use as in real life gamma of an option is never zero and delta is never constant? The above video of delta-gamma VAR obviously gives more accurate result. Moreover, if we calculate 95 pc VAR of a short call option then we lose if underlying share price increases, so we need Z score of the right hand side of the curve. As stock price follows log normal distribution , so do we consider Z-score of 1.95 for VAR calculation at 95 pc in such case?