Taylor series approximation - why does it overstate a long call/put option VaR?

[Mezzala95]

As the title says, could somebody please explain why the Taylor series approximation overstates a long call/put option VaR and vice versa for the short option position?

I'm revising through the chapters and realised I forgot how this is meant to work!



Thanks all!

 

[Lu Shu Kai FRM]

Hi @Mezzala95 ,

David's post i.e. https://www.bionicturtle.com/a-note-about-delta-gamma-value-at-risk-var-as-taylor-series/ explains it really well. If I recall, it is actually the opposite? Long call/put lowers VaR vice versa for the short option position.

 

[Mezzala95]

Hi @Mezzala95 ,

David's post i.e. https://www.bionicturtle.com/a-note-about-delta-gamma-value-at-risk-var-as-taylor-series/ explains it really well. If I recall, it is actually the opposite? Long call/put lowers VaR vice versa for the short option position.

@lushukai thank you for helping me to recall this!

After reading your comment and link, I remembered that I had actually saved (to a word doc) an old post of yours on this exact concept!

You provided the below bullet points and I had used that to learn the first time around. Absolutely kicking myself for forgetting these concepts, thanks again!

 

[sugnjin]

However, since VaR is calculated by multiplying the second moment by the z value, doesn't the effect of positive or negative numbers in other terms disappear?

ex ) var(ds-ds^2) = var(dS) + var(dS^2) (since, cov(dS,dS^2) = 0)