How to quickly sketch a second order greek profile for a vanilla position?

Question

Assume that you are given an arbitrary payoff profile for European vanilla position (e.g. butterfly). How to make a back of the envelope sketch of a second order greek profile for it (i.e. plot showing dependency of a greek w.r.t. to spot or vol)? I'm interested in major second order greeks like Dvega/Dvol, Dgamma/Dspot, Dgamma/Dvol, Dvega/Dspot. The sketch should at least correctly show signs and relative value (i.e. highs/lows) of the greek.

Answer 1

• Use a pen, paper, lower the pen to touch the paper, and start sketching your intuition. ;-)

• If that sounds too simplistic then you could shift spot or implied vols by a percentage or point value and recalculate the shift impact either on spot or otherwise apply the shift to the closed form solution of those greeks you attempt to evaluate. As you evaluate a basic option and its greeks this should be a fairly easy exercise.

Answer 2

If your "European vanilla options" are restricted to piece-wise linear pay-offs, then the following may help:

Remark: I assume you are looking for a rule of thumb to get the profiles without the use of a computer.

All piece-wise linear pay-offs can be decomposed into a sum of digital options and call options with different notional (possibly negative) and strike. Thus you may learn the greek profile of these two by heart and then geometrically add the profiles according to the decomposition of your vanilla option.