Sketching Option Greek Profiles from Calls and Digital Options
Summary
The question asks how to sketch second-order Greek profiles for a European vanilla payoff, such as a butterfly, without computing a full profile. It is concerned with how Greeks vary as spot or volatility changes, including vanna, vomma, and the changes in gamma with spot or volatility.
One proposed rule of thumb applies when the payoff is piecewise linear: decompose it into calls and digital options at different strikes, allowing for positive or negative notionals, then combine the known Greek profiles geometrically. Another reply suggests shifting spot or implied volatility and recalculating the Greeks, or applying those shifts to their closed-form formulas. The advice is qualitative and does not provide worked profiles or sign rules; its usefulness depends on familiarity with the component options and careful recalculation.
Key ideas
- A piecewise linear European payoff can be represented as a sum of calls and digital options at different strikes.
- The component options' Greek profiles can be combined to estimate the profile of the full position.
- Positive and negative notionals in the decomposition determine whether component profiles add or subtract.
- Spot and implied volatility shifts followed by Greek recalculation offer another way to inspect profile changes.
Tags
Full text
# How to quickly sketch a second order greek profile for a vanilla position? # How to quickly sketch a second order greek profile for a vanilla position? 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 by Christian Fries (score 4) https://quant.stackexchange.com/a/7106 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. ## Answer by Matt Wolf (score 2) https://quant.stackexchange.com/a/7105 - 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.
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