When Portfolio Greeks Add Across Option Positions

Summary

The note asks whether portfolio gamma and vega, like delta, can be calculated by summing the Greeks of each position. The answer says that in linear valuation models, prices and their Greeks add across positions. It specifically identifies Black–Scholes as a setting where this additivity holds.

The answer also limits the rule: value adjustments can introduce nonlinearities, making portfolio aggregation more complicated. The document does not explain particular adjustments, quantify their effects, or distinguish model risk from position-level aggregation. The practical lesson is to sum position Greeks under a consistent linear pricing setup, then account separately for nonlinear valuation effects when the model includes them.

Key ideas

• Under linear valuation models, portfolio prices and Greeks aggregate by summing position values and sensitivities.
• Black–Scholes is given as an example where this additivity applies.
• The same summation principle applies to gamma and vega as well as delta in that setting.
• Value adjustments can introduce nonlinear effects that complicate portfolio Greek aggregation.

Tags

# Can I add the greeks of individual postions to obtain greeks for the portfolio


# Can I add the greeks of individual postions to obtain greeks for the portfolio












I understand that the delta of an option portfolio is just the sum of the deltas of the individual option positions.

What about the other Greeks like gamma and vega? Do the vega and gamma of a portfolio also equal the sum of the individual vegas and gammas of the option positions?

## Answer by Mark Joshi (score 6, accepted)

https://quant.stackexchange.com/a/16543

most models in financial maths are linear so prices and Greeks just add. This is in particular true of Black--Scholes so Yes.

However, once one starts taking into account value adjustments non-linearities appear and it is a lot more complicated.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.