Aggregating Greeks Across Multi-Leg Derivative Strategies

Summary

The document addresses whether a multi-leg options position can have a net delta or other Greeks. When the derivatives share a common underlying, their deltas and most other Greeks can be added to estimate the position’s combined sensitivity. For a call spread, for example, the net delta is the sum of the deltas of its legs, with position signs accounted for.

The answer warns that aggregation can hide important information when legs reference different underlyings. A single total may obscure the distinct risks across assets, and some quantities, such as moneyness, are not meaningfully summed as Greeks are. Even so, broad totals are used in practical risk reporting, including summaries of interest-rate exposure across currencies and maturities or exchange-rate exposure across currencies. The note gives a concise rule of thumb rather than a calculation procedure or treatment of nonlinear interactions, scenario risk, or differences in how sensitivities are defined across products.

Key ideas

• A strategy’s Greek exposure can be calculated by summing the Greeks of its derivative legs on a shared underlying.
• Use position signs when combining long and short legs.
• Aggregating risks across different underlyings may conceal material details.
• Not every measure is additive; moneyness is given as an example of a quantity that cannot be netted like a Greek.
• Portfolio risk reports may still present broad aggregated rate or currency sensitivities.

Tags

# How are the greeks defined for the two legs or more strategies with regards to options?


# How are the greeks defined for the two legs or more strategies with regards to options?












I am to figure out something, and can't find any reference. I wonder: does it make sense to talk of a delta or other greek of a strategy? It seems that you can't put a price exactly on a call spread for example, so would that mean that delta metrics for a call spread would be simply the deltas for each option of the call spread?

## Answer by Dimitri Vulis (score 5, accepted)

https://quant.stackexchange.com/a/64339

If you have two or more options (or other derivatives) with the same common underlying, then you can add their deltas and most other greeks (but not e.g. moneyness). But if the legs have different underlyings, then netting their risks may lose important details.

Having said that, risk reports showing total interest rate delta across all currencies and tenors, or exchange rate delta across all currencies are quite common in practice.

Related question: Aggregate Greeks calculations

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