Scaling and Aggregating Option Greek Exposures
Summary
The document explains why option risk should be assessed using position-level Greeks rather than the Greek quoted for one contract. It gives the example of a short call position and notes that contract multipliers and position size scale delta exposure. It then addresses whether gamma, vega, and theta can also be combined across positions.
The responses say that simple, consistently scaled Greeks are generally additive, while emphasizing that units must match: price moves for delta and gamma, volatility increments for vega, and time conventions for theta. Summing exposures across different underlyings can be misleading, especially for single-stock delta and gamma; cross-asset vega aggregation also depends on assumptions about volatility correlation. The discussion is conceptual and does not specify a universal scaling convention, so actual calculations must align each Greek's units and underlying assumptions.
Key ideas
- Position Greeks scale per-contract exposures by position size and contract multiplier.
- Simple Greeks can generally be added when their units and conventions are consistent.
- Delta and gamma exposures across different underlyings may not form a useful aggregate.
- Aggregating vega across assets requires assumptions about how their volatilities move together.
- Theta can be summed when measured using a consistent time convention.
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Full text
# Option greeks vs Position greeks # Option greeks vs Position greeks I know that when it comes to delta, you would calculate your position delta (of a stock position) as follows: ``` option delta * position size * 100 ``` For example if I am short 15 calls with a delta of 0.2, my position delta would be: ``` -0.2 * 15 * 100 = -300 ``` That figure of -300 shows how my position is impacted by directional movements in the underlying. That is why I don't just look at the 0.2 delta, I need to change it to my position delta. reference: http://www.optionsplaybook.com/managing-positions/position-delta/ My question is, do you do the same thing with vega, theta and gamma? I presume you do,...but I am new enough to options such that I need to ask. ## Answer by Todd Page (score 4, accepted) https://quant.stackexchange.com/a/24361 Both answers above are correct - you can simply add the greek exposures assuming you are using "simple" greeks like delta, gamma, vega, theta. However, two important points: - Make sure your underlying increments are the same (e.g. same 1pt vol move for vega calc, same price move for delta) - Be careful when adding greeks from different underlyings: Especially for delta and gamma, you can't add them from different stocks and expect good/usable results, especially if you are talking about single names. For Vega, you might be able to get away with a simplifying assumption that the underlying equity vol is correlated (depending on the names). For theta, you are fine summing everything since the underlying (time) is the same for all calculations. ## Answer by arodrisa (score 3) https://quant.stackexchange.com/a/24354 Depending on the Greek that you are calculating. You need to consider if they are additive or not, and how they take into account timing. In some cases you need to take into account that time is scaled or not, and so on.. Assuming Black-Scholes, and that they are correctly scaled, you can considere that Delta, Gamma, Theta, Vega and Rho are additive. ## Answer by HyperVol (score 2) https://quant.stackexchange.com/a/24339 Yes but only with delta and gamma and speed ( if you're using speed). for vega , it's scaled simply by vol points , i.e a factor of 100. for Theta , it's scaled by appropriate time period ( done by *sqrt(t) )
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