# 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.

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.

• Yes, absolutely. And you need to add them up over all options in your portfolio that have the same underlying. – noob2 Nov 20 '15 at 13:39
• Ok that's what I thought, just wanted to make sure. Thanks. – darkpool Nov 20 '15 at 13:42
• for the gamma it might be better to look at gamma*S^2 instead. See "dollar gamma". – mbison Nov 28 '15 at 11:44

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:

1. Make sure your underlying increments are the same (e.g. same 1pt vol move for vega calc, same price move for delta)
2. 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.

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.

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) )