# Effective gamma/vega hedging

I want an options position where I can short some options to pocket the premiums and benefit from the time decay. I also want to be vega and gamma neutral.

Is there an established way to find which are the most efficient contracts to hedge your gamma and vega for lowest cost, whilst maintaining as much theta as possible?

• If you are short options then you will also be short gamma and vega. To hedge away your negative gamma/vega exposure you would have to buy options and give up the premium you collected. – roz Nov 18 '19 at 17:20
• @roz You short options with a low gamma/theta ratio, and buy options with high gamma/theta ratios, leaving you gamma neutral but theta positive. – Avram Nov 18 '19 at 23:45

I think you may be missing two other important greeks here: vanna and volga

Theta is not balanced by gamma only, it is balanced by vega, gamma, vanna, and volga.

So, when you ask is there an established way, by which I think you mean is there a way to more or less have a free lunch, the answer is no, not really.

You will need to take risks, i.e. leave some things unhedged because you have a view on the market, to earn (or lose) money. Going back to your question: no you can't earn theta and hedge gamma and vega, unless you were really meaning (but I don't think you were) to leave your vanna and volga unhedged - which boils down to having a view on correlation and the vol of vol.

EDIT:

I would recommend everyone interested in this topic to try to get a hold of the not publicly available paper by:

M. Arslan, G. Eid, J. El Khoury and J. Roth, "The Gamma-Vanna-Volga Cost Framework for Constructing Implied Volatility Curves", Deutsche Bank Working Paper

This is a very illuminating paper. The only thing they missed is the Vega contribution to theta (which arguably could be smaller than the other components).

• I think gamma and Volga clearly contribute to theta, since they represent convex exposure to movements in the underlying and the vol. I think vanna would contribute to Theta only if there is some correlation between underlying and vol. I believe Vega by itself should not contribute to theta. – dm63 Nov 19 '19 at 13:01
• @dm63 Yes vanna contributes to theta when there is correlation. I am assuming this is the case in general, even in FX there is some correlation. Regarding Vega: that is a tricky one. Like you I initially thought it shouldn't. But Vega is related to the drift of implied volatility. IV has a drift - it is not a martingale as it is not a tradable. So the drift part would be a bleed or gain of order $dt$ that is not balanced by anything, which is not possible, unless it is balanced by theta as well. – ilovevolatility Nov 19 '19 at 14:04
• that is interesting, thanks. – dm63 Nov 19 '19 at 23:56
• Thanks muchly for the reply :) I'm not missing vanna and volga, I'm just not interested in them for this specific problem. It's trivial to balance just gamma or vega by just doing a standard ratio write. It's just a little trickier trying to find the combinations of contracts to balance vega too. But it's certainly possible, even if I have to resort to brute forcing the different combinations. – Avram Nov 20 '19 at 10:55