Using Option Greeks to Hedge Delta, Gamma, and Vega

# Hedging, Delta, Gamma, Vega


# Hedging, Delta, Gamma, Vega












I sometimes find it difficult to see, how to hedge a portfolio.

Let say, that I created a product consisting of an Asian call (strike 1), Vanilla call (strike 2), and an Asian Put (strike 1) on a stock called ABC. Now let say the the delta of the total product is 60%, Gamma is 1,5% and Vega is 1,5.

Now If I SHORT this "product", then I can delta-hedge the portfolio by going LONG in the underlying (Stock ABC) by 0,70 for one product I sell. I think this is correct?

But what about the gamma and the vega?

So I can gamma-hedge as well, but here I cannot just by/sell the underlying. I need an option on the underlying? ANd this option need to have a gamma of 1,5, but do I need to buy or sell the option??

And waht about Vega?

I hope you guys can help me! Thanks,

## Answer by wchyk-cyw (score 2, accepted)

https://quant.stackexchange.com/a/29781

Greeks are essentially the a set of results under certain scenario analysis and they are 'local' to the market condition you use to price the options in the first place, local meaning the changes of certain market parameters are not huge, 1 percent spot move, 1 vol point move etc. Usually the lower order greeks are easier to hedge, such as Delta. However, the higher order ones are less so, such as vanna and volgamma. If you want to neutralise your gamma, sure buy/sell some short dated options, vega maybe slightly longer dated options. But you will find as the spot and the vol surface change in live market your greeks will change too and you will have to re-hedge again.

In the end, you need to ask yourself the purpose of carrying your position, are you a market maker who just wants to earn bid/ask spread and carry fairly risk neutral book or you are a buy-side client where you do want to buy and hold certain positions and be exposed to certain risks where you think the opportunities are.

Hope you find this useful, as I think a conceptual understanding of the purpose of hedging is a prerequisite to an answer with numbers. If you don't like your risk due to a certain option, liquidate that option, don't put on more options to bandaid it and further complicate your book with more strikes and expiries.

## Answer by nbbo2 (score 0)

https://quant.stackexchange.com/a/29779

Greeks have a sign as well as a magnitude. You hedge by taking on the opposite of what you have (hedge positive delta with negative delta, and so on).

Long put and long call have positive gamma, shorting either of them gives negative gamma. Long put and long call have positive Vega. Finally long call has positive delta, long put has negative delta and long underlying has positive (1.0) delta.

Now to answer your question directly: if your portfolio has a Gamma of -1.5 (if I understood your example correctly you have shorted something with Gamma +1.5), so that's a negative number, to hedge you must take onboard some positive Gamma. You can do it by being long a put or long a call.