# How to Hedge delta and gamma of a put option simultaneously?

Say you took a short put position of 100 options (as you feel the option is undervalued). This put has a Delta of -0.5, so to make the portfolio delta-neutral you short 50 shares of the underlying asset correct? Now let's say the put has a gamma of -0.59, how would you make the portfolio gamma-neutral aswell as delta neutral, and vice versa if you were to add another greek (i.e. vega)?

• 1 option contract is for 100 shares so if you are short 100 options with a delta of -.50, you'd have to short 5,000 shares to be delta neutral. May 12, 2019 at 11:05
• Yes correct, my fault. How would you make it gamma neutral concurrently? May 13, 2019 at 7:43
• Nick aa in theory you can, these greek letters represent mathematical derivative and is additive. Therefore you can just write out a linear combination of a few different option contracts and solve the coefficients in front of each term to make every greek you care about =0, it will not be 0 permanently but only at the specific time. The question is, why do you want to do that?
– user67084
May 26, 2019 at 5:40

The easiest way to do it is to first neutralize your gamma with another option, then neutralize your delta with the underlying.

For example, consider the following options chain: https://i.stack.imgur.com/55J5a.jpg (sorry, StackExchange for some reason isn't allowing me to add the image here directly – feel free to edit and fix it).

That's SPY for June 21st, 2019.

For example, you could sell 100 contracts of the Put 281, which would give you a gamma of -350. Then you can buy 90 contracts of the Call 285, which gives you a gamma of +351. Your net gamma is +1, which is neutral enough.

Now, this will not leave with delta neutral: you'll have +4540 delta from the short puts, plus +4014 delta from the long calls. Your net delta is 8554, which is far from neutral.

You then go ahead and sell 8554 shares of SPY, and you're done. You have neutralized gamma and delta.

Now, you'll be exposed to a few other things:

• you'll have slightly negative theta (-5)
• you'll have negative vega (-310)

You could reverse all of this, e.g., buy the put, sell the call, buy the shares, and that would lead to opposite signs on theta and vega.

If you want to neutralize other greeks, it's also possible, just add a 3rd option contract and then solve some equations.

But keep in mind that the greeks aren't static, so your position will soon not be gamma- and delta-neutral anymore. Any larger movements will completely trash this balance.

Stay in cash so all greeks are Zero.

Gamma indicates how much the delta of the option will change as the price of the underlying moves.

You could reduce the gamma of your position by buying or selling another option with similar gamma. That option would also likely have delta as well, so would need additional delta hedging.

Alternatively, you could just continue to delta hedge as the delta changes. If that is cheaper than buying or selling your gamma position, then that might make more sense.

You could also hedge vega using the same kind of method - if vega is too high, sell some options with vega, and adjust for the change in delta by buying or selling stock. However the cost of hedging may eliminate any profits you may have made from your initial position.