Gamma Neutral Hedging is the construction of options trading positions that are hedged such that the total gamma value of the position is zero or near zero, resulting in
the delta value of the positions remaining stagnant no matter how strongly the underlying stock moves.

Gamma Neutral Hedging - Introduction

The problem with
delta neutral hedging is that even though it prevents the position from reacting to small changes in the underlying stock,
it is still prone to sudden big moves which can take option traders off guard with no time to dynamically rebalance the position at all.
This is where Gamma Neutral hedging comes in. By hedging an options trading position to Gamma Neutral, the position's delta value is completely
frozen and when used in conjunction with a delta neutral position, the position's delta value stays at 0 no matter how widely the underlying
stock moves, thereby keeping the value of the position completely stagnant. Such a position is known as a Delta Neutral Gamma Neutral
Position.

Purpose Of Gamma Neutral Hedging

As explained above, the main purpose of Gamma Neutral Hedging is to keep the
delta value of a position completely stagnant no matter how the
underlying stock moves. This has 3 purposes; 1. To reduce the
volatility of an
options trading position by
keeping delta low and stagnant so that
the value of the position neither surges nor ditches strongly with the underlying stock. 2. To make a profit from speculating in
implied volatility,
which is represented by
Options Vega. 3. To seal in profits made so far during volatile times.

Reduction Of Position Volatility

Gamma is another way of representing the amount of volatility of an options trading position. Big Gamma values lead to big changes in delta
value, resulting in exponential gains or losses. By going Gamma Neutral, position delta is fixed no matter how much the underlying stock moves,
producing a highly predictable and calculable income based on the delta value. This is known as a Delta Positive, Gamma Neutral Position.

Delta Positive, Gamma Neutral Example:

I want to keep delta value at about 0.6 so that I make $0.60 out of every $1 rise in MSFT without any surprises.
MSFT's trading at $28.60 and its May27.5Calls have 0.779 delta and 0.18 gamma while its Oct27.5Calls have 0.697 delta and 0.085 gamma. I
would short 1 contract of May27.5Calls for every 2 Contracts of Oct27.5Calls.

Position Delta = (0.697 x 2) - (0.779) = 0.615

Position Gamma = (0.085 x 2) - (0.18) = -0.01 (which is very near to complete zero and can be regarded as gamma neutral)

Many veteran options traders may argue that there is completely no sense in establishing a delta positive gamma neutral position since
taking a normal delta positive, gamma positive position would reduce the delta as the stock goes down, reducing losses and extends
delta as the stock goes up, increasing wins exponentially. Well, this is actually useful for options traders taking
LEAPS positions
on their favorite stocks for the long term and yet want to reduce potential damage during volatile times.

Trading Implied Volatility

Why are Delta Neutral, Gamma Neutral positions perfect for trading volatility? That's simply because the only significant options greek that remains unhedged in
a delta neutral, gamma neutral position is the Vega! Gamma moves in line with
theta, as such if total portfolio gamma is at or near zero, so will
the position's theta value. A Completely Gamma neutral position would also have completely zero theta, making it impossible to make money through
time decay. A delta neutral, gamma neutral position would be long Vega, creating a position which will not be affected by any kind of moves in the
underlying stock while increasing in value should implied volatility rises!

Delta Neutral, Gamma Neutral Example:

MSFT's trading at $28.60 and its May27.5Calls have 0.779 delta, 0.024 Vega and 0.18 gamma while its Oct27.5Calls have 0.697 delta, 0.071 Vega and 0.085 gamma. I will go delta neutral and gamma neutral while keeping vega positive by buying 5 sets of the original delta positive and gamma neutral
position mentioned above and then hedging it by shorting 3 shares of MSFT.

Position Delta = ([(0.697 x 2) - (0.779)] x 5) - 3 = 0.075 (which is very near zero and can be regarded as delta neutral)

Position Gamma = ([(0.085 x 2) - (0.18)] x 5) = -0.05 (which is very near to complete zero and can be regarded as gamma neutral)

Position Vega = ([(0.071 x 2) - (0.024)] x 5) = 0.59

Sealing In Profits

If a period of high volatility is to be expected and your options trading position has made a good profit so far, instead of sealing in the profits by
selling the position, thus reaping no further rewards, you could actually perform a delta neutral gamma neutral hedge to completely seal in the
profits! A delta neutral gamma neutral position is not moved either by moves in the underlying stock nor
time decay! Yes! Gamma neutral positions
are also automatically theta neutral! However, when implied volatility rises as the period of high volatility approaches, be it nearing
earnings release or FOMC meetings, the position stands to gain in value due to rising volatility!

How To Establish Gamma Neutral Position?

There are various ways to establish Gamma Neutral positions and it is up to your creativity and options trading objectives. As long as you
understand what kind of options produces what kind of gamma, it is up to your creativity to put offsetting options together like we did with
the examples above. A comprehensive understanding of Options Gamma is definitely needed in this case. Here is a quick reference table:

Type

Delta value

Gamma Value

Long Call Option

Positive Delta

Positive Gamma

Short Call Option

Negative Delta

Negative Gamma

Long Put Option

Negative Delta

Positive Gamma

Short Put Option

Positive Delta

Negative Gamma

Being long or short the underlying stock does not affect Gamma at all because stocks do not produce gamma.

How To Establish Delta Neutral Gamma Neutral Position

There are 2 steps involved in establishing a Delta and Gamma neutral options trading position.

Step 1: Get Gamma Neutral

It is always easier and neater to get the position into Gamma Neutral first by buying or selling an offsetting option of the same
underlying stock with either a further or nearer expiration date.

Delta Neutral, Gamma Neutral Step 1 Example:

MSFT's trading at $28.60 and its May27.5Calls have 0.779 delta, 0.024 Vega and 0.18 gamma while its Oct27.5Calls have 0.697 delta, 0.071 Vega and 0.085 gamma. I am now holding 10 MSFT's Oct27.5Calls and will first make it Gamma Neutral by selling 5 May27.5Calls.

Position Gamma = ((0.085 x 10) - (0.18) x 5) = -0.05 (which is very near to complete zero and can be regarded as gamma neutral)

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