Subject:
 Learn what delta neutral is and the various how to achieve a delta neutral position.
 Delta Neutral Trading  Definition
 Delta Neutral Trading  In Layman Terms
 Delta Neutral Trading  In Layman Terms
 Delta Neutral Trading  Who Is It For?
 Basics of Delta Values & Delta Neutral Positions
 Delta Neutral Trading  Terms And Jargon
 Delta Neutral Trading
 Delta Neutral Trading  Option Only Example
 Delta Neutral Trading  Option + Stock Example
 Delta Neutral Trading  Purpose
 1. Delta Neutral Trading  To Make A Profit
 What is delta neutral options trade
 2. {/PARAGRAPH}
Delta Neutral Options Strategies
 Example of Delta Neutral Hedging For Stocks 
 Example of Delta Neutral Hedging For Options 
 Delta Neutral Hedging  Step By Step
 Delta Neutral Hedging : Step 1
 Delta Neutral Hedging : Step 2
 Delta Neutral Hedging : Step 3
 Profiting From PositionDelta Neutral Trading
 Delta Neutral Hedging  Short Or Long Options?
 Delta Neutral Trading  Considerations
 Delta Neutral Trading  Definition
 Delta Neutral Trading  Dynamic Delta Hedging (Dynamic Hedging)
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 Example of Dynamic Delta Hedging
 Delta Neutral Hedging
 Delta Neutral Trading  Mathematics
Learn what delta neutral is and the various how to achieve a delta neutral position.
Delta Neutral Trading  Definition
An option position which is relatively insensitive to small price movements of the underlying stock due to having near zero or zero delta value, hence "neutral" in terms of delta.
Delta Neutral Trading  In Layman Terms
Do you wish to know how to profit no matter if the market went up or down?
Or you simply wish to make no losses should the market went down?
Delta Neutral Trading is the answer!
Delta Neutral Trading  In Layman Terms
In layman terms, delta neutral trading is the construction of positions that do not react to small changes in the price of the underlying stock. No matter if the underlying stock goes up or down, the position maintains it's value and neither increases nor decreases in price. In options trading, this is also known as Delta Neutral Hedging or Delta Neutral Trading. In order to understand delta neutral trading, you must first learn what are Delta Value and other options greeks.
Delta Neutral Trading and Delta Neutral Hedging are excellent strategies made possible only by the use of options, and an indispensible tool in every professional options traders' arsenal.
Delta Neutral Trading  Who Is It For?
Delta Neutral Trading and Delta Neutral Hedging are for option traders who wants no directional risk nor bias.
Why would anyone want to put on a position that does not react to movements in the price of the underlying asset? That's the magic of options trading!
Because even if the options position isn't reacting to changes in the price of the underlying asset, it could still profit from other factors such as Time Decay and changes in Implied Volatility! Furthermore, Delta neutral hedging not only removes small directional risks but is also capable of making a profit on an explosive upside or downside breakout if the position's gamma value is kept positive.
As such, delta neutral hedging is also great for profiting from uncertain, volatile, stocks that are expected to make huge breakouts in either direction.
Basics of Delta Values & Delta Neutral Positions
Delta Neutral Trading  Terms And Jargon
An options contract with 0.5 delta value is referred to as having "50 deltas" (each contract represents 100 stocks, so 0.5 x 100 = 50).
100 shares is referred to as having "100 deltas" as each share has a delta value of 1.
There are 2 forms of delta neutral hedging, known as Static Delta Hedging and Dynamic Delta Hedging. Static Delta Hedging means setting a position to zero delta and then leave it to unwind on its own. Dynamic Delta Hedging is to continuously reset the delta of a position to zero as the price of the underlying stock unfolds.
Delta Neutral Trading  Option Only Example
An At The Money (ATM) call option theoretically (actual values may differ slightly) has a delta value of 0.5 and an ATM put option also should have a delta value of 0.5.
Buying both the call option and put option results in a delta neutral position with 0 delta value. Conversely, shorting (Sell To Open) a call option generates 0.5 delta while shorting a put option generates +0.5 delta.
0.5 (call option)  0.5 (put option) = 0 Delta
Buying both the call option and put option at the same at the money strike price is a popular delta neutral option trading strategy, called a Long Straddle, profiting when the underlying stock moves up or down significantly.
Delta Neutral Trading  Option + Stock Example
A share has a delta value of 1 as it's value rises by $1 for every $1 rise in the stock. If you own 100 shares of a stock, you can make a delta neutral position by buying 2 contracts of it's at the money put options with delta value of 50 per contract.
100 (delta value of 100 shares)  100 (2 x 50) = 0 Delta
Any small drop in the price of the shares will be instantly offset by a rise in the value of the put options so that the value of the overall position do not change.
Conversely, any small rise in the price of the shares will also be offset by a drop in the value of the put options so the value of the overall position do not change in either direction. This is an extremely popular option trading technique used by option traders who own shares and wishes to protect the value of that position when the stock reaches a strong resistance level.
This is a good option trading technique for option traders who holds shares for the long term to hedge against drops along the way. 
Delta Neutral Trading  Purpose
There are 2 purposes for going delta neutral on a position and are favorite option trading techniques of veteran or institutional option traders. I call them Delta Neutral Trading and Delta Neutral Hedging.
1. Delta Neutral Trading  To Make A Profit
Delta Neutral Trading is capable of making a profit without taking any directional risk. This means that a delta neutral trading position can profit when the underlying stock stays stagnant or when the underlying stock rallies or ditches strongly.
This is fulfilled in 4 ways :
1. By the bid ask spread of the option. This is a technique only market makers can execute, which is simply buying at the bid price and simultaneously selling at the ask price, creating a net delta zero transaction and profiting from the bid/ask spread with no directional risk at all.
This is also known as "Scalping". (Some may argue that this is not truly delta neutral trading but I am just going to include it for completeness sake.)
2. By time decay. When a position is delta neutral, having 0 delta value, it is not affected by small movements made by the underlying stock, but it is still affected by time decay as the premium value of the options involved continue to decay.
An options trading position can be set up to take advantage of this time decay safely without taking significant directional risk and one such example is the Short Straddle options strategy which profits if the underlying stock remains stagnant or moves up and down insignificantly.
3. By Volatility.
What is delta neutral options trade
By executing a delta neutral position, one can profit from a change in volatility without taking significant directional risk. This options trading strategy is extremely useful when implied volatility is expected to change drastically soon.
4. By creating volatile option trading strategies. Even though delta neutral positions are not affected by small changes in the underlying stock, it can still profit from large, significant moves.
One example of such an options trading strategy is the famous Long Straddle which we mentioned above.
This is because a typical delta neutral position is still Gamma positive, which increases position delta in the direction of the move, allowing the position to gradually profit in either direction.
2.
Delta Neutral Options Strategies
Delta Neutral Hedging  For Protection
Delta Neutral Hedging is an options trading technique used to protect a position from short term price swings. This is particularly useful for long term stocks or LEAPs option buy and hold strategy.
The advantage of using delta neutral hedging is that it not only protects your position from small price changes during times of uncertainty such as near resistance or support levels, but it also enables your position to continue to profit from that point onwards if the stock rises or falls strongly.
Example of Delta Neutral Hedging For Stocks 
John owned and held 1000 shares of Microsoft for $27 per share on 14 March 2007.
On 14 May, when Microsoft was trading at $31, John determined that a resistance level has been reached and wanted to perform a delta neutral hedge against a short term price change while being able to profit should MSFT rally or ditch strongly from this point. John bought 20 contracts of July31put to execute the delta neutral hedge.
1000 (delta of 1000 shares)  1000 (delta of 20 contracts of at the money put options) = 0 delta
If MSFT rallies strongly from this point onwards, the put options simply expire worthless while the stocks continue to gain in value, allowing the position to continue profiting after the cost of the put options has been offset by the rise in the stock price.
If MSFT ditches from this point onwards, the put options will eventually gain in price faster than the stocks as 20 contracts represents 2000 stocks of MSFT and its delta will gradually become higher due to the positive gamma, eventually generating a higher negative delta than the stock's positive delta, allowing the position to profit as long as MSFT continues to fall.
A delta neutral hedging for stocks actually creates a Synthetic Straddle options trading position.
Example of Delta Neutral Hedging For Options 
John owned and held 10 contracts of Microsoft's March 2008 LEAPs call option at the strike price of $20 on 14 March 2007 when MSFT was trading at $27. On 14 May, when Microsoft was trading at $31, John determined that a resistance level has been reached and wanted to perform a delta neutral hedge against a short term price change while being able to profit should MSFT rally or ditch strongly from this point.
Assuming the LEAPs call options has a delta value of 0.8, John bought 16 contracts of July31put to execute the delta neutral hedge.
800 (delta value of LEAPs options)  800 (delta value of 16 contracts of at the money put options) = 0 delta
If MSFT rallies strongly from this point onwards, the put options simply expire worthless while the LEAPs options continue to gain in value, allowing the position to continue profiting after the cost of the put options has been offset by the rise in the LEAPs options.
If MSFT ditches from this point onwards, the 16 put options will eventually gain in price faster than the 10 LEAPs call options, allowing the position to profit as long as MSFT continues to fall.
Delta Neutral Hedging effectively "Locks In" the profits on your long term position right at the point the delta neutral hedge is put in place while allowing you to continue holding your favorite stock or LEAPs. Without delta neutral hedging, the only way you can seal in profits would be through selling the position, which isn't something you always want to do. Options positions attain delta neutral through hedging based on a hedge ratio of 1.
Delta Neutral Hedging  Step By Step
Delta Neutral Hedging : Step 1
 Determine the total delta value of your current position. If you are holding 100 shares, then you are long 100 deltas. If you are holding options, then you need to determine the total delta of your options by multiplying the delta value of each option by the number of options.

Delta Neutral Hedging : Step 2
 Determine the kind of delta neutral hedge needed.
If your position is long deltas, then you will need negative deltas as hedge and if your position is negative deltas, then you will need positive deltas as hedge.
Long call options / Short Put options = Positive deltas
Short call options / long put options = Negative deltas
If your position is long 100 deltas, you will need to produce short 100 deltas in order to result in zero delta.
You can do that through selling call options or buying put options. 
Delta Neutral Hedging : Step 3
 Determine the total delta value needed to hedge.
After determining what kind of hedge your position needs, you should now work out how many of those hedges you need by the following formula : (Total Delta Now / 100) / Delta Value Of Chosen Hedge Options
Delta Neutral Hedging  Short Or Long Options?
As you have learnt from above, both short call options and long put options produce negative deltas, so what is the difference between the two in a delta neutral position?
Short call options puts time decay in your favor and results in additional profits should the underlying stock remain stagnant but it's drawback is that the downside protection it offers is limited to the price of the short call options.
If the underlying stock falls more than the cost of the short call options, your position will start to make a loss. Long put options offers unlimited downside protection and eventually allows the position to profit should the underlying stock drop significantly but the drawback is time decay, and can result in a small loss due to the erosion of premium value should the underlying stock remain stagnant.
Delta Neutral Trading  Considerations
As we all know, the delta value of stock options changes all the time.
Delta Neutral Trading  Definition
Any change in the delta values will affect the delta neutral status of a delta neutral position. The rate of change of delta value to a change in the underlying stock is governed by the GAMMA value.
Gamma value increases the delta of call options as the underlying stock rises and increases the delta of put options as the underlying stock falls.
It is exactly this gamma effect that allows a delta neutral position to make a profit no matter if the underlying stock moves up or down strongly. A position can be made to be totally stagnant no matter how strongly the stock moves if the position is hedged Delta and Gamma neutral.
Days left to expiration also affects the delta value of out of the money options. The nearer to expiration, the lower the delta of out of the money options becomes.
Delta Neutral Trading  Dynamic Delta Hedging (Dynamic Hedging)
Delta value in option trading changes all the time due to Gamma value, moving a delta neutral trading position slowly out of its delta neutral state and into a directional biased state. Even though this behavior allows delta neutral trading positions to profit in all directions, in a delta neutral position that is created in order to take advantage of volatility or time decay without any directional risk, the delta neutral state needs to be continuously maintained and "resetted".
This continuous resetting of an option trading position's delta value to zero is Dynamic Delta Hedging or simply, Dynamic Hedging.
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Example of Dynamic Delta Hedging
John wishes to profit from the premium value of XYZ company's Feb $50 Call options. He summons all his option trading knowledge and decides to perform a delta neutral hedging to eliminate directional risk while selling the Feb $50 Call options in order to reap it's premium value as profit.
XYZ stocks is $50 now. It's Feb $50 Call options is $2.50 ,delta value 0.5, gamma value 0.087 and theta value 0.077.
:: Here is John's initial delta neutral position :
Long 100 XYZ shares + Short 2 contracts of Feb50Call.
(100 deltas) + ( 0.5 x 200) = 100  100 = 0 delta
John's delta neutral trading position is delta neutral upon execution and will decay at a rate of $15.40 (0.077 x 200) per day, all else being constant and will eventually make the whole premium value of $500 ($2.50 x 200) as profit.
:: 5 days later, XYZ stock rose by $1 to $51.
XYZ stocks is $51. Feb $50 Call Options is $3.00, delta value 0.587, gamma value 0.083 and theta value 0.075.
The Feb $50 Call option's delta value rose 0.087 due to the gamma value of 0.087 when the position was established.
Delta Neutral Hedging
John's position becomes :
(100 deltas) + (0.587 x 200) = 100  117.4 = 17.4 deltas
This means that from now on, John's position is no longer delta neutral and will lose $17.40 for every $1 rise in the underlying stock.
:: John performs Dynamic Delta Hedging or Dynamic hedging.
John buys an additional 17 shares of XYZ stocks through his option tradng broker.
His position now becomes:
Long 117 XYZ shares + Short 2 contracts of Feb50Call.
(117 deltas) + (0.587 x 200) = 117  117.4 = 0.4 deltas
Position now is only short 0.4 deltas, which is effectively delta neutral. This is dynamic delta hedging.
As you can see from the above dynamic delta hedging example, such procedure is tedious and requires constant effort and monitoring.
This is why dynamic delta hedging is an option trading technique mostly performed by professional option traders such as market makers. Again, in order to protect the position from wild swings in the underlying stock in between the dynamic rebalancing of the delta neutral position, the position can also be constructed to be gamma neutral as well.
Read about how Gamma Neutral Hedging is done.
Delta Neutral Trading  Mathematics
Delta Neutral Portfolio = n_{1}D_{1} + n_{2}D_{2} = 0
Where D_{1} = Delta value of the original options.
D_{2} = Delta value of hedging options. n_{1} = Amount of original options. n_{2} = Amount of hedging options.