Options "Greeks" are sensitivities of the option to various exposures of risk including time decay and volatility. The names are taken from the actual Greek names.
Greek

Sensitivity to

Delta

Δ

Change in option price relative to change in underlying asset price (ie Speed)

Gamma

Γ

Change in option Delta relative to change in underlying asset price (ie Acceleration)

Theta

Θ

Change in option price relative to change in time left to expiration (ie Time Decay)

Vega

Κ

Change in option price relative to the change in the asset's volatility (ie Historical Volatility)

Rho

Ρ

Change in option price relative to changes in the Risk Free Interest Rate (ie Interest Rates)

Zeta

Ζ

Percent change in option price per 1% change in implied volatility (ie Implied Volatility)

The Basics

The option delta is the rate of change of the option price compared with the rate of change of the underlying asset price.
In other words delta measures the speed of the option position compared with that of the underlying asset.
Delta =
 rate of change in Option price rate of change in underlying asset price 

When the asset price is At the Money (ATM) the delta value will be around 0.5 (as a general rule). This means that for every $1 the stock moves, the option will move at a speed of
around half of that. Obviously as the asset price deviates away from the ATM point, then the delta will change too, away from 0.5.
ATM = +/ 50 deltas, ie moves at half the speed of the underlying asset
Remember that 1 share has a delta of +/ 1, and 1 option contract represents 100 shares, therefore 1 ATM option will have a delta of +/ 50.
You can think of delta as being the probability of the option expiring In the Money. So a delta of +/ 50 is saying the option has a 50/50 chance of expiring In the Money.
Example
If you buy 100 shares of AMZN (+100 deltas), you would need to buy 2 ATM Puts (50 deltas each) for a Delta Neutral Position.
Remember that Delta means speed. The greater the leverage of your position,
the greater potential exposure to speed. For example, if you buy a call option, the underlying
stock may increase by 10% whilst your call option may increase by 100%. This leverage is great
when it's in your favour, but not so good when it's against you. Taking the same example, if you
buy a call and the underlying stock decreases by 10%, your call options may decrease in value by near
100%. This risk needs to be hedged. The term "hedge" is associated with the process of
reducing risk.
Delta Neutral Trading is a vast topic in itself, which will be covered in Special Article sessions within this site. It is a method of trading whereby your
position delta on the totality of your spread trade is one where the sum of the deltas equals zero. The idea is that this conveys a "hedged" position, whereby the risk is reduced.
Delta Neutral Traders do this on the basis that they can continually make profitable adjustments to their trade as the asset price fluctuates. The adjustments (usually selling part of
the profitable side) bring the spread trade back to a delta neutral position (ie where the sum of the deltas for that position equals zero), whilst also capitalising on profitable side of the
trade.
A popular technique is to make the profitable adjustments back to delta neutral when the underlying asset has moved by 20% in either direction.
Remember that Delta Neutral does NOT mean risk free! Deltas are NOT linear.

Delta Neutral still requires you to manage the Time Decay.

Longer term options will generally have lower deltas to shorter term options.

Your position Delta on your trade is also known as your "Hedge Ratio".

Delta is principally affected by Time left to expiration and Price of the underlying asset.

Some futures Delta neutral trades can require no margin sometimes (and with certain brokers)

With calls, Delta increases as the underlying asset price increases. Call deltas are always positive. Note that when you sell a call (naked) your position is delta negative.

With puts, Delta decreases as the underlying asset price decreases. Put deltas are always negative. Note that when you sell a put (naked) your position is delta positive.
TRADE (US stock options)

DELTA (+ or )

COMMENT

Buy 1 share

+1

Buying a share has a delta of +1

Sell 1 share

1

selling a share has a delta of 1

Buy ATM call

+50

Why +50? Because 1 stock option contract represents 100 shares. So 100 * 0.5 = +50

Buy Call

+

A long call always has a positive delta

Sell ATM call

50

Why 50? Because 1 stock option contract represents 100 shares. So 100 * 0.5 = 50

Sell Call



A short call always has a negative delta

Buy ATM put

50

Why 50? Because 1 stock option contract represents 100 shares. So 100 * 0.5 = 50

Sell ATM put

+50

Why +50? Because 1 stock option contract represents 100 shares. So 100 * 0.5 = +50

Buy Put



A long put always has a negative delta

Sell Put

+

A short put always has a positive delta

ATM Straddle

0

The long call delta and long put delta effectively cancel each other out

ATM Strangle

0

The long call delta and long put delta effectively cancel each other out

Bull spreads

+

With a Bull Call Spread, the long call has a higher delta than the short call. With a Bull Put Spread, the short put has a higher negative delta than the long put, but remember that because you're selling it, 2 minuses make a plus.

Bear spreads



With a Bear Call Spread, the short call has a higher delta than the long call, but the delta is negative because you're selling it. With a Bear Put Spread, the long put has a higher negative delta than the short put.

Example: (Bull Call spread)
XYZ = $100
Buy 10 Jan 100c

Delta =

+500


Sell 10 Jan 105c

Delta =

470

(say)


Hedge Ratio =

+30


Example

You buy 100 shares of a stock. Each $1.00 your stock rises,
you make $100 * $1.00 = $100. Each $1.00 your stock falls, you lose $100.

Alternatively, by buying call options you could make $300 when your stock rises by $1.00?
However, you
can also lose $300 for every dollar the stock falls?
This is the concept of leverage.
If the stock falls from $50 to $45:

Your shares will decrease by $5.00 per share and you'll lose $500, a loss of 10%. Out of the
$5,000 you started with, you now have $4,500.

Your options will decrease by $5.00 and you'll lose $500, a loss of over 70%. Out of the
$700 you started with, you now only have $200.
Can you now see why we might want to do something about the speed of the options price movements and why we might
want to offset (or hedge) Delta?
When we buy an option, we always want enough time to be right. We also want to make sure that modest swings
in the stock price aren't causing uncomfortably fast and wild movements in our options position. This is
why we want to hedge Delta, or in other words, slow down the speed of
the percentage movement of our options position compared with that of the underlying asset.
Figures assume trading 1 contract
Underlying Asset Price

Delta

Gamma

ATM

Around 0.5

High

NTM

Around 0.5

High

Deep ITM

Around 1 (high)

Low

Deep OTM

Low

Low
