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### Delta Δ

#### The Basics

• The option delta is the rate of change of the option price compared with the price movement of the underlying asset price. In other words, delta measures the speed of the option price movement as compared with movement of the underlying asset.

• You can think of delta as being the probability of the option expiring In the Money. As a general rule, ATM (At the Money) call options have deltas of 0.5. Therefore, for every \$1.00 the stock moves, the call will move at approximately \$0.5, that is, half the distance of the underlying stock. Inevitably, as the stock price moves away from the ATM position, the delta value will change too, away from 0.5.

• Because US stock options contracts represent 100 shares, the delta value of an ATM call option is represented as 50 instead of 0.5. One individual share has a delta of one—because a contract represents 100 shares, [100 × 0.5 = 50].

• A delta of +/− 50 is saying the option has a 50% chance of expiring In the Money. This makes complete sense because ATM options have a 50% chance of expiring In or Out of the Money.

• ATM = +/− 50 deltas—that is, moves at half the speed of the underlying asset.

• ATM calls have a delta of 0.5 meaning that for every one point the stock rises, the option will increase by 0.5 points.

• ATM puts have a delta of −0.5 meaning that for every one point the stock falls, the option price will increase by 0.5 points.

• If you buy an ATM call, then you have a delta of 0.5.

• If you sell an ATM call, then you have a delta of −0.5.

• If you buy an ATM put, then you have a delta of −0.5.

• If you sell an ATM put, then you have a delta of 0.5.

• All bought calls have a positive delta.

• All sold calls have a negative delta.

• All bought puts have a negative delta.

• All sold puts have a positive delta.

##### Example 6.1.1.

 If you buy 100 shares of AMZN (+100 deltas), you would need to buy two ATM puts (−50 deltas each) for a Delta Neutral position.

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