# Delta

The option delta measures the rate of change of the option price relative to the rate of change of the price of the underlying security. This can be summarised as a formula below:

Delta = Rate of change of option price  Rate of change of price of underlying security

### Delta can reflect probability of option ending in the money

The delta can be thought of as the probability of the option expiring in the money. For example, At The Money call options can have deltas of 0.5 in general.  This means that as the price of the underlying security moves by \$1, the price of the option moves by \$0.50. This results in a delta of 0.5. This can also be interpreted as a 50% probability of the option ending up In The Money.

### Delta of long call vs long put

A long call will have a positive delta.A short call will have a negative delta.  A long ptr will have a negative delta. A short put however will have a positive delta.

• A long ATM call will have a delta of 0.5
• A short ATM call will have a delta of -0.5
• A long ATM put will have a delta of -0.5
• A short ATM put will have a delta of 0.5

### Why is delta important?

The delta of a position is representative of the amount of leverage in a position. This can be illustrated by an example.

The share price of XYZ Corporation is \$50.  Trader A buys 100 shares of XYZ Corporation which cost him \$5000. Trader B buys 1 call option contract. For the purposes of this example, the delta of the option is 1. This means that for every dollar move in the underlying security, XYZ Corporation, there is a corresponding dollar move in the call option. Trader B spends \$5 on that call option contract and pays \$500 in total to initiate the position.

If the price of the underlying security increases to \$55, the table below will explain the profit percentages.

 Cost Profit Profit percentage Long 100 shares \$5000 \$500 10% Long 1 call option contract \$500 \$500 100%

Hence, in instances where there is a significant spike in the price of the underlying security, the holder of the call option with a delta of 1 will reap a good percentage profit.

If the delta of the call option is 0.5, this is the profit percentage comparison between the long stock position and the long call position.

 Cost Profit Profit percentage Long 100 shares \$5000 \$500 10% Long 1 call option contract \$500 \$250 50%

As you can see, the profit percentage is less with a delta of 0.5. Although a delta of 1 is advantageous to a call holder in terms of profit, imagine the consequences when the price of the underlying security decreased to \$45 instead.

The table below will illustrate the comparisons of loss percentages.

 Cost Loss Loss percentage Long 100 shares \$5000 \$500 10% Long 1 call option contract \$500 \$500 100%

The call option could lose its entire value and become worthless. In this case, with a delta of 1, the trader loses the entire option premium.

This is also the reason why traders may want to study option delta and hedge or offset the delta. A trader who understands delta wants to ascertain that moderate price movements against his position will not cause a drastic decline in option value. This is the reason that delta hedging occurs, especially among professional traders. Delta hedging will slow down the speed of the percentage movement of an option position.

Delta neutral trading refers to the hedging of delta where the position delta of a trade is actively brought to 0. When this happens, the risk of a drastic decline to the trade’s value is lessened when the trade goes wrong. A popular technique involves selling the profitable side of a trade and bring the trade back to delta neutral when the price of the underlying security has moved 20% in either direction.

### Other considerations to make when making delta neutral trades

• Delta neutrality requires actively managing time decay
• Near-term options will have higher deltas than longer-term options
• The position delta is also known as the “hedge ratio”
• The delta is affected by the price of the underlying security and the time to expiry.
• The delta of long calls increases when the price of the underlying security increases.
• The delta of long puts decreases as the price of the underlying asset decreases.

### Summary and guidelines to Delta Neutral Trading

 Position Delta (+ or -) Remarks Long 100 shares +100 Each share purchased has a delta of 1. Short 50 shares -50 Each share sold = delta of -1 Long ATM call +50 1 call option contract represents 100 shares. 100 x 0.5 = +50 Short ATM call -50 100 x -0.5 = -50 Long call + A long call has a positive delta. The price of the call option increases when the price of the underlying security rises. Short call – A short call has a negative delta. Long ATM put -50 100 x -0.5 = -50 Short ATM put +50 100 x 0.5 = +50 Long put – Long puts have negative deltas Put option premiums decrease when the price of the underlying increases. Short put + Short puts of positive deltas. Deep ITM call +100 A deep in the money call will have a total delta of +100. 100 x + 1 = +100 . the maximum is +100. Every move of 1 point will be matched by a 1 point move in the option price. Deep OTM call 0 Each deep OTM call have delta of 0. Deep ITM put -100 Maximum delta is -100. Deep OTM put 0 Deep OTM puts have very little chance of expiring in the money. ATM Strangle 0 ATM Straddle 0 Bull Spreads + Delta is partially hedged for a bull spread. Bear Spreads – Negative delta is partially hedged for a bear spread.