# Delta

Delta is a crucial metric in options trading that measures an option’s price sensitivity to the underlying asset’s price movement. It is also commonly used to proxy the probability of an option expiring in the money.

It is one of the option Greeks determining the price of an option. The other commonly used Greeks are gamma, theta, vega, and rho.

## Understanding delta:

**Price sensitivity**: Delta represents how much an option’s price will change for every $1 move in the underlying asset.**Call option example**: If you own a call option on SPX with a delta of 0.5, and SPX increases by $1, the price of the call option is expected to increase by $0.50.**Put option example**: If you own a put option on SPX with a delta of -0.4, and SPX decreases by $1, the price of the put option is expected to increase by $0.40.

**Probability indicator**: Delta can also be interpreted as the approximate probability that an option will expire in the money.**Call option example**: If an SPX call option has a delta of 0.5, it implies there is roughly a 50% chance the option will expire in the money.**Put option example**: If an SPX put option has a delta of -0.4, it suggests there is about a 40% chance the option will expire in the money.

### Practical use of delta:

**Hedging**: Traders use delta to hedge their positions. A portfolio with a net delta of zero is considered delta-neutral, meaning its value is relatively insensitive to small movements in the underlying asset.**Position sizing**: Delta helps determine the size of a position. For example, if you want to create a position that mimics owning 100 shares of SPX, you could buy multiple call options with a total delta of 100.**Probability assessment**: Delta helps traders estimate the likelihood of an option expiring profitable. For instance, an SPX call option with a delta of 0.7 has a higher probability of expiring in the money than one with a delta of 0.3.

### Example scenario:

Let’s say SPX is trading at $4400. You are considering buying a call option with a strike price of $4450 and a delta of 0.2.

**Price sensitivity**: If SPX rises to $4410, the call option’s price would increase by approximately $2 (0.2 delta x $10 increase).**Probability**: The 0.2 delta indicates there’s about a 20% chance that SPX will be above $4450 at expiration, making the call option profitable.

By understanding and utilizing delta, traders can make more informed decisions, manage risk better, and optimize their strategies for different market conditions.