# Intro to Greeks Part 1: What is Delta?

If you are an option trader, chances are that you have heard of the Greeks. But if you don’t trade spreads or more multi-leg options strategies you probably don’t care about what they are or how to use them. Some are more crucial to understand than others but if you want to be a better options trader overall and have different strategies in your arsenal then it’s great to know about them. I wanted to do a series of posts discussing the Greeks of options markets and which ones to pay attention to most. Starting with likely the most important one if you are trading directionally, and that’s delta.

**What is Delta?**

Delta is simply the rate of change of an options price based on a 1 point move in the underlying stock price, if all else stays equal. Delta is the main greek options traders use to measure what their directional exposure is in a position or the portfolio overall. Some of the key uses of delta are:

- Gauging Direction
- Understanding Risk Exposure of Delta
- Hedging Needs
- Probability of Option Expiring ITM

**Gauging Direction**

The delta of an option trade tells you what directional move in a stock will benefit the option. Delta can be positive for a long delta position or negative for a short delta position. Naturally a long delta trade benefits from the stock rising in price, while a short delta trade benefits from the stock declining. The easiest way to show an example of positive delta is a long call because if the stock price rises, this increases the value of the option. If the option has a delta of 50, the call option will rise by $0.50 for every $1.00 increase in the stock price, assuming all other greeks stay equal. Delta ranges on a scale from -1 to +1 for options and since each option is worth 100 shares of stock you will hear traders refer to delta as a number between 0 and 100 most of the time.

As the example below shows an options chain of AAPL options expiring about 1 month away, the at the money 180 strike shows a positive 0.50 delta on the call option side and a negative -0.50 delta on the put option side. You can clearly see that delta decreases the further away from the current stock price you go. Similarly if you short calls then you would be creating a negative delta position while shorting puts would create a bullish positive delta position. If the stock price rises this is good for put sellers as the put value will decrease. No matter what option you buy or sell there will always be a delta value attached to it and thus you are either long or short delta’s based on the position created.

**Understanding Risk Exposure of Delta’s**

Another way to look at delta is to see how much it changes as the stock price moves. If an at-the-money option with 1 month to expiration has a 50 delta then a fully in-the-money option at expiration will have a 100 delta. But a lot happens in between that time and its when the delta moves in relation to movements in the underlying stock that can either greatly benefit or hurt the option trader. The movement of delta for each point the stock moves is called “gamma” and that will be a more advanced discussion at another time since it’s a second order Greek with less importance to most traders.

As the stock moves for you or against you, the delta of the option will move accordingly. This can result in the position growing delta’s or shrinking the delta exposure. Anticipating delta changes and thus the risk to your position or portfolio as a whole can be a great way to prepare for what risks are possible. If you are an option buyer you will benefit more for every point the stock price moves in your favor. This is how options values can increase exponentially. If you are an option seller, you will benefit less for each point the stock moves in your favor. If you sold a 50 delta put and the stock rallies, that put option might now be a 25 delta put so essentially your position ‘size’ has been cut in half based on the option delta shrinking. This is an example of gamma, as the delta expands or shrinks based on each increase or decrease in the stock price.

Generally this fluctuation of delta is seen as a benefit to long option holders and a risk to short option holders. This is because as an option delta increases towards 100 delta that makes the position larger for the option buyer as the trade gets more long with expanding delta’s. On the flip side, if an option delta declines and heads towards zero, that is good for the option seller but the position shrinks as the option seller has a short option losing value and delta. The more a delta drops the more risk increases for an option seller holding options that are nearly worthless. Of course the goal as an option seller is to see options decrease in value but waiting until expiration for them to expire worthless creates unneeded risk since the gamma of the option can still change if the stock makes an unexpected move and so the loss can be steep and fast if the stock reverses. For these reasons it’s crucial to understand the risk of a trade based on how delta changes through time.

**Hedging Needs**

Options are also a heavy focus when it comes to the world of hedging. Whether you are hedging for your own portfolio or if a large market maker firm is taking a position and hedging it based on delta risk, there is a lot of importance on how delta influences hedging. For example dealers or market makers are usually trying to be delta neutral when holding options positions so if they sell a 50 delta call on TSLA to a customer that purchases that call option, they will immediately go in and buy 50 shares of TSLA to hedge their delta risk on the position.

You can see in the risk graph below the pink line shows that the market maker would have a neutral looking profit and loss graph if they perfectly hedged that short call option with the 50 shares of long TSLA. If the stock went up another 50 points then the delta exposure would be -6.8 deltas for each option the market maker sold. So as the stock price rises the hedging needs increase for the dealers and they would have to buy more shares of TSLA to stay delta neutral. You can see how this can create a “gamma squeeze” of sorts if you multiply this example by billions of dollars of risk in a stock as has commonly happened during the momentum markets of 2020-2021. Knowing the delta of the option is absolutely critical for traders or dealers who need to hedge off every trade they take. This happens on a large scale every day in the markets with millions of contracts trading and needing to be hedged with stock by the market making firms.

**Probability of Option Expiring ITM**

Finally, delta is also a great quick way to estimate the probability of an option expiring either OTM or ITM. If a short put has a delta of -0.25 then that is estimating the option has just about a 25% chance to expire in the money (ITM). Meaning it has a probability of 75% to expire worthless or out of the money (OTM). This is one of the best ways to easily see what the options market is expecting or pricing into a stock based on a certain timeframe. You can see below that the AAPL January 185 calls have a 34 delta which shows a probability of expiring ITM around 31.6%. Pretty close to the actual delta so it makes for a handy estimate.

Also, by simply doubling the delta you can estimate the probability of a touch of that strike price by expiration. Based on the options pricing models, it’s a useful way to see if your expectations are inline with the market or not. If an option has a 40 delta that means the probability of the stock at least touching the strike price is about 80%. A 25 delta would indicate more of a 50/50 chance of a touch and if you have an option with a 15 delta then you are expecting to see that probability of a touch more closer to 30%. So clearly this is a nice way to use the options market to gauge what is being expected and form your trade idea from there.

**Takeaways:**

- Delta is the rate of change of an option’s price given a $1.00 move in the underlying price, all else equal.
- Delta can change with movements in the stock price, this is called gamma.
- Delta can be used to determine hedging needs of option and stock portfolios.
- Delta can be used to estimate what the probability of expiring in-the-money the option has.