# What is Option Delta?

Trading options without knowing your greeks is like flying a plane without looking at your flight instruments. Knowledge of your greeks is ABSOLUTELY NECESSARY to trade options. They are like the “vital signs” of your portfolio, that can tell you if your portfolio is healthy, or about to get sick. The more complex your option strategy, the more important it is to be able to read these signs – they’ll help you to extract more money from the market, or avoid losing money in the future.

There are a few greeks you need to know (mainly delta, gamma, vega, and theta), but we’ll start with delta.

#### Option Delta

Delta is the simplest greek to understand.

Delta is the expected change in price of an option when the underlying asset moves by $1

This means that if you have an option with a delta of 0.5, then for every $1 increase in the stock, the option should increase by $0.5. On the other hand, if your option had a delta of -0.5, then for every $1 increase in the stock, your option would LOSE $0.5.

Call options almost always have POSITIVE DELTA between zero and plus one. They INCREASE in value as the underlying asset goes up.

Put options almost always have NEGATIVE DELTA, between zero and minus one. They DECREASE in value when the underlying asset goes up.

As expiration nears, the delta of an **in-the-money** **call** will move towards 1, whereas the delta of an **out-of-the-money call** will move towards zero. This is because, as expiration nears, the in-the-money call is likely to be exercised and turned into stock, whereas the out-of-the-money call is unlikely to be exercised so is virtually worthless and won’t react to the stock’s price movement at all.

For puts options it is very similar. The delta of an **in-the-money put** will move towards -1, whereas the delta of an **out-of-the-money put** will move towards zero as it becomes more obvious that it will be worthless at expiration. This means we can think about delta in another way:

We can think about option delta as the probability that the option will end up in the money at expiration. For example, a delta of 0.5 means that there is about a 50% chance that call option will end up in-the-money at expiration. A delta of -0.2 would mean there is about a 20% chance of that put ending up in-the-money at expiration

Now while this is a useful way to think about delta, you should be aware that it is not a proper textbook definition – it is really a side-effect of the way delta is calculated.

The following table is real data taken from a broker that shows the deltas of individual calls and puts with various strike prices, when the stock is at 1160 (the blue highlighted row).

In this example the underlying asset is the Russell 2000 index currently trading at 1160. The bright yellow line highlights an **in-the-money call** **option** and an **out-of-the-money put** **option**. The bright blue line highlights **at-the-money call and put options**. The bright green line highlights an **out-of-the money call** **option** and an **in-the-money put** option. Notice how the deltas of the calls decreases as the strike price increases, and how the deltas of the puts get more negative as strike price increases. The table shows very well how delta is affected by the how close the strike price is to the price of the underlying asset. Here is a graph of that data above that shows the same thing:

#### How stock volatility affects option delta

If we think about delta as the chance that the option will end up in-the-money at expiration, then clearly the volatility of the stock will affect an option’s delta. If the stock moves up or down by 50% or more every day, then there is plenty of chance for almost any option to end up in-the-money. Take a look at Tesla (TSLA). This is a stock that is very volatile, so even when the stock is at $200, there is still a moderate chance that within the next month it could fall to $100. This means the delta of a $100 strike put option might be around 0.1 or 0.2. Compare this to McDonalds (MCD), which is a very stable company whose stock hardly fell at all during the 2008 crisis. If the stock is trading at $100, there is only a very small chance that it will fall to, say, $50 within the next month. This means the delta of a $50 strike put option would be very close to zero.

If the volatility of a stock changes, it can change the deltas of the options. and cause you to make or lose money pretty quickly. When prices of options change due to changes in stock volatility, we call this **VEGA RISK**.

#### How time to expiration affects Delta

If we think about delta as a measure of the probability that the option will expire in-the-money, then it is common sense that if an option is way out-of-the-money and has very little time left until expiration, then it will have a delta close to zero, as there is very little time left for the stock to move a lot. If it is already way in-the-money and has very little time left until expiration, then it will have a delta close to 1 (if it is a call option) or -1 (if it is a put option). Essentially, at expiration, a call’s delta MUST be either zero (out of the money) or +/- 1 (in the money). Therefore, as time moves onward, deltas of options tend to gravitate towards these values. Take a look at this chart. With a lot of time left until expiration (171 days) the line is fairly flat. As time to expiration decreases, the line gets more curvy – i.e. the delta gravitates towards 1 or -1.

This results in something interesting around option expiration time – the deltas of at-the-money options tend to swing around wildly. Here’s an example:

Say you have a call option with a strike price of $25 and there is only one day left until expiration. The stock is also currently trading at $25, so the delta of the option is around 0.5. If the stock increases to $26, the probability of the call ending up in-the-money just increased a LOT simply because there is not much time left for the stock to go back down before the option expires. If you owned this call you would have suddenly made money on it. If you had sold it, you would suddenly have lost most of your money.

This is why trading options around expiration time can be pretty dangerous – small changes in the stock can cause very large changes in delta, and therefore very large changes in your profits.

This neatly introduces us to a second greek you need to know – GAMMA. Gamma is the rate of change of delta, i.e. how quickly delta changes. We don’t generally want delta to change too rapidly because it means we can lose (or make) money very quickly. As we approach expiration we say that our **GAMMA RISK** increases – our rate of change of delta increases which means that even though we’ve made money up until that point, we can lose it all in a matter of hours.

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