# Options trading delta definition

This means that the delta value of in the money calls tends to move towards 1 as expiration approaches or -1 for put options while the on out of the money options will usually move towards 0.

There are essentially two main ways that an options trader can use delta. It's important to remember, though, that this value is only an indication of how the price of an option is likely to change and not a guarantee of how it will change.

The primary use of delta is to give you an idea of how much money you will make if the underlying stock moves as you expect it to or how much you will lose if the underlying stock moves in the opposite direction. This can then help you determine which options give you the best value for money in terms of taking advantage of what you expect to happen.

For example, you might believe that stock in Company X is going to increase in price by a certain amount over a specific period of time. By studying the delta values of the relevant calls with different strike prices you can then try to work out how to maximize your potential returns, or minimize your potential losses.

At the money contracts will be cheaper than in the money contracts, and out of the money contracts will be cheaper still. By comparing the price of those contracts with their delta values, you can work out how much you would expect to make if Company X does move as you expect it to. It may be that you stand to make a better return on your investment with the cheaper out of the money contracts, or it may be that the in the money contracts will work out better for you.

The second main use is based on probability. The delta value of an option can be used to determine the approximate probability of it expiring in the money. The closer the delta value is to 0, the less chance it has of finishing in the money. Conversely, calls options with a delta value close to 1 and puts options with a value close to -1 have a very high chance of finishing in the money. By studying the delta values of the relevant calls with different strike prices you can then try to work out how to maximize your potential returns, or minimize your potential losses.

At the money contracts will be cheaper than in the money contracts, and out of the money contracts will be cheaper still. By comparing the price of those contracts with their delta values, you can work out how much you would expect to make if Company X does move as you expect it to.

It may be that you stand to make a better return on your investment with the cheaper out of the money contracts, or it may be that the in the money contracts will work out better for you. The second main use is based on probability. The delta value of an option can be used to determine the approximate probability of it expiring in the money.

The closer the delta value is to 0, the less chance it has of finishing in the money. Conversely, calls options with a delta value close to 1 and puts options with a value close to -1 have a very high chance of finishing in the money.

Although the calculations behind delta aren't specifically related to probability in this sense, it's still a reasonable way to gauge the rough likelihood of an option expiring in the money.

In turn, this can help you know which trades to make as you can weigh up the risks involved in a trade against the strength of your expectation for what will happen to the relevant underlying stock.

When creating spreads, it can be a good idea to calculate the total delta value of the spread. This is a simple calculation where you just add up the value of all your positions. For example, if you owned two calls that had a value of. Delta values can also be used to set targets for your trades, and to decide at what point you should close a trade and take your profits or cut your losses. Technically, this is not a valid definition because the actual math behind delta is not an advanced probability calculation.

However, delta is frequently used synonymously with probability in the options world. Usually, an at-the-money call option will have a delta of about.

As an option gets further in-the-money, the probability it will be in-the-money at expiration increases as well. As an option gets further out-of-the-money, the probability it will be in-the-money at expiration decreases. There is now a higher probability that the option will end up in-the-money at expiration. So what will happen to delta?

So delta has increased from. So delta in this case would have gone down to. This decrease in delta reflects the lower probability the option will end up in-the-money at expiration. Like stock price, time until expiration will affect the probability that options will finish in- or out-of-the-money.

Because probabilities are changing as expiration approaches, delta will react differently to changes in the stock price.

If calls are in-the-money just prior to expiration, the delta will approach 1 and the option will move penny-for-penny with the stock. In-the-money puts will approach -1 as expiration nears. If options are out-of-the-money, they will approach 0 more rapidly than they would further out in time and stop reacting altogether to movement in the stock. Again, the delta should be about.

Of course it is. So delta will increase accordingly, making a dramatic move from. So as expiration approaches, changes in the stock value will cause more dramatic changes in delta, due to increased or decreased probability of finishing in-the-money.

But looking at delta as the probability an option will finish in-the-money is a pretty nifty way to think about it. As you can see, the price of at-the-money options will change more significantly than the price of in- or out-of-the-money options with the same expiration.

Also, the price of near-term at-the-money options will change more significantly than the price of longer-term at-the-money options. So what this talk about gamma boils down to is that the price of near-term at-the-money options will exhibit the most explosive response to price changes in the stock.