# Definition option delta

The actual delta value of an option will largely depend on two factors: Delta value isn't fixed, and it changes based on market conditions. It will increase as an option gets deeper into the money and decrease as it gets further out of the money. Therefore the delta value of a call will move nearer towards 1 when stock is rising, and nearer towards 0 when stock is falling. On a put it will move towards -1 when the stock is falling, and towards 0 when the stock is rising. Options that are exactly at the money will usually have a value that is very close to.

The rate at which the value will change in relation to how the price of the underlying security is moving is measured by another of the options Greeks: The other main factor that affects the delta value is the time left until expiration, because the less time there is until the expiration date, the less time there is for the price of the underlying security to change. Therefore, an option is more likely to stay in its current state of moneyness the closer the expiration date is.

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.

Calls have positive delta, between 0 and 1. That means if the stock price goes up and no other pricing variables change, the price for the call will go up. If a call has a delta of. Puts have a negative delta, between 0 and That means if the stock goes up and no other pricing variables change, the price of the option will go down.

For example, if a put has a delta of -. As a general rule, in-the-money options will move more than out-of-the-money options , and short-term options will react more than longer-term options to the same price change in the stock. As expiration nears, the delta for in-the-money calls will approach 1, reflecting a one-to-one reaction to price changes in the stock. As expiration approaches, the delta for in-the-money puts will approach -1 and delta for out-of-the-money puts will approach 0.

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. 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. But if your forecast is wrong, it can come back to bite you by rapidly lowering your delta. But if your forecast is correct, high gamma is your friend since the value of the option you sold will lose value more rapidly.

Time decay, or theta, is enemy number one for the option buyer. Theta is the amount the price of calls and puts will decrease at least in theory for a one-day change in the time to expiration. Notice how time value melts away at an accelerated rate as expiration approaches. In the options market, the passage of time is similar to the effect of the hot summer sun on a block of ice. Check out figure 2. At-the-money options will experience more significant dollar losses over time than in- or out-of-the-money options with the same underlying stock and expiration date.

And the bigger the chunk of time value built into the price, the more there is to lose. Keep in mind that for out-of-the-money options, theta will be lower than it is for at-the-money options. However, the loss may be greater percentage-wise for out-of-the-money options because of the smaller time value. Obviously, as we go further out in time, there will be more time value built into the option contract.

Since implied volatility only affects time value, longer-term options will have a higher vega than shorter-term options.