# How and why option delta can change

The delta of an option is a very useful thing to know. It tells us one way to hedge the option against losses from a movement in the underlying. It can indicate the likelihood that the option will finish in-the-money. And it can tells us how to use the option as a hedging instrument if we have a position in the underlying. But the delta of an option is not generally constant for long. An option’s delta can change for several reasons. This is important to understand. If for example we have delta-hedged the option, then this hedge may not be fully effective if the delta changes. Here we will consider three of the main factors that can alter option delta.

## Option delta can change when the underlying moves

As the underlying price changes, option deltas can change. Consider an at-the-money call option whose strike is equal to the current spot price. This will have a delta of 50%; it has a 50:50 chance of expiring in- or out-of-the-money. If the spot product rallies in price, the call has a *better* than 50:50 chance of expiring in-the-money and so its delta will be higher than 50%. To know by how much the option delta will change, we need to look at the option *gamma*. Gamma is usually standardised to show the change in delta for a certain change in the underlying price.

## Option delta can change when implied volatility changes

Imagine the implied volatility of options is 25% and that a call has a 10% delta. Now suppose the implied volatility increases to 50%. This can be interpreted as traders thinking the underlying product price will be twice as volatile. So would you expect the delta of the option to change from 10%? In general, you should, because the more volatile the underlying product price, the greater the chance of the option expiring in-the-money, and remember that the option delta can be viewed as the chances of expiring in-the-money.

Gamma is the 2nd order Greek that tells us how an option delta changes when the underlying price moves. *Vanna* is the Greek that tells us how much the delta changes when the implied volatility changes. Vanna is sometimes also known as DdelV or delDdelV. Whatever we call it, this 2nd order Greek is important to understand. You will find an interesting Volcube article all about option vanna here.

## Option delta can change as time passes

An option with a 10% delta today, may will have a different delta in a month’s time even if nothing else happens. Time erodes the* optionality* of options; it eats away at their extrinsic value. It also affects the option delta and it is easy to understand why. An option with a 10% delta can be thought to have a 10% chance of expiring in-the-money. But if the underlying price does not move but time continues to pass, this option’s chances of expiring in-the-money start to fall. Remember that at expiration, all out-of-the-money deltas falls to zero. So between now and expiry, the delta will change simply because time is passing.

This effect can be important for option traders. If you have a delta-hedged portfolio that is approaching expiration, then even a weekend passing can make a big difference. Suppose we own the 10% calls and we have delta-hedged on Friday by selling 10 contracts of the underlying for every 100 lots of the calls we own. Now suppose on Monday that time has eroded the delta of these calls to 7%. Well, now we only need to be short 7 contracts of the underlying. So we need to buy back 3 contracts. Some option traders will start to account for this on Friday and anticipate the time decay in their delta. Rather than wait until Monday to buy back all 3 contracts, they might decide to start buying on the Friday. This is very much a question of personal judgement, but it is obviously very important to understand how the portfolio’s delta will change over time due to time itself.

The 2nd order Greek that indicates by how much delta changes with respect to time is known as *charm*. Although not too many traders tend to know their portfolio charm, it is something they will intuitively be aware of. If they own delta-hedged calls, they will tend to know that they need to gradually reduce the size of the hedge over time.

There are other reasons for delta to change, but these are the principle three. Make sure you have these under your belt and you will have a far better understanding of the dynamics of your option portfolio’s delta.

You can of course use the Volcube option market simulator to learn about these effects and also practise trading options under a variety of conditions.