What is delta in Options Trading? – The Most Important Key Figure

What is the Option Delta? The option delta is one of the so-called option greens and offers the possibility to determine the price development of options and other derivatives.

It is therefore a sensitivity indicator that determines how the option price reacts if the underlying price of the underlying asset rises or falls. Other factors influencing the option price, such as the fall in fair value, are hidden.

The delta value is also used to determine the delta position. The delta position can be used to determine the number of shares, which is represented by an option position.

The option delta in practice

If the price of a share or other underlying asset rises or falls, the price of the option concluded on it also changes.

Let us assume that an investor enters into a call option and the underlying stock price slowly rises above the agreed strike. The option is now in the money. This makes the option more valuable for the options trader. Conversely, this also applies to put options. If the stock price falls towards or below the strike, the option becomes more valuable.

It is important to know that it always refers to the change in the stock price over one monetary unit, about €1 or $1. With call options, the delta value always assumes a value between 0 and 1 (always positive). With put options, the delta value is always between 0 and -1 (always negative). For example, a delta of -0.50 € means that the price of the option increases by 0.50 € if the stock price falls by 1 €.

Example

A delta of 0.50 to a call option indicates that the price of the option increases by €0.50 if the share price increases by €1. Conversely, the option price falls by €0.50 if the share price falls by €1.

For example, if the original option price based on a share quoted at €50 was €2 and now increases to €2.50, this means that the option price increases by 25%, even though the share price would only increase by €1 to €51 or by 2%. If an investor holds an option over 100 shares and would now sell it again, he could make a profit of €50 from the sale of the call option alone, as he would now receive a €250 premium.

How does the delta change over time?

The specification of the option delta is always only a snapshot. The further a call option is out of the money, the closer it comes to zero. The further the option is in the money, the closer the value of the delta approaches 1. In addition, the delta of an in-the-money call option increases faster the shorter the remaining time to expiration. In the case of out-of-the-money call options, the delta decreases correspondingly faster. Call options that are close to the money have a delta of around 0.5. For put options, the same statements apply only with a negative delta and in relation to falling prices of the underlying.

Calculating the Delta of Options

The derivation of the option delta is quite complicated. It is based on the Black Scholes option price formula. But don’t worry, the values are displayed by your options broker. Put simply, the option delta is the quotient of the option price change and the underlying value change:

What is the delta position?

The delta position is the number of stocks represented by an option position. For example, if you own 10 call options with a contract size of 100 shares each and the delta is 0.5, i.e. close to the money, the delta position is 500 (10 options x 100 shares x 0.5).

This value is important if an existing options portfolio is to be set up delta-neutrally to make it less susceptible to price changes in the underlying stocks overall. This is also known as delta hedging. In this case, one would have to build up an opposite position with a negative delta position of -500, i.e. with puts.

The same can be achieved by selling 50 shares short for a call position with a position delta of 0.5 over 100 shares. Why? Because the option delta of the 100 shares is always 1 and with 50 shares 0.5.


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