What is Delta in Options - Why Use Delta?

What is Delta in Options - Why Use Delta?

eDelta Pro uses Delta to define the backtesting strategies. This has several advantages.

What is Delta in Options?

Technically, the value of the option's delta is the first derivative of the value of the option with respect to the underlying security’s price. Delta is a first derivative.

Delta shows how the the changes in the underlying prices affect the price of the option contract.

For example, assume an investor is short a call option with a delta of -0.30 (we refer to this as a 30 Delta Call, without the decimal or sign). Therefore, if the underlying stock increases by $1, the option's price would theoretically decrease by 30 cents, and the opposite is true as well.

But Delta has more practical applications.

Delta is an indicator of the moneyness of the option.

Delta is commonly used by traders as a measure of (percent) moneyness. Delta values are not identical to the actual percent moneyness, but for practical cases these are quite close.

For example if the expiration was today, and the option contract would make money, it is said to be in the money (For example 84 Delta) , while if it would not make money it is said to be out of the money (16 Delta) , and if the current price and strike price are equal, it is said to be at the money (50 Delta). If you are short seller, it's the inverse; the 16 Delta short Put will be OTM and will be profitable.

Delta as a Proxy of probability

Delta can also be used as a Proxy of probability. In this example of AAPL we use Delta to calculate the probability of success of a short put.

  • AAPL @ $187.63
  • Short 180 Put:  +16 Delta
  • Probability ITM: 16%
  • Probability OTM: 84%
  • Probability of touch: 32% (2x16%)

Remember, these are “rule of the thumb” approximate probabilities. But for everyday trading - and backtesting - they are very useful.

Delta For Backtesting

We use Delta to define our strategies for backtesting. There are several advantages for doing this.

First by using Delta you are defining a position independently of the price of the underlying (The values are normalized). We can thus achieve consistency between different periods of time and different underlying.

For example a 30 Delta Short Strangle, will be the same strategy whether the stock is at $100 or $200. You can compare strategies results in 2012 when the stock was at $40 to a strategy in 2018, when the stock is at $120. 

In this example, the strangle consist of selling a Put and a Call both at 16 Delta, equivalent to one standard deviation. Delta neutral strategy.

Or half standard deviation, if we use 30 Delta Option on the PUT side, resulting on a more bullish strategy:

Using other Parameters

Now image we use a different criteria. We will define our strategy as out of the money percentages. 

Sell a PUT that is 0.5% OTM. Well depending on the volatility of the underlying this PUT may have very different probabilities of success.  The blue curve represents a high volatility stock. The orange, a low volatility. The Short PUT sold at 0.5% OTM will have significantly different probability of ending ITM.

Finally, using Delta allows you to replicate the trades you optimize in EDeltaPro Backtesting engine in your day to day trading.