In this post I explain, as simply as possible, what the delta is in the context of options trading and how to use it.

But before I start, we need to be clear of some basic definitions:

* ITM (In The Money): In case of a call option it means that the option strike price is lower than the actual price of the underlying (stock). In case of a put option, it is the opposite.

* ATM (At The Money): The strike price is the same as the price of the underlying.

* OTM (Out of The Money): In case of a call option it means that the option strike price is higher than the actual price of the underlying. It is the opposite for the put options.

Now that we clarified some of the definitions, let's get back to our delta.

In short, the delta shows us the option price movement in relation to the price movement of the underlying (e.g. stock). The delta values are normally displayed as decimals but they are actually percentages ranging between -1 and 1 (or -100% and 100%).

As we can see below, it can be represented by an 's' curve which has the following critical attributes:

The option price movement cannot exceed the price movement of the underlying, therefore it's capped at 1 (100%). What it means is that the if the underlying moves up $1 then the maximum move of a deeply ITM (in the money) option cannot be more than $1.

The option price movement is 50% (0.5 delta) of the price movement of the underlying when the strike price is ATM (at the money). For example, if there is a $100 stock and we look at an option with a strike price of $100 then we can expect the option price to change by roughly $0.50 when the price of our stock moves $1 in any direction.

The option price movement is $0 when the strike price is relatively far out of the money. E.g. the price of a call option with $150 strike may not move at all when the underlying goes from $100 to $105.

The price movement of the option either accelerates or decelerates. The below diagram shows three random (stock) price levels with identical price movement (orange line) and the size of the price movement change (delta) (green line).

The closer the option expiration date the steeper the S curve is.

So how do we use this?

First of all, we can use the delta to determine the level of risk we want to take. The lower our delta is the higher our probability to profit from the trade, but higher probability also means lower profit potential.

We can use it when we are directionally bias about a stock.

For example, if you are certain that a stock is going to go up then you can buy far OTM call options and make more profit than most people can't even dream of. In order to understand this point, let's take a look at two scenarios assuming that our stock price is at $100.

We could buy an $80 call option for, let's say, $20.50. Remember that each option covers 100 stocks so this particular option would cost us $2050. Why is it so expensive? It's because the strike price is $20 ITM (100-80), which represents the intrinsic value and there is a $0.50 risk premium, which represents the extrinsic value. So if the price of the underlying goes up by $10 then we can rightfully assume that the $80 call option value will be about $30.50. In other words, we would be making $1000, which is equivalent to buying 100x stocks at $100 and sell the stocks for $110.

Our other option is to buy $120 call option for let's say $0.05. It's dirt cheap because it's far OTM and has pretty much no intrinsic value and the probability of the stock reaching $120 is considered very low. But when the price of the underlying is approaching the $120 strike price then the probability increases significantly, therefore the value of the option also increases significantly. It may go up to $0.50, which doesn't sound like much at face value so let's put it into perspective: If you invested the same amount as in the previous case ($2050) then you would walk away with $20,500.

We could also use it to hedge our portfolio.

This leads me to the put options, which has exactly the same curve as the call option but the delta is a negative figure because if the price of the underlying goes down then the price of the put option goes up.

Imagine if you combine the call and the put options (selling a strangle).

The most important factor to note is that when the price of the underlying increases then it accelerates the call option price movement while decelerates the put option price movement. If the price of the underlying drops then it works the opposite way. For this reason it is strongly recommended that such positions are kept delta neutral as much as reasonable.

Another way to hedge our position is to use different expirations.

As mentioned at point 5 above, the further away the option expiry is, the flatter the delta curve is. On the diagram below the peach coloured line shows the longer expiration, while the blue line shows the shorter expiration. Note the length of the green lines in the circled area. The same price movement results in smaller change in the option price when the expiration is further away (the green line is shorter).

I hope this makes sense.

Let me know if you have any questions.