It's All Greek to Me: Options Delta (A Practical Guide)

In this series, I will give a brief overview of the option greeks. These values underlie options pricing in accordance to the Black-Scholes model. I'll try to describe how these apply to option valuation in the real world and some rules of thumb for using these values.


The most basic greek of an option is its delta. The delta is the numerical amount that the option's value increases or decreases relative to movements in the underlying stock. The delta can range from .00 to 1.00. An option that is deep out-of-the-money will have a delta closer to .00, indicating that its value will hardly change with movements in the underlying. Deep in-the-money options hold deltas closer to 1.00, indicating that the option's value will increase uniformly with changes in the underlying.

When you buy an option with a high delta, you are in essence paying a premium for the increased probably that the contract will expire in-the-money. Let's look at an example:

Options grid for Apple with an expiration of (7) days with AAPL trading at 94.74

The option with the highest delta that is also out-of-the-money is also known as being "at-the-money". The 95-call and 94.29-put would be at-the-money in the above grid. These contracts command a high premium despite the fact that they are out-of-the-money. This is due to the fact that the markets place a high probability that these contracts will eventually expire in-the-money.

A large portion of the premium for these contracts is derived from its delta. An option buyer purchasing an at-the-money contract may justify the premium for the high probability that the option won't expire worthless. Had the buyer bought an option at a strike further out-of-the-money, they run the risk of the contract expiring worthless and losing the entire premium payed for the contract. On the opposite side of the contract, a seller of the contract is seeking to collect a high premium for the increased risk of the option expiring in-the-money. So we arrive at our first rule of thumb.

1. An options delta roughly translates to the probability that the contract will expire in-the-money.

Notice the call option delta for the 95 strike. The market is placing a 45% probability that Apple will be trading at or above $95 in seven trading days. The same put option indicates that there is a 56% chance of Apple trading at or below $95.

At-the-money contracts have among the highest appreciation potential amongst any of the strikes. However, for the very same reason, these contracts also expose the buyer or seller to the highest amount of risk. The underlying must move in that exact direction in a relatively limited amount of time for the option trader to profit off the contract.

Now let's look at the 95 strike straddle. The summation of the absolute value of the deltas for the call and put options at this strike is approximately 1, or in other words, there is a 100% chance that Apple will be trading at a value above, below, or at $95 in 7 trading days which intuition tells you must be true.

The straddle of that strike also gives you another piece of valuable information.

2. The price of the straddle of the at-the-money strike will give you the approximate range at which the markets predict the underlying will be trading by the time of expiration.

I want to emphasize that this rule only applies for at-the-money straddles (in the above example, the 95-strike and 94.29-strike). Let's apply this rule:

The price to buy the straddle at the 94.29-strike costs $2.23. The price of Apple when I queued this order was $94.74. We can then extrapolate that the markets expect Apple to be trading between $96.97 and $92.06 in seven days.

This range also approximates the amount that the markets are "pricing in" to a contract. This concept of "pricing in" is one of the most fundamental ideas underlying derivatives. We'll explore this concept, also known as volatility, in the next part of this series.