# Understanding Delta: A Deep Dive into the Options Greek

## Breaking down the value of using delta in options trading

Sep 6, 2021 at 1:00 PM

Delta is the second Greek letter used in options trading. Delta can easily be quantified as the change in option price relative to the difference in the underlying equity. Thus, the delta of an option is a mathematical function of the market value of the underlying equity. In essence, delta is a quantitative representation of how much an option's value will change based upon changes in the underlying equity.

Derived from the Greek word "deltos," delta is a mathematical measure that determines the change in the price of an option contract in reaction to a \$1 move in the underlying asset. Delta is dependent upon how far away an option contract's value is from being at-the-money. At-the-money is when a call or put option's strike price is equal to or very near the market price of the underlying security.

The option delta measures the sensitivity of an option's price to a change in its underlying stock. Thus, option delta indicates the chances that the option will be in-the-money at expiration. An option is in the money when it has intrinsic value. A call is in the money when the market price of the underlying stock is greater than the option's strike price. A put is in the money when the market price of the underlying stock is lower than the option's strike price.

This article explores how Delta is calculated, its effect on your options positions, and why this simple arithmetic indicator can be so valuable.

## Delta is a Key Number in Options Trading Models

To begin trading options, you first need to understand what delta means. Delta is a measure of the price sensitivity of an option contract to changes in the underlying asset price (stock, index, etc.). The value of the delta indicates how much the option price will change when the underlying price changes.

When trading options, delta can be considered as the price difference between a strike and a call. Where the price ends up is based on the relative strength of the two options at that time. Delta has two things in common: a percentage and it is a number. It seems like the two things have the same role in what is happening here, but this is not the case.

Premium options traders take the price difference between two options as given, and then they adjust their positions accordingly by buying or selling these options. When this happens, the broker has to pass along this premium to you as an investor to have a profitable trade.

## Understanding Delta is Key to Expertly Trading Options

Delta is the first and easiest to understand of the option Greeks. Delta tells you how much an option's price changes given a change in the underlying security's price—or more simply, delta tells you how much money you can make if you buy an option.

The quantitative measure describes the relationship between an option's value and the change in the operation of the underlying asset. An excellent way to think about the delta is to imagine that it represents 'directional probability' - it can be thought of as the likelihood that an option will end up in the money at expiration.

Delta of 0.5 means there is a 0.5% probability of the contract being in the money at expiration. Therefore, if you buy an at-the-money call option, the equity's delta will be 0.5 (and likewise for a put). A change in the price of the underlying equities can directly impact the cost of options as they track with their respective movements.

When trying to understand the intricacies of options trading, new traders may often feel a bit overwhelmed. However, the delta is one component that even experienced traders must understand and keep in mind while trading.

There are two ways to calculate deltas: using actual data or theoretical data. The first way involves using accurate historical market data of competitors or related companies. The second way is using what is referred to as an option pricing model. Each approach has its advantages and disadvantages, but they both allow you to develop a mathematically valid delta for an option.

Investors use Delta to estimate the probability that a stock will move in the same direction as most underlying options contracts. For example, say that you invest \$50,000 in Chevron (CVX), and you decide to use options to hedge your long investment position. However, instead of delta hedging with actual CVX shares, you choose to use options for leverage. Accordingly, you sell to open one option contract of September \$90 strike price calls with a delta of 50%.

A numerical measure of the amount an option's price will change in response to a one-point change in the cost of the underlying security. Delta, always between 0 and 100, represents the probability that the option will be in the money at expiration. So, for example, a delta of 50 means there's only a 50% chance that the option will finish in the money; 25 means a 75% chance, Delta of 200 indicates an 80% probability, and so forth.

## Concluding Thoughts on Options Trading Using Delta

Delta tells you how much the price of the underlying will move when the price of your option changes. But since Delta is expressed as a percent, this means you what percentage of a stock's total movement will be accounted for by your option.

Think of this Greek as you think of a stoplight. A delta of 100% is equivalent to no hedge at all: If the price changes by \$1 per share, you lose \$1 per share. A delta of 50% is equivalent to stopping on a yellow light and not stopping on a red one. An option with a delta of 25% would be like stopping on a green light only if the cross traffic was clear; otherwise, the driver would keep going and potentially get rear-ended.

The amount by which an investment changes in response to a change in the underlying security price is an important performance indicator for any options trader. Many people define the Delta of an option as the probability that it will be in the money at maturity, irrespective of how its underlying stock moves. But that definition doesn't tell you anything about how the Delta of an option will change depending on how the underlying stock price behaves.

Think of Delta as a ratio between the expected change in an option's value due to a one-point move in the stock, and the expected change in the stock due to a single point.

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