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Delta is one of the most important risk metrics for options traders to use when it comes to options pricing. In this post, we will take a look at what delta is and what makes it so important when it comes to options trading.

Summary

  • Delta is a metric that estimates the change in an option’s premium for every $1 move in the underlying
  • The delta values can be positive and negative
  • Call option deltas are between 0 and 1, put option deltas are between -1 to 0

What is Delta?

In options, delta is a metric that estimates the change in an option’s premium for every $1 move in the underlying. It is used as a gauge to help traders understand the cost of taking directional exposure in a stock. Delta is also used as a way to figure out the amount needed to be delta neutral. Additionally it can be used to also calculate the probability that an option will expire in the money.

Delta values can be both positive and negative.

They range from 0 to 1 for call options and –1 to 0 for put options. So, when looking at an options chain, delta values will be negative on the put side and positive on the call side.

For example, if a call option has a delta of +$0.55, this means that if the price of the stock went up by $1 per share, the options premium would increase by $0.55. On the flip side, if a put option has a delta of -$0.55, this means that if the price of the stock went down by $1 per share, the options premium would increase by 0.55.

Understanding an Options Delta

Delta is one of the five Greeks used in options trading. For options traders, delta is an important metric to help them make sense of the cost associated with taking a directional risk. It’s also useful in helping traders determine how the value of an option will change as the price of the stock moves up and down.

The change and behavior in delta for call options depend on if the option is in-the-money, at-the-money, or out-of-the-money. It’s important to understand how delta changes the further it gets in the money or out of the money. The graph below illustrates how the moneyness of an options delta changes.

Moneyness and Delta

delta
option delta vs moneyness

Call Options Delta

A call options contract with a delta of +0.50 is considered at-the-money. The delta for out-of-the-money call options gets closer to 0 the further out of the money it is and also the closer it gets to the stock options expiration date.

The deeper in-the-money a call options contract gets the closer it gets to a delta of 1. The opposite is true for put options.

Put Options Delta

A put options contract with a delta of -0.50 is considered at-the-money. The delta for put options gets closer to 0 the further out-of-the money the option gets and as expiration approaches. The deeper in-the-money a put option gets, the closer the delta gets to -1.

Understanding this key relationship between the moneyness of an option, the expiration date, and the impact it has on the delta is instrumental in making sense of delta.

Important Note: The gammaof an option measures the change in delta for a single $1 change in the underlying.

What is Delta Neutral?

Delta neutral is a term that is used to describe a portfolio strategy or options trading mechanism that balances positive and negative deltas against each other. Being delta neutral in an options trade means that the net exposure in either direction is hedged or offset by a corresponding position in the opposite direction.

For example, let’s assume that you purchased a long call option with a delta of +0.65. To become delta-neutral, you have to purchase a put option that has a delta of -0.65. This would make your options trade “delta neutral”. By getting into the put option you balance the two deltas against each other. Effectively the net delta becomes 0, effectively hedging your risk.

Being delta-neutral is a mechanism for hedging your risk in the market or in an individual stock. Delta-neutral strategies are used by options to take advantage of implied volatility and the time decay of options.

How is Delta Used by Options Traders

Delta can be used in a few different ways by traders. The behavior of delta in call and put options are used by hedge fund managers, portfolio managers, traders, and investors to more effectively hedge risk. It can also be used as a measure of how much the price of an option will change if the price of a stock moves by $1.

If you have a certain amount of exposure in an individual stock and you want to hedge your risk, you can do so by being aware of how your current delta exposure. Once you know your net delta exposure, you can buy or sell the appropriate options to become delta neutral.

Examples of Delta

Let’s assume that you are bullish on the price of AMD stock and you decide to purchase a $140 call expiring in 1 month. The current price of AMD is $135, but you have reason to believe it will go up within the next month. The $140 call option costs you $5.50 in premium and has a delta of +$0.37. This means that for every $1 dollar move in the price of AMD, your options premium will increase by 0.37.

After a month goes by the price of AMD has rallied to $142 per share. How much would your options contract be worth now? At the end of the expiration, your option would be $2 in-the-money. However, for every $1 move up in the underlying from when you purchased the contract you would be up $0.37.

Your total gain would be $0.37 x 7 ($142 – $135) = $2.59

FAQ’s


What is the Delta of a Single Share of Stock?

The delta of being long on a single share of stock is +1.0. The delta of being short on a single share of stock is -1.0.

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