Option trading using delta

Options Delta.

Options Delta is probably the single most important value of the Greeks to understand, because it indicates how sensitive an option is to changes in the price of the underlying security. In simple terms, it will tell you, in theory, how much the price of an option will move in relation to each $1 movement in the price of the underlying asset.

An option with high delta will move in price significantly in proportion to the price movements of the underlying security, while one with low delta will move less often. On this page we look at the characteristics of delta and how you can put it to use.

Characteristics of Delta.

The delta value of an option is usually expressed as a number between -1 and 1, although it can also be between -100 and 100. This number basically tells how much the price of the option will move for every $1 the price of the underlying asset moves by.

For example, a delta value of .50 (or 50 if the -100 to 100 scale was being used) would mean that the price would theoretically increase $.50 for every $1 the price of the underlying security increases by, and fall $.50 for every $1 the price of the underlying security falls by.

A negative delta value, such as -.50, would mean that the price option would move in the opposite direction to the price of the underlying security. So a delta value of -.50 would mean that the price would theoretically fall $.50 for every $1 the price of the underlying security increases by, and increase $.50 for every $1 the price of the underlying security falls by.

Calls have positive delta values, between 0 and 1, because their value increases when the price of the underlying security goes up and falls in value when the price of the underlying security goes down. Puts have negative delta value, between 0 and -1, because their value falls when the price of the underlying security goes up and increases when the price of the underlying security goes down. The actual delta value of an option will largely depend on two factors: the moneyness and the time left until expiration.

Delta value isn't fixed, and it changes based on market conditions. It will increase as an option gets deeper into the money and decrease as it gets further out of the money. Therefore the delta value of a call will move nearer towards 1 when stock is rising, and nearer towards 0 when stock is falling. On a put it will move towards -1 when the stock is falling, and towards 0 when the stock is rising.

Options that are exactly at the money will usually have a value that is very close to .50. The rate at which the value will change in relation to how the price of the underlying security is moving is measured by another of the options Greeks: Gamma.

The other main factor that affects the delta value is the time left until expiration, because the less time there is until the expiration date, the less time there is for the price of the underlying security to change. Therefore, an option is more likely to stay in its current state of moneyness the closer the expiration date is.

This means that the delta value of in the money calls tends to move towards 1 as expiration approaches (or -1 for put options) while the on out of the money options will usually move towards 0.

Putting Options Delta to Use.

There are essentially two main ways that an options trader can use delta. It's important to remember, though, that this value is only an indication of how the price of an option is likely to change and not a guarantee of how it will change.

The primary use of delta is to give you an idea of how much money you will make if the underlying stock moves as you expect it to (or how much you will lose if the underlying stock moves in the opposite direction). This can then help you determine which options give you the best value for money in terms of taking advantage of what you expect to happen.

For example, you might believe that stock in Company X is going to increase in price by a certain amount over a specific period of time. By studying the delta values of the relevant calls with different strike prices you can then try to work out how to maximize your potential returns, or minimize your potential losses.

At the money contracts will be cheaper than in the money contracts, and out of the money contracts will be cheaper still. By comparing the price of those contracts with their delta values, you can work out how much you would expect to make if Company X does move as you expect it to. It may be that you stand to make a better return on your investment with the cheaper out of the money contracts, or it may be that the in the money contracts will work out better for you.

The second main use is based on probability. The delta value of an option can be used to determine the approximate probability of it expiring in the money. The closer the delta value is to 0, the less chance it has of finishing in the money. Conversely, calls options with a delta value close to 1 and puts options with a value close to -1 have a very high chance of finishing in the money.

Although the calculations behind delta aren't specifically related to probability in this sense, it's still a reasonable way to gauge the rough likelihood of an option expiring in the money. In turn, this can help you know which trades to make as you can weigh up the risks involved in a trade against the strength of your expectation for what will happen to the relevant underlying stock.

When creating spreads, it can be a good idea to calculate the total delta value of the spread. This is a simple calculation where you just add up the value of all your positions. For example, if you owned two calls that had a value of .60 and one put with a value of -.40, then your position has a total delta value of .80 (2 x .60 = 1.2, plus -.40 - .80).

Delta values can also be used to set targets for your trades, and to decide at what point you should close a trade and take your profits or cut your losses.

Delta.

What is 'Delta'

The delta is a ratio comparing the change in the price of an asset, usually a marketable security, to the corresponding change in the price of its derivative. For example, if a stock option has a delta value of 0.65, this means that if the underlying stock increases in price by $1 per share, the option on it will rise by $0.65 per share, all else being equal.

BREAKING DOWN 'Delta'

Delta values can be positive or negative depending on the type of option. For example, the delta for a call option always ranges from 0 to 1, because as the underlying asset increases in price, call options increase in price. Put option deltas always range from -1 to 0 because as the underlying security increases, the value of put options decrease. For example, if a put option has a delta of -0.33, if the price of the underlying asset increases by $1, the price of the put option will decrease by $0.33. 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 often used in hedging strategies, and is also referred to as a hedge ratio.

Delta Behavior Examples.

BigCorp is a publicly traded corporation. Shares of its stock are bought and sold on a stock exchange, and there are put options and call options traded for those shares. The delta for the call option on BigCorp shares is .35. That means that a $1 change in the price of BigCorp stock generates a $.35 change in the price of BigCorp call options. Therefore, if BigCorp’s shares trade at $20, and the call option trades at $2, a change in the price of BigCorp’s shares to $21 means the call option will increase to a price of $2.35.

Put options work in the opposite way. If the put option on BigCorp shares has a delta of -$.65 then a $1 increase in BigCorp shares' price generates a $.65 decrease in the price of BigCorp put options. Therefore, if BigCorp’s shares trade at $20, and the put option trades at $2, and then BigCorp’s shares increase to $21, the put option will decrease to a price of $1.35.

How Delta Dictates Behavior.

Delta is an important calculation (done by computer software), as it is one of the main reasons option prices move the way that they do – and an indicator of how to invest. The behavior of call and put option delta is highly predictable and is very useful to portfolio managers, traders, hedge fund managers and individual investors.

Call option delta behavior depends on whether the option is "in-the-money," meaning the position is currently profitable, "at-the-money," meaning the option's strike price currently equals the underlying stock's price, or "out-of-the-money," meaning the option is not currently profitable. In-the-money call options get closer to 1 as their expiration approaches. At-the-money call options typically have a delta of 0.5, and the delta of out-of-the-money call options approaches 0 as expiration approaches. The deeper in-the-money the call option, the closer the delta will be to 1, and the more the option will behave like the underlying asset.

Put option delta behaviors also depend on whether the option is "in-the-money," "at-the-money," or "out-of-the-money" and are the opposite of call options. In-the-money put options get closer to -1 as expiration approaches. At-the-money put options typically have a delta of -0.5, and the delta of out-of-the-money put options approaches 0 as expiration approaches. The deeper in-the-money the put option, the closer the delta will be to -1.

Delta Spread.

Delta spread is an options trading strategy in which the trader initially establishes a delta neutral position – by simultaneously buying and selling options in proportion to the neutral ratio (that is, the positive and negative deltas offset each other, so that so that the overall delta of the assets in question totals zero). Using a delta spread, a trader usually expects to make a small profit if the underlying security does not change widely in price. However, larger gains or losses are possible if the stock does move significantly in either direction.

The most common delta spread is a calendar spread. The calendar spread involves constructing a delta neutral position using options with different expiration dates. In the simplest example, a trader will simultaneously sell near-month call options and buy call options with a later expiration in proportion to their neutral ratio. Since the position is delta neutral, the trader should not experience gains or losses from small prices moves in the underlying security. Rather, the trader expects the price to remain unchanged, and as the near month calls lose time value and expire, the trader can sell the call options with longer expiration dates and hopefully net a profit.

Options Trading Strategies: Understanding Position Delta.

The article Getting To Know The Greeks discusses risk measures such as delta, gamma, theta and vega, which are summarized in figure 1 below. This article takes a closer look at delta as it relates to actual and combined positions - known as position delta - which is a very important concept for option sellers. Below is a review of the risk measure delta, and an explanation of position delta, including an example of what it means to be position-delta neutral.

[ Need a refresher on options before you dive into deltas? Review the basics of options, from simple puts and calls, to strangles and straddles in Investopedia Academy's Options for Beginners course. ]

Simple Delta.

Let's review some basic concepts before jumping right into position delta. Delta is one of four major risk measures used by option traders. Delta measures the degree to which an option is exposed to shifts in the price of the underlying asset (i. e. stock) or commodity (i. e. futures contract). Values range from 1.0 to –1.0 (or 100 to –100, depending on the convention employed). For example, if you buy a call or a put option that is just out of the money (i. e. the strike price of the option is above the price of the underlying if the option is a call, and below the price of the underlying if the option is a put), then the option will always have a delta value that is somewhere between 1.0 and –1.0. Generally speaking, an at-the-money option usually has a delta at approximately 0.5 or -0.5.

Figure 2 contains some hypothetical values for S&P 500 call options that are at, out and in the money (in all these cases, we will be using long options). Call delta values range from 0 to 1.0, while put delta values range from 0 to –1.0. As you can see, the at-the-money call option (strike price at 900) in figure 2 has a 0.5 delta, while the out-of-the-money (strike price at 950) call option has a 0.25 delta, and the in-the-money (strike at 850) has a delta value of 0.75.

[Delta is just one of the major risk measures skilled options traders analyze and make use of in their trading strategies. You can learn the other forms of risk and beocme an options trader yourself by taking Investopedia Academy's Options Course. Learn the same knowledge successful options traders use when deciding puts, calls, and other option trading essentials.]

Keep in mind, these call delta values are all positive because we are dealing with long call options, a point to which we will return later. If these were puts, the same values would have a negative sign attached to them. This reflects the fact that put options increase in value when the underlying asset price falls. (An inverse relationship is indicated by the negative delta sign.) You will see below, when we look at short option positions and the concept of position delta, that the story gets a bit more complicated.

At this point, you might be wondering what these delta values are telling you. Let's use the following example to help illustrate the concept of simple delta and the meaning of these values. If an S&P 500 call option has a delta of 0.5 (for a near or at-the-money option), a one-point move (which is worth $250) of the underlying futures contract would produce a 0.5 (or 50%) change (worth $125) in the price of the call option. A delta value of 0.5, therefore, tells you that for every $250 change in value of the underlying futures, the option changes in value by about $125. If you were long this call option and the S&P 500 futures move up by one point, your call option would gain approximately $125 in value, assuming no other variables change in the short run. We say "approximately" because as the underlying moves, delta will change as well.

Be aware that as the option gets further in the money, delta approaches 1.00 on a call and –1.00 on a put. At these extremes there is a near or actual one-for-one relationship between changes in the price of the underlying and subsequent changes in the option price. In effect, at delta values of –1.00 and 1.00, the option mirrors the underlying in terms of price changes.

Also keep in mind that this simple example assumes no change in other variables like the following:

Delta tends to increase as you get closer to expiration for near or at-the-money options. Delta is not a constant, a concept related to gamma (another risk measurement), which is a measure of the rate of change of delta given a move by the underlying. Delta is subject to change given changes in implied volatility.

Long Vs. Short Options and Delta.

As a transition into looking at position delta, let's first look at how short and long positions change the picture somewhat. First, the negative and positive signs for values of delta mentioned above do not tell the full story. As indicated in figure 3 below, if you are long a call or a put (that is, you purchased them to open these positions), then the put will be delta negative and the call delta positive; however, our actual position will determine the delta of the option as it appears in our portfolio. Note how the signs are reversed for short put and short call.

The delta sign in your portfolio for this position will be positive, not negative. This is because the value of the position will increase if the underlying increases. Likewise, if you are short a call position, you will see that the sign is reversed. The short call now acquires a negative delta, which means that if the underlying rises, the short call position will lose value. This concept leads us into position delta. (Many of the intricacies involved in trading options is minimized or eliminated when trading synthetic options. To learn more, check out Synthetic Options Provide Real Advantages.)

Position Delta.

Position delta can be understood by reference to the idea of a hedge ratio. Essentially, delta is a hedge ratio because it tells us how many options contracts are needed to hedge a long or short position in the underlying.

For example, if an at-the-money call option has a delta value of approximately 0.5 - which means that there is a 50% chance the option will end in the money and a 50% chance it will end out of the money - then this delta tells us that it would take two at-the-money call options to hedge one short contract of the underlying. In other words, you need two long call options to hedge one short futures contract. (Two long call options x delta of 0.5 = position delta of 1.0, which equals one short futures position). This means that a one-point rise in the S&P 500 futures (a loss of $250), which you are short, will be offset by a one-point (2 x $125 = $250) gain in the value of the two long call options. In this example we would say that we are position-delta neutral.

By changing the ratio of calls to number of positions in the underlying, we can turn this position delta either positive or negative. For example, if we are bullish, we might add another long call, so we are now delta positive because our overall strategy is set to gain if the futures rise. We would have three long calls with delta of 0.5 each, which means we have a net long position delta by 0.5. On the other hand, if we are bearish, we could reduce our long calls to just one, which we would now make us net short position delta. This means that we are net short the futures by -0.5. (Once you're comfortable with these aforementioned concepts, you can take advantage of advanced trading strategies. Find out more in Capturing Profits With Position-Delta Neutral Trading.)

The Bottom Line.

To interpret position delta values, you must first understand the concept of the simple delta risk factor and its relation to long and short positions. With these fundamentals in place, you can begin to use position delta to measure how net-long or net-short the underlying you are when taking into account your entire portfolio of options (and futures). Remember, there is risk of loss in trading options and futures, so only trade with risk capital.

4 ways to understand option delta.

The delta of an option or of an options portfolio can be interpreted in several different and useful ways. Here are 4 of the best.

Delta as the change in option value for a change in the underlying product price.

The most basic definition of delta is as the change in an option’s value for a change in the price of the underlying product. If you have a call option struck on some cheese, then the delta of your call option tells you how much its value will alter when the price of the cheese changes. If the call has a delta of 20%, then for every $1 the price of cheese rises, the option will increase by 20 cents. Put options have a negative delta, so a cheese put with a delta of (-)20% will fall in value by 20 cents for every $1 the cheese price rises.

How is this useful?

This interpretation of delta is useful because it indicates the sensitivity of the option’s value to price changes in the underlying. If we have an understanding of how volatile the underlying product price is, then we have a handle on how exposed our option position is to these price changes. If the price of cheese very rarely moves more than 50 cents per day, then we might expect our 20% delta call option to rarely make or lose 10 cents per day. This gives us a useful indication of the basic price exposure we face.

Delta as the option hedge ratio.

Knowing how much the option value will change when the underlying product price changes, allows us to hedge appropriately. So if our put option has a delta of (-)20% then for every 100 options we trade, we need to hedge with 20 lots of the underlying (assuming a contract multiplier on the options of 1). This is easiest to see by working through a simple example. If the price of cheese is $100 and we own 100 lots of the 20% delta puts on cheese, then a $1 increase in the price of cheese will result in a 20 cent price fall in our put options. So we lose 20 cents * 100 lots = $20. To hedge this, we need to buy some cheese. The delta tells us how much cheese to buy as a hedge. We need to buy 20 lots of cheese, so that when its price rises by $1 we will make a $20 profit to counter the loss on the puts.

How is delta useful as a hedge ratio?

It should be obvious. The delta tells us exactly how to hedge options to prevent losses due to changes in the price of the underlying.

Delta as the likelihood of expiring in-the-money.

This one probably gets more weight than it should, but can be useful nevertheless. Basically, delta can under certain assumptions be seen as the probability or likelihood that an option will expire in-the-money. So a 20% delta call could be thought to have a 20% chance of expiring in-the-money.

This is used by some traders in order to select which options to trade. For example a trader might look for a put that has only a 10% chance of expiring in-the-money; he might want to take his chances on this put expiring worthless and short (write) the put option. Using the delta, the trader can find out which put (i. e.the put with which strike) this is. If cheese is trading at $100, the (-)20% delta put option with 3 months to expiry might have a strike of $92. The trader might therefore interpret the delta of the put to mean that this put has a 20% chance of expiring in-the-money. The same idea works for combinations of options (option strategies) to find the probabilities of a range of prices where the underlying might be when the options expire. For example if the cheese put with a 10% delta has a strike of $90, we might suggest that there is a 20% chance of the options expiring with the price of cheese below $92, a 10% chance of it expiring between $90 and $92 and a 10% chance of it expiring below $90.

Note of caution about option delta and probability of expiring in-the-money.

This probability is highly theoretical. It is not a FACT about the options that will always be true. All it means is that if every assumption in the pricing model that has been used to formulate the delta turns out to be true, then the delta can be interpreted as the probability of expiring in-the-money, in some cases. This is very unlikely to be the case consistently or even frequently. Volatility can be higher or lower than expected. Interest rates can move. Indeed, for some options where cost of carry or dividends are relevant, this interpretation of delta is even more precarious. Nevertheless, as a rule of thumb, option delta as the probability of expiring in-the-money is undoubtedly useful to know.

Delta as the equivalent position in the underlying product.

Probably the main use of delta in the markets. If we own 100 call options on cheese with a 20% delta, then this is equivalent to owning 20 lots of cheese from a risk perspective. We could neutralise this risk by selling 20 lots of cheese (the exact same idea as delta viewed as the hedge ratio) or we could trade options to achieve the same effect. For example if we buy 100 lots of the (-)20% delta puts on cheese, this will cancel out our +20% delta call delta. Our equivalent position in the underlying product becomes zero. When traders refer to being long or short deltas they mean long or short an equivalent amount of the underlying, whether this is coming from an option position or a straight position in the underlying.

All these interpretations come from the same definition of option delta. Indeed, they are identities ; exactly the same thing but viewed from a different perspective. All have their uses and every option trader must know how and when each is applicable. And of course, the best way to learn this is by trading options on Volcube!

Understanding the option Greeks is the key to successful option trading and risk management. This Volcube ebook guide offers an in-depth and intuitive guide to the most critical Greeks; delta, vega and theta. In clear, well-written English, each of the Greeks is defined and the market terminology employed by practising traders is explained. The fundamental […]