Delta explained – what is it and how can options traders use it?

Delta is the first of the Option Greeks. The notion “option greeks” is often used to indicate all the essential parameters of the option pricing model. These parameters help option traders in understanding how option prices change and behave.  

Managing an options portfolio successfully means managing the Greeks (of your positions and portfolio). Understanding “delta”, and the use of Greeks, is therefore a first step for every beginning options trader, who wants to understand and want to know what he is doing, in order to become a more profitable and successful option trader by managing the greeks.

Content

• Introduction
• Definition and explanation of the delta parameter in options trading
• Factors influencing the value of delta
• Interpretations of delta
• The practical use of delta

1. Introduction

Before we dive deep into the parameter delta, let me remind you how the options prices are determined. 

On the options exchange the options bid and ask prices are determined by the market forces of supply and demand. And more precise, by the actual buying and selling decisions of the people and institutions who trade options.  When there are more buyers than sellers, the bid price tends to rise, and when there are more sellers than buyers, the ask price tends to fall.

The options bid price refers to the highest price a buyer will pay for an option. The ask price refers to the lowest price a seller will accept for selling an option. The difference between these two prices is known as the spread; the smaller the spread, the greater the liquidity of the given security.

When the stock price changes, the price of the option also changes, but not necessarily by the same amount or direction. Various factors, like the type of option (call or put), how close the option’s strike price is to the stock price, the volatility, interest rates, and time remaining before the option expires, influence how much the option’s price will change. 

Nobody really knows which way the market or the stock price will move tomorrow, but it would surely help us, options traders, to know exactly how big the impact of a change in stock price or index will have on the price of the held option positions.

Delta can help us : delta helps us to show much (amount and direction) the option price is likely to change considering these different factors. This makes delta a crucial parameter for option traders because it helps us to take the guesswork out of the expected price movement of the option.

2. Definition and explanation of the delta parameter in options trading

Definition: Delta measures how much an option’s price can be expected to move for every $1 change in the price of the underlying stock or index. 

The symbol for delta is (Δ). 

The value of option deltas range from -1 to 1 and they can either be expressed as a decimal fraction or as a percentage, although traders will almost always refer to their values as whole numbers. For example : an option with delta 0.30 or 30% will be usually declared by traders as “thirty delta”.

What does the delta value mean exactly?

A positive delta means that the options price will increase if the price of the underlying will increase. A negative delta means that the options price will decrease if the price of the underlying will increase.

Call options have positive deltas between 0 and 1, because the options price will increase if the price of the underlying increases. Put options have negative deltas between -1 and 0, because the options price will decrease if the price of the underlying increases.

This should be clear since call options give the owner the right to buy the shares at the fixed strike price, so a rising share price increases the value of the option, so call delta is always positive. Correspondingly, since put options give the owner the right to sell shares at the fixed strike price, a rising share price will lower the value of the put option, so put delta is always negative. 

Other examples :

An option of $TSLA shares with delta of 0.40 means the option’s price will theoretically move $0.40 for every $1 change in the price of the underlying stock or index. So the higher the delta, the bigger the price change of the option. So if a call option is worth $2.00 and has a delta of 0.40, and the underlying stock increases from $235 to $236 per share (+$1), then the value of that option theoretically increases by $0.40 (from $2.00 to $2.40). If this is good or bad depends on the option position (long or short) you are holding.

Options deltas add up when trading different options of the same underlying. If you for example buy a call with a 0.25 delta of underlying $ABC and you buy another call of 0.10 and a put with a delta of -0.15 of the same $ABC underlying, then your combined position delta will be : 0.25 + 0.10 + (-0.15) = + 0.20

Attention for calculating delta when selling options: 

When selling options you need to factor in the shorting (=going minus the held option position) to determine the delta of the position. 

With puts having negative delta, selling a put means having positive delta, because two negatives (minus the put position and minus delta value) will result in a positive delta. 

Which makes complete sense in the mind of an option seller, whose goal is to sell the option for a higher price and to buy back at a lower price. 

So by selling a put option, the seller collects the premium and if the price of the underlying increases, the option price of the put will decrease ( as indicated by the negative delta), and the put seller can close his position by buying back the put option at a lower price and thus make a profit. So his short option position had a positive delta, because the value of his short position decreased when the price of the underlying moved up.

Let this sink in very well. It is key to understand this 100%.

Delta Characteristics for options

Call options:

• Call options have positive deltas between 0 and 1, because the options price will increase if the price of the underlying increases.
• At the money call options usually have a delta value near + 0.50
• The delta will increase (and approach 1.00) as the option gets deeper in the money (ITM).
• The delta of ITM call options will get closer to 1.00 as expiration approaches.
• The delta of out-of-the-money (OTM) call options will get closer to 0.00 as expiration approaches.

Put options: 

• Put options have negative deltas between -1 and 0, because the options price will decrease if the price of the underlying increases.
• At the money put options usually have a Delta near – 0.50
• The delta will decrease (and approach –1.00) as the option gets deeper ITM.
• The delta of ITM put options will get closer to –1.00 as expiration approaches.
• The delta of out-of-the-money put options will get closer to 0.00 as expiration approaches.

The closer an option’s delta is to +1 or -1, the more strongly the option’s premium responds to a change in the underlying security. And indeed a delta of 1 (or 100%) means that the options price changes one-for-one with the price of the underlying. It is clear that the underlying itself has by definition a delta of 1.

3. Factors influencing the value of delta

As mentioned above, the options delta is influenced by several factors. The most important ones are: 

• the underlying asset price
• the option’s strike price relative to the stock price
• the implied volatility
• time till expiration

It’s important to note that delta changes dynamically, on a permanent basis when trading occurs, due to these different factors and is not a precise or static prediction of price movements. Market conditions can alter delta rapidly, making it a more dynamic measure rather than an absolute one.

Let’s briefly touch upon the influence of the different factors on delta.

a. the underlying asset price

It’s not necessary to understand the math of the Black Scholes model behind delta in detail but for those interested, delta is defined more formally as the partial derivative of options price with respect to underlying stock price.

This means that also the value of delta itself changes as the price of the underlying changes. The extent to which this change itselfs occurs is another of the option Greeks, “Gamma”, but that will be a topic for another time. 

Just know that delta will vary together with the change of the underlying. 

b. the option’s strike price relative to the stock price

The choice of the strike price relative to the share price of the underlying will impact on the value of the option. If the strike price is close to the stock’s current price, the option is more likely to make money (get intrinsic value)  if the stock moves. This also gives it a higher delta.

If the strike price is far from the current stock price, the option is less likely to make money (move into an intrinsic value position) with small stock price changes, resulting in a lower delta. When chances are getting really small with far out of the money strike prices we will near 0 delta.

Examples make it easier to understand so let’s consider $IBM trading around $145 and a call option with strike price $200 with expiration in 53 days. 

$IBM is a stock that doesn’t move that much (as you can see on the options chain – expected move – 1 SD and 2 SD – if yopu don’t know what this is, please ignore it) so it is extremely unlikely that the call option will get in the money and gain intrinsic value.

In other words chances are close to 100% of the option expiring worthless. Not only is the price of the call option very low (200 strike between 0 bid price and 0.07 ask price) at the , the delta of this call option will be extremely low too – close to zero : even is IBM moves up a dollar, this will not change the probability that much for the option moving into the money zone.

In simpler terms, if you’re aiming for more profit potential, you could choose strike prices closer to the current stock price. However, if you’re aiming for a lower risk and potentially lower returns, you might choose strike prices farther from the current stock price.

An important case are the at the money options, whose strike price is equal to the current price of the underlying. in the example of IBM above, around the $147 strike. These options have a delta of 50% (although sometimes a bit of skew happens), which makes absolute sense with the share price sitting on the strike price, even intuitively you may argue that it is a 50-50 bet.

c. Implied volatility

Implied volatility is a critical factor in option pricing models like Black-Scholes. Higher implied volatility leads to higher option prices due to the anticipation of greater price fluctuations in the underlying asset. Conversely, lower implied volatility results in lower option prices as expected price swings decrease. Thus, implied volatility directly impacts the premium that option holders pay or receive when trading options.

This also means that a change in implied volatility also alters delta. When implied volatility is higher, the delta for out-of-the-money options increases, making them more responsive to price shifts. Conversely, it decreases delta for in-the-money options, reducing their sensitivity to price changes.

d. Time till expiration

Time decay, also known as theta, is the reduction in the value of an option as it approaches its expiration date. The passage of time has a significant impact on both delta and the option pricing.

As the time remaining to expiration becomes shorter, the time value of the option evaporates and correspondingly, the delta of in-the-money options increases while the delta of out-of-the-money options decreases.

This is logic if you consider that due to the shorter expiration the deep in-the-money options tend to behave as the stock, in other words delta tends to approach 1 for in the money options.

While for out of the money options, due to the shorter and shorter expiration, these options have a declining chance of being exercised, meaning that also their delta will approach zero the closer they get to expiration.

As an option approaches its expiration date, its delta tends to decrease. This means the option becomes less sensitive to small price movements in the underlying asset, particularly for out-of-the-money options. As an option approaches its expiration date, its delta tends to approach 1 for in the money options.

Below you can see an example of a put option for $PYPL with a 70 strike. With 4 days to expiration, and the put option deep into the money, has a value of around $11.25 and the delta of -0,98 is close to -1, meaning that the options value almost moves at equal pace as the changes of the stock.

If we compare this to option with the same strike but with a higher number of days till expiration, in this case 116 days, you will see the impact of more theta on delta.

I don’t want to go too deep into this delta-theta relationship here. It is important to realise that there is a relationship as described above. Understanding the definition of the delta in options trading or fully comprehending delta’s implications in relation to the other greeks are two entirely different worlds, the latter demanding a more in depth analysis, which is not the scope here in this starting level guide. 

But why does it matter then ?

As I said, everything is dynamic in options trading, and so is delta. If you own in the money options in your portfolio, we have just explained that this options delta will grow with the passage of time. This higher delta will make your position thus more sensitive and thus more vulnerable to moves in the underlying.

As expiration closes in, the profit/loss of your position will thus become more volatile. This is why I, together with all tasty-traders, prefer to counter this increased risk by managing our positions early (around 21 days) and that is why I rarely keep my options until expiration especially when they are in the money. The opposite is true for out of the money options, delta decreases and they become less sensitive to price movements. Understanding how delta’s change over time and making clear interpretations of the connected risks can be a game changer of becoming a master in managing your options.

4. Interpretations of delta

Let’s take a look now, in general, at how traders use delta and its link with probabilities to assess the likelihood of profitable outcomes. And more particularly, in the case of option sellers, like me, let’s also take a look at delta’s relation to the probability of the option expiring out of the money.

a. Delta as a sensitivity measure to assess directional risk 

By definition, delta measures the option’s directional exposure as delta measures how much an option’s price can be expected to move for every $1 change, up or down, in the price of the underlying stock or index. Delta clearly is an indicator for directional risk.

When your position is positive, you have a bullish position (you will benefit from the underlying moving up). If you have a position with a negative delta, you have a bearish position (because you will benefit from the underlying going down).

When I say position that can be just an individual option or a combination of option positions forming a stratgey.  Each individual leg of an option position has its own delta. The delta of the different legs can be combined to determine the net delta of the combined position and this allows us to assess the directional risk of the strategy as a whole.

Example : I have sold a put with strike $160 and a call with strike $200 in the underlying $AAPL at the moment trading at the price of $175. My delta’s are +0.25 for the put (short position  (-1) * (-0.25) negative delta for a put option = + 0.25) and -0.20 for the call (short position  (-1) * (+0.20) positive delta for a put option = – 0.20).The net delta of my position is + 0.25 – 0.20 = +0.05 or 5 delta meaning that with the current delta values, my position is slightly bullish because the value of my option position will increase with $5 (option contract of 100 shares) if the stock moves up $1.

Note that the delta of long stock (owning) itself is 1 or 100% and the delta of short stock is -1 or -100%. The delta of an option ranges between 1 to -1, which means the closer the (increasing) delta of the option is towards 1 or -1, the more the value of the option will move in tandem with the changes of the underlying. In other words the more sensitive the option has become to the movement of the underlying security and ultimately the premium consists of mostly intrinsic value.

That is why we consider delta also to be a sensitivity measure of the option to the underlying stock. A delta of 0 for example for a net delta strangle position is neutral in directional risk and is not sensitive for a price change of the underlying at that considered moment in time (because deltas are dynamic) 

b. Delta as the probability of the option expiring in the money (out of the money)

Traders often use delta to predict whether a given option will expire ITM. A delta of 0.35 is taken to mean that at that moment in time, the option has about a 35% chance of being ITM at expiration. 

A 1 or 100 % delta for a deep in the money call indicates that the option theoretically has a 100% chance of finishing in the money. And the same for a deep in the money put with a delta of -1 or -100%.

It is important to realize that delta clearly gives a good quick indication but that there are no certainties with options. As we have seen above, delta is constantly changing, and the interpretation of delta giving the exact probability of expiring in the money is only statistically true with a number of assumptions in place. 

As option sellers, we prefer the option losing value and/or even expire worthless. This means going more out of the money or staying out of the money. The same way that delta is a measure of an option being in the money at expiration, we can use delta as a measure for an option expiring out of the money. 

Essentially, a delta closer to 0 can be translated into a higher probability of being out-the-money at expiration. 

Example : a call for stock ABC with delta 0,35 indicates a probability of 35 % of being in the money at expiration but it also means a 65% chance of staying out of the money and expiring without any intrinsic value (worthless).

c. Delta as an equivalent position in the underlying

You can also think of delta as being an estimate of owning the number of shares of the underlying stock. A 0.30 delta option suggests that for a $1 move in the underlying stock, the option will likely gain or lose more or less the same amount of value as if you were owning 30 shares of the underlying stock.

Example: Imagine I own a call with delta 0.30 and the price of the option is $4 with the stock price at $200. With the delta of 0.30 we can expect the options price to move to $4.30 when the share price moves up $1. If I would close my position I would have a $30 profit. This is the equivalent of owning 30 shares of the stock moving from $200 to $201, which also result in a profit of 30 shares x $1. This example demonstrates that delta can be considered as share position in number equivalent to the delta value.

d. Delta as a ratio for hedging

Delta hedging is a trading strategy that aims at reaching a relatively neutral delta state that offsets the directional risk of the portfolio, associated with the market price movements of the assets in the portfolio. The hedge or the protection to market fluctuations is achieved through the correct use of options and stock. When a position is delta-neutral (delta close to 0), its value will not increase or decrease when the value of the underlying stays within certain bounds, in that given moment. 

If I aim to stay neutral and minimize his directional risk, I can use the delta parameter as a ratio to determine what is needed to hedge the position (protect the position or portfolio from stock or market fluctuations) and make it become more neutral. 

If for example I have a position or portfolio with a delta of + 0.50 (50%), then I know that if the underlying will move up $1, the value of the options will move up 0.50$ (*100 for an option contract of 100 shares = $50). Whether this is good or bad for me depends totally on my holdings (long or short).

But I can use the ratio to indicate that I can completely hedge against price fluctuations by adding a position or stock that has a delta of -0.50 (for example 50 short stock, a long put option with a 0.50 delta or a short call option with a 0.50 delta, all going down in position value when the underlying rises, or profiting when underlying value goes down).

So in this sense the delta can give you the “hedge ratio”, an indication of the needed delta’s as a counterweight needed to protect your position or go back to delta neutral state.

5. The practical use of delta – strategy selection and adjusting portfolio risk

Delta can be a real guide for people who trade options. It helps them estimate how the price of an option might change when the underlying changes. This helps them make smarter choices.

When you sell options, delta is your friend. It’s like a tool that helps you pick how risky you want to be. If you sell options with a high delta, you could get more money, but it’s riskier. It’s like aiming for a bigger prize but with a bigger chance of things not going your way. If you sell options with a low delta, you get less money, but it’s safer. It’s like going for a smaller prize, but you have a better chance of winning.

When it comes to options selling strategies, delta is instrumental in strategy selection. For instance, options sellers often use the delta of options to determine their preferred level of risk and potential reward.

Selling options with a higher delta means a greater probability of the option expiring in-the-money, but also providing a higher premium and carrying a higher risk of assignment. On the other hand, selling options with a lower delta offers a lower premium but reduces the probability of the option being exercised.

We need to carefully consider the risk we want to take, the market conditions, and our trading objectives when selecting an appropriate delta for options selling, tailoring our strategies to align with our overall trading approach and goals.

Delta is a parameter that comes into play when I want to have a clear idea how sensitive my positions are to underlying movements. Delta also helps me to estimate the probabilities of staying out of the money and delta plays an important role in my guiding portfolio parameter, the delta/theta ratio.

Constructing Strategies

Understanding delta helps in constructing strategies. For instance, a trader aiming for a neutral strategy might combine options with positive and negative deltas to create a position with overall low or zero delta, reducing risk.

Adjusting Portfolio Risk

Traders can use delta to adjust their portfolio’s risk exposure. If they want a more aggressive approach, they might choose options with higher delta for potentially higher returns and risk. Conversely, lower delta options might be chosen for a more conservative approach.

And of course delta is an integral part of my risk analysis with the delta/theta ratio.

I surely hope that this guide helps you to understand options delta. And that it was useful for you to better grasp the impact of the different variables on our trading.