Hello everyone and welcome back to moomoo. I'm options explorer. In today's [Options ABC], we'll be taking a look at another important option Greek: Delta.

Wordcount: 1400

Target Audience: Investors interested in option Greeks.

Main Content: What is Delta? How does it work? How to build a Delta Neutral Strategy?

In previous articles, I introduced one important Option Greek: Theta. Time value is a crucial component of an option's premium. As time passes, an option's time value will decrease. In such situations, understanding Theta - an indicator for measuring the time value of options - can be beneficial.

Today, we will focus on Delta and the construction of a Delta Neutral Strategy.

So, let's begin with a question: In a Delta Neutral Strategy, what should the Delta be?

1.What Is Delta?

Delta is an option Greek that measures an option's price sensitivity to changes in the underlying asset's price. Specifically, Delta indicates the amount by which the option price changes for every one-point move in the underlying asset's price. While all options prices are impacted by underlying asset price movements, the degree of sensitivity can vary significantly among different options and underlying assets.

For instance, a call option on an underlying asset that rises 10% may rise by 20%, while another call option rising 20% may track an asset that only increases 3%. The reason for this disparity lies in the differing degrees of sensitivity to changes in the underlying asset's price, indicating that their Delta values are not the same.

To further explain how Delta works, we can use two formulas:

Option Price Change = Delta * Underlying Asset Price Change

New Premium = Original Premium + Delta * Underlying Asset Price Change

Setting clear investment goals is crucial before investing. With Delta, investors can gain valuable insights into potential risks and rewards associated with different options, helping them establish a solid investment strategy that aligns with their objectives.

To further illustrate the concept of Delta, let's take Alice as an example. Suppose Alice purchased a PDD call option with a strike price of US$2.25 per share expiring on September 15th, 2023, with a contract multiplier of 100. At the time of purchase, PDD’s stock price was US$98.88, and she paid US$225 to open the position (US$2.25 * 100).

Assuming that the Delta value for Alice's option is 0.59 and remains constant, if PDD's stock price were to increase to US$103, her option's premium would be calculated as follows: US$2.25 + (US$103 - US$98.88) * 0.59 = US$4.0908. If PDD's stock price were to decrease to US$97, her option's premium would be calculated as follows: US$2.25 + (US$97 - US$98.88) * 0.59 = US$1.1408.

However, it's important to note that in real cases, Delta values are constantly changing due to variations in underlying asset prices and other market factors. We assumed that Delta remains constant for Alice's case only to help illustrate the relationship between Delta and option prices. Actual results may vary significantly.

2.What Are Delta's Features

1) The larger the absolute value of Delta, the higher the likelihood that the option will expire in-the-money. Generally, options closer to being in-the-money have a larger absolute Delta, while those further out-of-the-money have a smaller absolute Delta.

For at-the-money options, Delta values are typically around 0.5, reflecting their status as being equidistant from being in-the-money or out-of-the-money. Previously, we saw with Theta that at-the-money options have the highest Theta value since they are equally close to being in-the-money or out-of-the-money.

2) Call options have positive Delta value between 0 and 1, while put options have negative Delta values between -1 and 0.

This is because if the underlying asset rises in price, call option prices are likely to rise as well, while put options prices are more likely to decrease.

3) Delta is often influenced by implied volatility (IV), which represents the market's expectation for how much the underlying asset's price may fluctuate before expiration. For out-of-the-money options, Delta is positively related to IV, meaning higher IV leads to higher Delta values. For in-the-money options, Delta is negatively related to IV, meaning higher IV leads to lower Delta values.

Understanding Delta and its relationship with IV can help investors better allocate their investment. For example, let's say Alice sold an out-of-the-money call option, but then the market experiences a significant gap up. In this situation, the implied volatility would suddenly increase. Since Delta for out-of-the-money options is positively related to implied volatility, the Delta for this call option would also be pushed higher.

3.Hedging with Delta：Delta Neutral Strategy

Now that we've discussed the features of Delta, let's take a look at how hedging with Delta can help us achieve our risk management goals.

Delta hedging involves keeping the overall Delta of a position around 0 to hedge against risks in the underlying asset's direction. Let's explore some benefits of Delta hedging:

1)Use time decay to earn premiums

As we mentioned earlier, when Delta is 0, the whole position will be unaffected by minor changes in the underlying asset's price. However, the option premium will still be affected by time decay. Therefore, a seller can use Delta hedging to earn premiums through time decay.

2) Profit from volatility without directional bias

Under a Delta-hedged strategy, when the underlying asset's price does not change much, investors can profit from volatility changes.

For example, suppose Alice notices that the implied volatility for a call option she owns has reached a three-month high due to a recent surge in the underlying asset's price. With the expectation that the implied volatility will eventually revert to its historical means, Alice decides to sell a put option to gain profits from the expected drop in implied volatility. However, since she is worried that the underlying asset could continue to rise, she constructs a Delta Neutral Strategy: buying one at-the-money call option (Delta 0.5) and one at-the-money put option (Delta -0.5). The combination results in a Delta of 0, thereby hedging the direction risks. In summary, she can profit regardless of whether the underlying asset rises or falls.

To summarize, here are some commonly used methods to construct Delta Neutral Strategy:

Option + Stock

• Long a call option + short the underlying assets

• Short a call option + long the underlying assets

• Long a call option + long the underlying assets

• Short a put option +short the underlying assets

Option Combination

• Long a call option + short a call option

• Long a call option + long a put option

• Long a put option + short a put option

• Short a call option + short a put option

3)Reality Check: The Ideal vs. The Real

While Delta Neutral Strategies seem appealing, nothing lasts forever, especially in the unpredictable world of options trading. Delta is a real-time changeable value, which means its neutral state can only last for a moment. Therefore, traders need to continually adjust their positions to maintain an overall zero Delta. But remember, frequent trading can increase costs. Don't forget to think twice before making any moves.

That's all for today! Please feel free to leave a comment if you have any questions or thoughts.

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