Thank you for joining us in the second part of our "Understanding Delta: a key guide for Investors and Traders". Here, we'll continue our exploration of the multifaceted applications and nuances of this essential concept in options trading.

In this second part we'll be focusing on more advanced topics.

Delta hedging is a strategy used by traders to reduce the risk associated with the price movements of an underlying asset. By creating a portfolio that is 'delta neutral', traders can attempt to offset the impact of price changes in the underlying asset on the overall value of the portfolio.

The basic idea behind delta hedging is to create a portfolio where the combined delta of the assets is zero. This is achieved by taking a position in the underlying asset that is opposite to the delta of the options. For example, if you have a long call option with a delta of 0.6, you could hedge this position by shorting 60 shares of the underlying stock. This would create a delta neutral position, as the delta of the short stock position (-0.6) would offset the delta of the long call option (+0.6).

Delta hedging is often used by options market makers and institutional traders to manage risk. But also advanced retail options traders/investors use this technique/strategy, to keep a neutral balance in their portfolio. However, it's important to note that maintaining a delta neutral position requires frequent rebalancing of the portfolio, as the delta of an option changes with the price and volatility of the underlying asset, as well as with time.

In the next chapter, we'll explore how delta can be used in portfolio management, including how to calculate the overall delta of a portfolio of options and the underlying asset.

Delta is not only useful for individual option contracts but also plays a crucial role in managing a portfolio of options and underlying assets. By understanding the concept of delta, investors and traders can gauge the overall risk exposure of their portfolio to movements in the underlying asset's price.

Let's consider an example. Suppose you own 100 shares of a stock, which means you have a position of +100 delta because each share of stock has a delta of +1. Now, let's say you also own 2 put options on the same stock, each with a delta of -0.5. However, remember that each option contract represents 100 shares. So, the total delta for the options is -100 (because -0.5 * 2 * 100 = -100).

When you add the delta of the stock position (+100) to the delta of the option position (-100), the overall portfolio delta is 0. This means that for every $1 increase in the stock's price, the value of the portfolio would remain unchanged, because the gain in the stock position would be offset by the loss in the option position.

This is a simplified example, but it illustrates how delta can be used to manage risk and create a balanced portfolio. By adjusting the number and type of option contracts in a portfolio, an investor or trader can manipulate the portfolio's overall delta to achieve a desired level of exposure to the underlying asset's price movements.

Delta neutral strategies are a type of options trading strategy that aims to achieve a total delta of zero. This is done by combining positions with positive and negative deltas so that the overall delta of the assets in question totals zero.

In a delta neutral strategy, the trader creates a scenario in which the delta of the options and the underlying assets offset each other. This results in a position where small changes in the underlying asset's price do not affect the overall value of the position.

For example, let's say a trader owns 100 shares of a certain stock. The delta of this position is +100, as owning a stock has a delta of 1 per share. Now, the trader could open a position in options contracts with a total delta of -100. This could be achieved by buying 2 put options contracts with a delta of -0.5 each (remember, each options contract represents 100 shares).

By doing this, the trader has created a delta neutral position. This means that if the price of the underlying stock increases or decreases by a small amount, the change in value of the stock position will be offset by the change in value of the options position.

Delta neutral strategies are often used in hedging, where the aim is to reduce risk, rather than to achieve high returns. However, they are also used in premium selling strategies. In this case, a trader might sell options to collect the premium (the price of the option) and then hedge the delta risk by taking positions in the underlying asset to achieve a delta neutral portfolio. This way, the trader is not betting on the direction of the market, but rather on the time decay of the options. As options approach their expiration date, they lose value - a phenomenon known as time decay, or theta decay. This decay can provide profits for the premium seller, as long as the underlying asset's price doesn't move in an unfavorable direction too much, hence the need for delta neutrality.

These strategies can be complex and require a good understanding of options and their greeks, but they can provide a way to manage risk effectively in volatile markets.

As an option approaches its expiration date, its delta can change significantly. This is due to the effect of time decay, or theta, which is another of the "Greeks" used in options pricing. As time passes, the value of an option decreases, which can cause a change in delta.

For out-of-the-money options (options where the strike price is not favorable compared to the current price of the underlying asset), the delta will approach zero as the option nears expiration. This is because the probability of the option becoming in-the-money (profitable) is decreasing.

Conversely, for in-the-money options (where the strike price is favorable compared to the current price of the underlying asset), the delta will approach 1 for call options and -1 for put options as expiration nears. This is because the likelihood of the option remaining in-the-money is increasing.

At-the-money options (where the strike price is very close to the current price of the underlying asset) have deltas close to 0.5 for calls and -0.5 for puts. As expiration approaches, the delta of an at-the-money call option will either increase towards 1 or decrease towards 0, and the delta of an at-the-money put option will either decrease towards -1 or increase towards 0, depending on the movement of the underlying asset's price.

It's important to note that while delta can give an indication of an option's likelihood of ending up in-the-money at expiration, it's not a definitive probability measure. Other factors, such as implied volatility, can also impact an option's price and the likelihood of it being profitable at expiration.

In summary, time has a significant impact on delta. As an option's expiration date approaches, the delta can change rapidly, especially for at-the-money options. This is an important consideration for options traders, particularly those who hold positions over a longer period of time.

Let's look at some real-world examples to better understand how delta is used in options trading.

#### Example 1: Delta in Options Buying

Suppose an investor is bullish on stock Ahold (AD:xams), which is currently trading at €30.70. The investor decides to buy a call option with a strike price of €31 that expires in approx. 1 month. He can buy the option for €0.58 (bullet 1 in screenshot below) The delta of this call option is 0.41 (bullet 2 in screenshot below).