Delta

[00:00:00.07] - Speaker 1
In this lesson, we will talk about the delta, one of the most important Greeks that has a direct impact on the value of options. Let's start from the definition of the delta, which many of you already know. The delta indicator reflects the sensitivity of an options premium to changes in the price of the underlying. The delta is calculated as the change in the price of the option. As the price of the underlying changes by 1 percentage point, assuming constant other factors.

[00:00:24.26] - Speaker 1
In this course, the delta becomes very important. Being able to understand how the delta moves will help us better monitor the liquidity of the markets. When an investor buys or sells an option, there is a market maker who takes the risk. The market maker is long or short. But we also know that the market maker cannot stay completely long or short because that is not how they make money.

[00:00:45.22] - Speaker 1
Their strategy is to execute hedge against risk and profit from the increased transaction volumes through the bid ask spread for each trade. So during the day, the market maker dynamically buys and sells the underlying to remain delta hedged. The delta in this case helps us follow the liquidity. In fact, the market maker's book must always be delta neutral. To be delta neutral, it means that during the day, with the change of the spot and the other Greeks, the market maker is buying or selling the underlying, depending on whether it is long or short.

[00:01:15.10] - Speaker 1
Delta. We will use practical example to understand how delta varies and then show you how to be delta neutral. Understanding this activity will also help you better leverage our Q models in creating profitable strategies in the option market. Now, before talking about what affects the delta, we must understand what is the delta? The delta profile, the payoff, how to find its intrinsic value and how the moneyness affects the delta.

[00:01:41.22] - Speaker 1
We will try to understand how to evaluate an option by looking at the delta. And we will then show you how to analyze the delta on the option chain. This will prepare us for the section on delta hedging. In order to understand how to implement a delta hedging strategy and how market makers operates on a daily basis, we need to understand how delta moves. There are various factors that move the delta.

[00:02:03.06] - Speaker 1
The first we analyze is the price of the underlying. The spot price. For example, when the price of the SPX index goes up or down, it changes the delta of an option. This applies to both calls and puts. Here we can see what happens to the delta of our option if the underlying price increases.

[00:02:20.13] - Speaker 1
For call options, the delta is positive. In fact, with a positive change in the price of the underlying, the value of the option increases. Or with a negative change in the price of the Underlying the value of the call decreases. From a liquidity and delta hedging point of view, if the delta of a call increases, it means that to remain covered, we must also change our hedging. In fact, the change in the delta will also change our hedge ratio.

[00:02:44.28] - Speaker 1
We will show you how to calculate your hedge ratio later and show you how the change in the delta directly impacts our hedge. In the case of a put options, the delta is negative, the more the price of the underlying increases. In fact, there is an inverse relationship between the price of the underlying and the price of the option. If the price of the underlying goes down, instead, we see how the delta of our call becomes less and less positive. The opposite happens instead.

[00:03:09.12] - Speaker 1
For the put in this slide, we can see the delta profile. Understanding the profile of our Greek is essential for three reasons. First of all, it helps us understand how different Greeks relate to each other in the different parts of the curve. Later in the course, we will notice how the delta has a different relationship with the other Greeks. The profile then helps us understand how the delta varies based on the moneyness of the option.

[00:03:32.13] - Speaker 1
The delta is never static, and the more we move along the upward or downward curve, the more the option delta changes. Finally, the third reason is a question of valuation. As you will see in the practical part of the course, when we implement a strategy, it will be essential to understand the value of each criterion. We also want to understand the profile of each crit. Once the strategy is executed.

[00:03:53.19] - Speaker 1
Understanding the profile will help us to predict more accurately whether our strategy, based on all the other factors that we will study, will have a positive or negative risk reward and the probability of being successful. For now, let's focus on the delta profile because it will be important to master these concepts. Let's start by looking at the spot versus the delta of our call option. Based on the strike of our option, if the price of the underlying increases, we see how the delta also increases. On the other hand, the delta decreases when the price of the underlying goes down.

[00:04:24.04] - Speaker 1
Now let's use a practical example to understand how the delta curve changes. Let's take a call option and its payoff. In yellow, you can see the typical payoff of a call. If the price of the underlying increases and all other factors remain the same. We can see that the further we go to the right of the payoff, the more the option delta increases, the more our option gain in value.

[00:04:44.23] - Speaker 1
The more the delta increases. The more the delta increases, the more likely it is to enter in the money and be profitable. The opposite happens for A put. The more the price of the underlying decreases, the more the put becomes in the money. As you can see on this slide.

[00:04:58.15] - Speaker 1
On the right we show the movement of a delta of our call option with the increase of the underlying price. On the left we see the profile of the delta. This helps us visualize in a graphical way how the delta changes as the option becomes in the money. The same also applies to the delta profile of a put option. At this point we can see the relationship of an options moneyness and the delta.

[00:05:20.14] - Speaker 1
In the center you have the ATM strikes which stands for add the money. Lets take the delta profile of a call and see the relationship with the option minus the delta goes up the closer we get to in the money it decreases and approaches zero if we are out of the money here. Instead you can see what happens to the delta of a put. The more the price of the underlying force, the closer we get to in the money. In the next slide we will focus on pricing and option.

[00:05:46.15] - Speaker 1
It is important to distinguish between two values, the intrinsic value and the time value. Lets go back to the payoff of a call option. How can I see the time and intrinsic value? And what exactly are they? We start from the intrinsic value.

[00:06:00.14] - Speaker 1
It is calculated by subtracting the spot price from the strike price. It represents the profit if the holder of the option contract exercises at the current market value. The intrinsic value can be positive or zero, but not negative. Since it makes no sense to exercise a call option if the price of the underlying is below the strike price. The time value of an option is the difference between an option's market price and its intrinsic value.

[00:06:25.03] - Speaker 1
The time value represents the probability that the price of the underlying asset will rise above the strike price before the expiration date. The further away the expiration date of an option, the greater the time value as there is more time available for the price of the underlying to rise in value. In general, the time value decreases as you get closer to the expiration date. It is important to note that when the implied volatility increases, the time value of the option also increases. But why does implied volatility have this effect on time value?

[00:06:53.27] - Speaker 1
Let's try to understand this concept using two assets, one very volatile and one less volatile. In this slide we take the historical price of Procter and Gamble, a company that historically has a very low volatility. A volatility that is also reflected by the average price movement in the orange square. If instead we take Tesla, we can see that the price of this stock moves much faster than Procter. And Gamble.

[00:07:15.26] - Speaker 1
This means that if we buy an out of the money option with a very short expiration, let's say, for example, a weekly one Tesla option, have a better chance of entering in the money in that period of time and giving us a profit compared to a company like Procter and Gamble with a very low volatility and a less chance of entering in the money before expiration. So this is a very important concept because the more the volatility goes down, the more the time value of the option decreases, just like in the case of Procter and Gamble and Tesla. Now, if we go back to the previous example of a call, we can clearly see how the value of the option changes based on the change in the spot. The green part represents positive intrinsic value, while the red part represents negative intrinsic value. The intrinsic value is not the only value of the option.

[00:07:59.12] - Speaker 1
It is important to quantify the time value, which in this case is defined by the distance between the green line and the yellow line of the payoff. The same concept also applies for the payoff of the puts. As you can see in this slide, in green you have positive intrinsic value, while in red the puts has no value. Finally, the time value can be identified by the green line, just like in the case of the call option. We are now at the end of the lesson on Delta.

[00:08:23.07] - Speaker 1
We will look at the other Greeks in the next lessons.