Volatility and Vega

[00:00:00.10] - Speaker 1
We have spoken on several occasions during the course about the concept of volatility. Quite simply, it is the movement of the price of an underlying during a given period. When we study volatility, it is first of all necessary to understand what we are measuring, the unit of measurement, and the time frame. But first let's look at the definition. Volatility is a measure of change in the price of an asset, such as stock or a bond, over time.

[00:00:22.24] - Speaker 1
Volatility indicates the amount of uncertainty or risk associated with investing in a particular asset. The higher the volatility, the greater the price movement and the greater the risk for investors. Volatility can be measured in several ways, but the main one is the standard deviation of returns. This measure quantifies the average amount by which an asset's price deviates from its mean return over a specific period. Other measures, such as beta and implied volatility, are also used in different contexts to assess volatility.

[00:00:50.22] - Speaker 1
Volatility is an important factor to consider in managing investment risk and selecting an investment portfolio. It is important to note that volatility can be influenced by various factors including market sentiment, economic data, geopolitical events, and the change in supply and demand. We are now going to look at different types of volatility first and then look at the Greek vega. Let's start. First of all, it is important to distinguish between two types of volatility.

[00:01:15.26] - Speaker 1
We have historical volatility and implied volatility. Let's start with the historical one. Historical volatility, or hv, also known as statistical volatility, is calculated based on the actual price movement of an asset over a specific, specific time period. It measures the magnitude of past price fluctuations and provides an understanding of how volatile an asset has been in the past. Traders use historical volatility to assess the risk and potential return of an investment by studying its price behavior over time.

[00:01:43.28] - Speaker 1
Historical volatility is calculated by using an asset's past prices to determine a standard deviation of its returns. This provides a measure of the amount of uncertainty or risk associated with investing in that asset in the past. Historical volatility can be used to determine the future volatility of an asset and to help investors make informed decisions about the risk and diversification of their portfolio. Implied volatility, on the other hand, is a measure of the market's future expectations of volatility. It is derived from the prices of option contracts traded in the market.

[00:02:14.29] - Speaker 1
It reflects the market consensus of the future uncertainty and risk associated with the underlying asset. Implied volatility is not directly observable, but Rather is extracted from the price of an option which discounts its effect. For example, the price of a call option depends on the implied volatility of the underlying. The higher the volatility, the more likely it is that the price of the underlying will exceed the option strike at expiration, making it profitable. It is important to note that historical volatility is backward looking while implied volatility is forward looking as it takes into account market expectations about future volatility.

[00:02:49.15] - Speaker 1
Volatility is measured as the standard deviation of the price changes of the underlying asset. Quite simply, the standard deviation measures the amount of variability or dispersion around the mean. So if we have an historical average, it helps us understand how far the price is from the average. The greater the difference between the two, the greater the standard deviation. If the standard deviation is high, so it is the volatility and vice versa.

[00:03:12.29] - Speaker 1
When we look at volatility, it is necessary to be able to analyze it and to obtain the daily movement, also known as a daily return or daily movement. Here we can see the formula. There are 252 trading days in a year excluding weekends. We can take the square root of 252. This gives us 16 and this is the number that can help us find the daily movement.

[00:03:32.22] - Speaker 1
Let's take an example as this concept tends to be very important because it helps us understand the potential of market movement. If our volatility is 32%, we use 16 to arrive at the daily move and we will see that our daily move is 2%. It is important to note that 16 works for markets that are only open during the week, for example the stock market or the option market. What we can say at this point is that implied volatility can be seen as the future expectation of historical volatility. It reflects the sentiment of market participants regarding a potential magnitude of future price changes in the underlying asset.

[00:04:04.16] - Speaker 1
But be careful because it is an expectation but it should be seen as a future proxy. Historical and implied volatility do not always match. Let's try to understand why in the next slide. This is a chart from our Q models. Implied volatility comes from the supply and demand in the option market and from the market positioning of long or short karma or going long or short options.

[00:04:26.00] - Speaker 1
This is one of the reasons why we use volumes and open interest in our models to calculate the gamma exposure of an index or stock. That exposure to gamma allows us to know if the market maker is a long option and therefore long gamma or vice versa. When the market maker is long gamma, it means that they are short volatility and this can help us use options more effectively. Implied and historical volatility are close but do not always coincide. Implied volatility is typically used to price an instrument based on option volumes.

[00:04:53.29] - Speaker 1
In some cases, when implied volatility cannot be calculated for a specific asset, an investor can use historical volatility as a proxy. In this graph we have the historical one month volatility of the SPX and the vix. In this chart we use the VIX as the proxy for implied volatility. As we can see, the VIX tend to always trade at a premium to historical volatility, so we can use this spread as a checking tool for arbitrage opportunities. In fact, traders can trade a spread between historical and implied volatility.

[00:05:22.06] - Speaker 1
We have also added a chart of implied and historical volatility in our QModa's main chart. Here you can quickly understand, for example, if the price of the SPX is trading at a premium versus its historical volatility. You can also use the main level table to quickly understand the volatility regime. There are two categories to describe this regime. We have positive where in this scenario implied volatility is greater than historical volatility and we have negative where implied volatility is lower than historical volatility.

[00:05:50.10] - Speaker 1
Now let's look at another chart where we have the historical average of historical and implied volatility and the typical minimum and max movement of historical and implied volatility. In the first box we can see that on average the implied volatility is higher than the historical one. This is due to what we said before where implied volatility due to uncertainty tends to be priced at a premium compared to historical volatility. If we look at the next section we see that implied volatility tends to be less volatile than the historical one, especially when we look at the historical volatility of near maturity options. We saw when we studied Gamma and Delta that the closer you get to the expiration and the up demand strikes, the more volatile the market movements are.

[00:06:28.01] - Speaker 1
For this reason, the historical volatility of this option near expiration is very high. At this point, let's reconnect the concept of Gamma with implied volatility when comparing long options and short options or long Gamma and short gamma. When we are long option, we are long Gamma. In this case we want the market movement to be higher than the implied volatility. If we are long Gamma, we pay a premium and theta plays against us if the option does not enter in the money quickly.

[00:06:51.25] - Speaker 1
If instead we are short options, we are short gamma, receiving a premium. We want the market to move less than the implied volatility. We want the theta to work for us. Now that we talked about the two types of volatility, we can focus on the Greek that follows the volatility. In the next section, we will study vega.

[00:07:07.22] - Speaker 1
Let's start with the definition. The vega of an option is the measure of the sensitivity of options prices to changes in the underlying implied volatility. It measures how much the price of an option is expected to change for a 1 percentage point change in implied volatility if all other factors remain constant. We know that the Gamma and theta Greeks have exposure to historical volatility. Or rather, we know that Gamma and theta helps us understand whether we are gaining or losing based on the exposure we have to historical volatility.

[00:07:35.12] - Speaker 1
Vega, on the other hand, shows the exposure to future expectations through implied volatility. This is an important point because as we said in the previous section, historical and implied volatility do not always go in the same direction. For this reason, it is also very important to follow Vega. Looking at the different Greeks is important because it helps us to understand what risk our option is exposed to, in which direction these Greeks are going and our risk. And if these Greeks have a positive or negative relationship.

[00:08:01.22] - Speaker 1
At this point, we know that if we are long options, our Vega is positive. But why? Because when we are long options, implied upside volatility is good for our position. If you recall from the previous section, as the volatility of an out of the money option increases, its time value increases the closer the option gets to money. In this case, thanks to the increase in volatility, the value of our option also increases.

[00:08:24.03] - Speaker 1
And finally, options that have a long term maturity have a positive Vega increase in volatility increases their value. Volatility increases the uncertainty that long term options will enter in the money before expiration. An option that has no volatility has no movement and therefore no value. What we said before is important and must be repeated. An option increases in value due to volatility because its time value increases.

[00:08:48.09] - Speaker 1
If we go back to this chart, we see that the time value is higher when we are close to add the money because uncertainty is higher. If this is true, then the vega also is at the highest value close to at the money, because if Vega increases, it increases the time value. Especially when we get close to at the money. The more time passes, the more the value of Vega decreases. Options with longer expirations have a higher Vega because they have more sensitivity to volatility, which increases the uncertainty that the option could end up in the money.

[00:09:14.29] - Speaker 1
And as you can see here, the profile becomes clearer as time passes. The more the Vega profile decreases very close to expiration. The vega has little effect on the value of the option. Let's take an example. Vega is expressed as a monetary quantity per unit of volatility.

[00:09:29.24] - Speaker 1
If the vega of our option is 0.15 and the volatility increases by 1%, this means that the value of our options increases by $0.15. Now that we have learned the different Greeks, let's continue with the theoretical part of the course. We will then put everything together in the practical section.