# Professional Trading through Option Theory

## 15.1 - Framework

Now that we have understood Delta, Gamma and Theta, it is time to learn about the Vega Option Greek. As most people know, Vega is the rate at which the option premium changes in relation to volatility. The question is: What exactly is volatility? This question was asked to many traders and they all answered that volatility is the movement of the stock exchange. If you share a similar opinion about volatility, it is time to fix that.

Here is the agenda. I imagine this topic will spread over several chapters.

1. We will be able to understand volatility.
2. Learn how to measure volatility
3. Practical Application of Volatility
4. Learn about the different types of volatility
5. Understanding Vega

Let's get started.

## 15.2 -The concept of Moneyball

You may have seen the movie 'Moneyball' in Hollywood. It's the true story of Billy Beane, a manager for a US baseball team. This movie tells the story of Billy Beane and his young colleague and how statistics can be used to identify talented but low-profile baseball players. This was a novel and disruptive method, one that was not common at the time.

Watch the Moneyball trailer here.

This movie is a great film, not only because of Brad Pitt but also because it conveys a message about business and life. While I won't go into detail, let me share some of the Moneyball methods to explain volatility.

Although the discussion below might not seem to be related to stock market, please do not get discouraged. It is pertinent and will help you understand the term "Volatility", I can assure that.

Consider 2 batsmen, and the total runs they have scored in 6 consecutive matches. (CHART)

The captain of the team is you. You must choose between Mike or Billy for the 7 th match. You should choose a reliable batsman. This means that the batsman you select should be in a position where they can score at least 20 runs. Which one would you choose? Based on my experiences, I've noticed that people approach the problem in one way or another.

1. Calculate the total score of the batsmen (also known as Sigma) and pick the player with the highest score to play the next game. Or...
2. Calculate the average, also known as'Meaning', number of games scored - choose the batsman who has a higher average.

Let's do the same thing and see how many numbers we get.

• Billy's Sigma = 20 +23 +21 +24 + 19 +23 = 130
• Mike's Sigma = 45 +13 +18 +12 +26 +19 = 133

Based on the sigma score, Mike is likely to be selected. Let's calculate the average or mean for each player and see who is better.

• Billy = 130/6 = 21,67
• Mike = 133/6 = 22,16

Mike is a worthy candidate from both the mean perspective and the sigma perspective. Let's not forget that we aren't done yet. The idea is to pick a player that can score at most 20 runs. With the information we have (mean, sigma), it is impossible to determine who can score at minimum 20 runs. Let's continue our investigation.

We will first calculate the deviation from mean for each match. We know that Billy's average is 21.67 and that he scored 20 runs in his first match. The deviation from the mean in the first match is 20 - 21.67 = and 1.67. He scored 1.67 runs less than his average score. It was 23.67 = +1.33 for the 2 matches,meaning that he scored 1.33 more runs than his average score.

This diagram shows the same for Billy.
(IMAGE 1)

The middle black line is the average score for Billy. The double-arrowed vertical line shows the deviation from that mean for each match. Now we will calculate another variable, 'Variance.

Variance simply refers to the summation of squares of the deviation divided with the total number observations'.It may sound dangerous but it is not. The total number observed in this instance is equal to the number of matches played.

Variance can also be calculated as -

Variance = [-1.67 2+ (1.33)? 2+ (-0.67)?2+ (+2.33)?2+ (-2.67)?2+ (1.33)]/6
6. = 19.33
= 3.22

We will also define another variable,'Standard Deviation'(SD), which is calculated as:

std deviation = variance

The standard deviation for Billy then is -
= SQRT (3.22)
= 1.79

Mike's standard deviation is 11.18.

Let's add all the numbers or statistics here.
(CHART)

We all know what 'Sigma' and 'Mean' mean, but what about the SD. The deviation from the average is represented by the Standard Deviation.

Here's the textbook definition for SD " Statistics use the standard deviation, also known as the Greek letter Sigma, to measure the variation or dispersion in a set data values.

Do not confuse the two sigmas. The total is also known as the Greek symbol sigma and the standard deviation is sometimes called sigma. To refer the total we use The Greek symbol s.

SD can be used to project the runs that Mike and Billy will score in their next match. This projected score can be obtained by subtracting the SD from their average.
(CHART)

These numbers indicate that Billy will likely score between 19.81 to 23.39 in the 7 th match, while Mike could score between 10.98 to 33.34. It is difficult to predict if Mike will score at least 20 runs, as Mike's range is so wide. He can score 10, 34, or any other number in between.

Billy is more consistent, however. He is not a great hitter or a good player, so his range is small. He can be expected to be consistent, scoring anywhere from 19 to 23. In other words, choosing Mike over Billy in the 7 th match could be risky.

Let's go back to the original question: Which player is more likely score at least 20 runs? The answer is obvious: Billy. Mike is more risky than Billy, but Billy is more consistent and cautious.

In principle, this allowed us to assess the riskiness of these players using " Standard Deviation". Therefore, 'Standard Deviation must be'risk'. Volatility is the level of risk associated with a stock or index in the stock market. Volatility can be defined as a percentage of the standard deviation.

I have chosen the definition of volatility from Investopedia: "A statistical measure that measures the spread of returns for a security or market index." You can measure volatility by measuring the standard deviation and variance of returns from the same security or market index. Generally speaking, the standard deviation is higher than the risk.

If Infosys and TCS have volatility of 25% and 45 percent, respectively, then Infosys clearly has lower price movements than TCS.

## 15.3 - Few Food for thought

Let's make a prediction before I close this chapter.
Today's Date = 15 July 2015
Nifty Spot = 8547
Nifty Volatility = 16.5%
TCS Spot = 2585
TCS Volatility = 27%

Can you predict where TCS and Nifty will trade in 1 year?
Yes, we can.Let's use this no . s for something good-
(CHART)

The above calculations indicate that Nifty will trade between 7136 to 9957 in the next year. All values between have varying probabilities of occurring. Accordingly, the probability that Nifty will trade between strong>7136 and 9957 on the 15th July 2016 could be 25%, while the probability that it will trade around 8600 could be 40%.

This brings us to an exciting platform.

1. We have estimated the Nifty range for one year. Can we also estimate the Nifty range that Nifty will trade in the next few days, or the range Nifty will trade until the series expiry?
1. This will allow us to spot options that could expire worthless and be able to sell them now to make a profit.
2. Nifty's range of trades in the next year was calculated as 7136 and 99757. But how confident are we? This range can be expressed with confidence.
3. How can we calculate volatility? Yes, I know that we have discussed this earlier in the chapter. But is there a simpler way to calculate Volatility? We could use MS Excel to help us!
4. Nifty's range was calculated by estimating its volatility at 16.5%. What if volatility changes?

In the following chapters, you will find answers to all of these questions!

### Keypoints

1. Vega is the rate at which the premium changes in relation to volatility.
2. Volatility does not refer to just market up-and-down movements.
3. Volatility can be described as a measure of risk.
4. The standard deviation is used to estimate volatility.
5.    Standard Deviation can be extracted through the square root of variance.
6. Given its volatility, we can calculate the stock price range.
7. The stock's range is a sign of its volatility, or risk.