# Volatility

A measure of the rate of fluctuations in the prices of a security over time

A measure of the rate of fluctuations in the prices of a security over time

Volatility (Vol for short) is a measure of the rate of fluctuations in the prices of a security over time. It indicates the levels of risk and uncertainty that are associated with the price changes of a security. Investors and traders calculate the volatility of a security to assess past variations in the prices to predict their future movements.

Vol is determined either by using the standard deviation or beta. Standard deviation measures the amount of dispersion in a security’s prices. Beta determines a security’s volatility relative to that of the whole market. Beta can be calculated using regression analysis.

It measures the fluctuations in the security’s prices in the past. Historical Vol is used to predict the future movements of prices based on previous trends. However, it does not provide insights regarding the future trend or direction of the security’s prices.

It refers to the volatility of the underlying asset, which will return the theoretical value of an option equal to the option’s current market price. Implied Vol is a key parameter in option pricing. It provides the forward-looking aspect on future price fluctuations.

The simplest approach to determine the volatility of a security is to calculate the standard deviation of its prices over a period of time. It can be done by using the following steps:

- Gather the security’s past prices.
- Calculate the average price (mean) of the security’s past prices.
- Determine the difference between each price in the set and the average price.
- Square the differences from the previous step.
- Sum the squared differences.
- Divide the squared differences by the total number of prices in the set (find variance).
- Calculate the square root of the number obtained in the previous step.

You want to find out the Vol of the stock prices of ABC Corp. for the past four days. The stock prices are given below:

- Day 1 – $10
- Day 2 – $12
- Day 3 – $9
- Day 4 – $14

To calculate the volatility of the prices, we need to:

- Find the average price:
$10 + $12 + $9 + $14 / 4 =**$11.25** - Calculate the difference between each price and the average price:

Day 1: 10 – 11.25 =**-1.25**

Day 2: 12 – 11.25 =**0.75**

Day 3: 9 – 11.25 =**-2.25**

Day 4: 14 – 11.25 =**2.75** - Square the difference from the previous step:

Day 1: (-1.25)^{2 }=**1.56**

Day 2: (0.75)^{2 }=**0.56**

Day 3: (-2.25)^{2 }=**5.06**

Day 4: (2.75)^{2 }=**7.56** - Sum the squared differences:

1.56 + 0.56 + 5.06 + 7.56 =**14.75** - Find the variance:

Variance = 14.75 / 4 =**3.69** - Find the standard deviation:

Standard deviation =**1.92**(square root of 3.69)

In the example above, the standard deviation indicates that the stock prices of ABC Corp. usually deviate from its average stock price by $1.92.

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