EBF 301
Global Finance for the Earth, Energy, and Materials Industries

Volatility

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There are many parameters to calculate the volatility. One indicator is calculating the moving (rolling) standard deviation for the changes of price rather than the actual price.

A change in price is also called a return in finance. It can be simply calculated as:

change= P t P t1 P t1 = P t P t1 1

Example:

We calculate the price changes (return) in the third column and then calculated the 10-period daily standard deviation for the returns. This is a measure for volatility.

Feb. Futures crude oil NYMEX Arithmetic Change 10-period daily standard deviation
2-Jan-18 60.37
3-Jan-18 61.61 2.05%
4-Jan-18 61.98 0.60%
5-Jan-18 61.49 -0.79%
8-Jan-18 61.73 0.39%
9-Jan-18 62.92 1.93%
10-Jan-18 63.6 1.08%
11-Jan-18 63.81 0.33%
12-Jan-18 64.22 0.64%
16-Jan-18 63.82 -0.62% 0.93%
17-Jan-18 63.92 0.16% 0.78%
18-Jan-18 63.96 0.06% 0.88%
19-Jan-18 63.38 -0.91% 0.80%
22-Jan-18 63.66 0.44% 0.85%
23-Jan-18 64.45 1.24% 0.85%
24-Jan-18 65.69 1.92% 0.83%
25-Jan-18 65.62 -0.11% 0.86%
26-Jan-18 66.27 0.99% 0.93%
29-Jan-18 65.71 -0.85% 1.08%
30-Jan-18 64.64 -1.63% 1.08%
31-Jan-18 64.82 0.28% 1.14%

Note:

Return can be calculated using the mathematical method P t P t1 P t1 or using the natural log method. Log change (return) can be calculated using the following equation:

change (return) = Ln( P t )Ln( P t1 )=Ln( P t P t1 )

In the following table both methods are used to calculate the price change (return). As you can see, surprisingly, both methods give very similar values. The natural log method might be preferred for computational purposes.

Feb. Futures crude oil NYMEX Arithmetic Change Natural Log Change
2-Jan-18 60.37
3-Jan-18 61.61 2.05% 2.03%
4-Jan-18 61.98 0.60% 0.60%
5-Jan-18 61.49 -0.79% -0.79%
8-Jan-18 61.73 0.39% 0.39%
9-Jan-18 62.92 1.93% 1.91%
10-Jan-18 63.6 1.08% 1.07%
11-Jan-18 63.81 0.33% 0.33%
12-Jan-18 64.22 0.64% 0.64%
16-Jan-18 63.82 -0.62% -0.62%
17-Jan-18 63.92 0.16% 0.16%
18-Jan-18 63.96 0.06% 0.06%
19-Jan-18 63.38 -0.91% -0.91%
22-Jan-18 63.66 0.44% 0.44%
23-Jan-18 64.45 1.24% 1.23%
24-Jan-18 65.69 1.92% 1.91%
25-Jan-18 65.62 -0.11% -0.11%
26-Jan-18 66.27 0.99% 0.99%
29-Jan-18 65.71 -0.85% -0.85%
30-Jan-18 64.64 -1.63% -1.64%
31-Jan-18 64.82 0.28% 0.28%