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Theory and Modern Applications

Table 2 Descriptive statistics of the annual gold spot price, its natural logarithm, and its logarithm returns. Source: Data from Bloomberg XAUUSD

From: Calibration of the exponential Ornstein–Uhlenbeck process when spot prices are visible through the maximum log-likelihood method. Example with gold prices

Annual

Standard Spot Price

Natural Logarithm

Logarithm return

Mean

573.70

6.14

4.90%

Standard deviation

415.65

0.65

19.07%

Skewness

1.34

0.41

0.97

Kurtosis

3.56

2.67

5.23