Absolute prices

Commodity prices are expressed in such diverse units as cents per pound, dollars per bushel, and yen per dollar. Since we will be interested in price changes rather than in absolute prices, and since we will be wanting to compare price change distributions across a number of different commodities, it will be immensely useful to express all price changes as percentages of their absolute price levels.
If every daily price change- whether the commodity be soy- beans, live cattle, sugar, or Japanese yen- is made dimensionless by dividing that price change by the absolute price of its future and then multiplying by one hundred, then all resulting measures of “spread” will be expressed as dimensionless percentages and will thereby be directly comparable. (If every option price is also expressed as a percentage of its futures price, then every option price will also be expressed in the same units as the daily price changes in its future.)  One thing is immediately clear from the “spread” of each of these distributions about its mean value: During 1996, coffee prices were much more variable than silver prices.
The degree of “spread” of a set of numbers about the average value (mean) of that set of numbers is most commonly specified by its standard deviation, a statistic which can be calculated for any set of numbers or for any continuously variable distribution. The calculation of the standard deviation of a set of numbers involves taking the square root of squares of differences from the mean. Another measure of spread of a distribution is its mean absolute h a t i o n , which, in the case of daily price changes, is the average value of these price changes taking all readings as positive. In classical statistical analysis, the mean absolute deviation is much less used than the standard deviation. This is unfortunate, since the mean absolute deviation as a measure of variability has many advantages, not least of which is its ease of visualization and its simplicity of calculation.
Be that as it may, there is no denying that the standard deviation is the statistic conventionally used in developing option price models. Realistically, therefore, and for comparison purposes if for nothing else, the standard deviation has to be incorporated into any independently derived option pricing formula that I or anyone else dares to come up with!

Tags: commodities, commodity prices, debt, interest, loans, spread