# **Summary**

Commodity prices have historically been one of the most volatile of international prices. Measured volatility (the standard deviation of price changes) has not been below 15% and at times has been more than 50%. During many periods the volatility of commodity prices has exceeded the volatility in exchange rates and interest rates. The cause of the large price variations are disturbances in demand or supply. Stockholding leads to some price smoothing but when stocks are low, prices can jump very sharply. As a result, commodity price series have two important features. First, they display non-stationarity. Second, there are periods when prices jump abruptly to very high levels (or fall to very low levels) re!ative to their long run average. These two features make it very difficult to determine the long-term price trend and the nature of the underlying distribution of prices.

The high levels of commodity price volatility make price forecasting extremely difficult and, indeed, large ex-pgs deviations of realized prices from forecasted prices are common. This has motivated the practice of providing probability ranges around the forecast. This, in turn, requires forecasts of future price volatility which, given the uncertainty about the nature of the true price distribution, has also proven difficult. One potentially useful source is the volatility torecasts imbedded **Ln** prices of options written on commodity prices traded on exchanges. Options give the holder the right to buy (call) or sell (put) a certain commodity at a certain date at a fixed (exercise) price. Option prices depend on a number of variables, one of which is the expected volatility over the horizon to the maturity date. Thus, given a specific theoretical model, market prices of options can be used to derive the market's expectation of price volatility and the price distribution.

This paper provides a systematic analysis--covering several commodities--of the ability of different methods of forecasting commodity price volatility. Daily prices of commodity options and other variables were collected for seven commodities (cocoa, corn, cotton, gold, silver, sugar and wheat). The volatility forecasts implicit in the option prices were then extracted using several techniques. The paper compares several different forecasts of commodity price volatility, divided into three categories: (1) forecasts using only expectations derived from options prices; (2) forecasts using only time series modelling; and (3) forecasts which combine market expectations and time series modelling. Methods (1) and (2) have been used extensively in the literature, while use of method (3) for this purpose is new. The paper finds that combining market expectations and time series modelling (method (3)) gives volatility forecasts which outperform both market expectations forecasts and time series forecasts as well as the naive forecast based on historical volatility. This iesult hold both in and out of sample for virtually all commodities considered. These results hold promise for deriving probability distributions for commodity price forecasts which will perform considerably better than methods now being used.