POLI(Y RESEARC-H WORKING PAPFR 1226

# **Summary findings**

> Comnmodity prices have historically been amiong the most volatile of international prices. Measured volatility (ttie standard deviation of price changes) has

> not been below _15_ percent and at times has been **morc** than 50 percent. Ofte the volatility of comimiiodity vptio(.1 prices has exceeded that of exclhanige rates and inttrest rates.

The large price variations aire caused by disturbances in demand and supply. Stocklioldinig leads to some1c price smoothing, **but** wheni stocks ire low, prices CnI **jurnp** sharply. As a resLult, commnodity price series are not stationary and in some periods they jump abruptly to high levels or fall precipitously to low levels relative to their long-run average. 'Thus it is difficult to determine long-term price trends and the uriderlying distribution of prices, The volatility of commodity prices makes price forecasting difficult. Indeed, realized prices often deviate greatly from forecasted prices, which hals led to the practice of giving forecasts probability ranges. But assigning probability raniges reqtiii s forecasting future price volatility, which, given uncertainties about true price distribution, is difficult.

**Onie** potentially useful source of intormiatio n for forecasting volatility is thle volatility torecasts imbedded in the prices of optionis written o0n comniodities traded in exchanges. Options give the holder thle right to buy (call) or sell (put) a certain

> CoMiModit at a cert ain dILt at a ti xed (exercise) _price._

> Options prices depend on several vari-bles, ofne ot W hic i **iI** th eCxpected volatilitN up to the nuat i- ir date. Given a spc.ific th oretical nodel, thc lmarket prics **ot** _CMhe_ **_[I_** e(1d to derive tht market s expc.;tions about price volatility and the price distribmrior.

> Kroner, Krnafsev, anid C(lae'sens svstemalticalvl analyze differe-rt iet hods' abilities to for Ccast comimiOdity price volatiiity (for several ioniniodities). They collccted the daily prices of comimniodity options anci other variables for seven commodities (cocoa, corni, cotton, gold, silver, sugar, and wheat). They extracted the volatility forecasts iilplicit in options prices using icveral techniqUes. They compared several volatility forecasting methods, divided into three categories:

(I) Forecasts usinig only expcctations derived from options prices.

(2) ForCCasrs uSitng 0nIv timei-series miodeliig. (3) Forecasts rhat cormilniie market expe';tations and time-series mocdeling (a nue mthtocd devised for this purpose),

> Ihtiv fir d that the volartili-y forecasts prodLce ih metho o d 3 ( tpertiorm the firsr two as vell as hth naive torecast hased on historical *olatilitv IThis result hiolds horh in and on t of simple for almost all conmmtodities consiid-red.

This papera product of the Debt and Internationial F inince l)Ivision, Ir rerna t ional con omics Department **-is** part of a larger effort in the departmenit to study the short- and long- run behavior of primary conimiodity prices and the implications for developing countries of movemernts in these prices. The study was funded hy the Bank's Research Support Budget under the research rroject 'Measurernent of Commodity Price Vo!atility" (RPO 676-73). Copies of this paper are available free fro<m the World Bank, 181 8 H Street NW, Washlington, D)C 20433. Please contact Faten Hatab, room H8-099, extension 35835 (22 pages). November 1993.

_I 7'he Poliy iResearch Working Paper Series disse ;inatcs t!u nd:ings of isork in_ /'r,jgr(5s _t; 'ii. ,u'a;e tfc exfl'hanve d_ **_O,WS_** _.,',Ut development issues. An objective of the series is toget thte findin's ourt_ **_quicklv._** _c en in the presentatri_ **_<arc_** _, lss thn tuil;_ **_),Iise/l. Ii'_** _papers carrv the names of the authors and ihould bcl_ **_used_** _and_ **_(u,d zco'rditnel._** _/lI'iendins._ **_rnt,'r(_** _letv,uns,_ **_.iand_** _,rn, lsiois_ **_are,_** _te| authors' own and should not be attributed to) the 'Torld liank, its 1 .xCcutii_ **_'lri 'if_** _t, r'._ **_lr_** _a_ " **54**

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