【正文】 a pure credit instrument ?Whichever way the price of the spot rate of exchange moves, one party always has an incentive to default(違約動機） Eg,FX,$163。 情況三： 10月 26日，美元利率上升至： i$=%，導致 新元匯率貶值至： St$/s$ =$$ 因此，在 10月 26日，到 12月 16日交割的期貨合約價格就變?yōu)椋? Futt,T$/s$ = St$/s$ [(1+i$)/(1+is$)]Tt＝ ()[(1+%)/(1+%)][51/365]=$$（以此價格賣出） 此時，公司在期貨市場的損失為： Profit on futures: Futt,T$/s$ Fut0,T$/s$ =$$$$ =－ $$ 由于新元貶值，公司債務成本節(jié)約，即公司收益為： Loss on underlying short position in the spot currency: (St$/s$ E[St$/s$ ])=($$ $$=+$$ 凈收益＝ － $$ +$$ ＝ +$$，收益總額為： $3000 所得增加是因為新加坡利率上升，基差改變所致。） In this case, the currency of the underlying exposure (f1) is different from the currency of the futures contract (f2). In the delta hedge, spot rate changes (std/f) were regressed on changes in futures prices (futtd/f). In the cross hedge, std/f2 is substituted for the independent variable futtd/f2 because ? the maturity of the futures contract is the same as that of the underlying transaction in the spot market, and ? futures prices converge to spot prices at maturity. An example of a CME cross hedge ? It is now January 18. You need to hedge a DKr （丹麥貨幣） 100 million obligation due on June 16. ? Spot (cross) exchange rates are $, €, and $€. ? A CME € futures contract expires on June 16 with a contract size of €100,000 ? In this cross hedge, there is a maturity match but a currency mismatch. ? Based on st$/DKr = a + b st$/€ + et , you estimate b = with r2 = . ? How many CME futures contracts should you buy to minimize the risk of your hedged position? The cross hedge solution Optimal hedge ratio: NFut* = (amt in futures)/(amt exposed) = b ? (amt in futures) = (b)(amt exposed) = ()(DKr100 million) = DKr104 million or €78 million at (DKr104m) (€) or 780 contracts. ? With an rsquare of , this is a fairly high quality hedge. DeltaCross Hedge （德爾塔交叉套期保值） ? 總結： most general case is the deltacross hedge. ? A deltacross hedge is used when there is both a currency and a maturity mismatch std/f1 = a + b futtd/f2 + et the underlying exposure and the futures contracts are in the same currency, then f1 = f2 = f and the hedge is a delta hedge. there is both a maturity and a currency match, then a futures hedge is nearly equivalent to a forward market hedge. std/f = a + b std/f + et 由于 std/f 與 std/f 的相關系數(shù)為 +1，所以，是完全套期保值（ r2=1），套期保值比率為 NFut*=b＝－ 1，此時期貨套期保值與遠期套期保值是等值的，貨幣風險可以完全消除。 例如，一家英國公司有加元債務，可以利用美元期貨的多頭來規(guī)避匯率風險，因為，美元與加元是高度相關的。 Switzerland) CME Chicago Mercantile Exchange (.) CBOT Chicago Board of Trade (.) Euronext (Amsterdam, Brussels, Lisbon, Paris, London) NYMEX New York Mercantile Exchange (.) BMamp。F Bolsa Mercadorias amp。為加元債務避險的美元套期保值法：加元債務的現(xiàn)貨價格變化率與美元期貨價格變化率的關系如下： st163。/$+ et 當二者的期限匹配時，上式可變化為： std/f1 = a + b std/f2 + et f1 = currency in which the underlying exposure is denominated f2 = currency used to hedge against the underlying exposure （由前面的公式轉化而來，由即期匯率變化率替代期貨匯率變化率是因為期貨到期時的價格與即期匯率具有趨同性。） Maturity mismatches and Delta hedges ? Futures hedge is called a delta hedge when there is a mismatch between the maturity