第3章用于汇率风险管理的衍生产品：货币期权与期权市场

Chapter 3Derivative Securities for Currency Risk ManagementCurrency Options and Options Markets 圣经故事。在 圣经 创世记 第 29章曾经提到过，大约在公元前 1700年，雅克布用七年的劳动购买了一个准许他与拉班的女儿拉结结婚的期权。但是后来，拉班违约了，他强迫雅克布与自己的大女儿利亚结了婚。雅克布照办了，但是，他深爱的仍然是拉结。于是，他购买了另一个期权，即再劳动七年以换得与拉结结婚。这一次，拉班没有食言。最后，雅克布娶了两个老婆，生了 12个儿子。圣经故事、橄榄压榨机与荷兰郁金香 橄榄压榨机故事。古希腊的数学家和哲学家泰利斯在橄榄丰收之前利用期权获得了低价使用橄榄压榨机的权利。据说，他是第一个利用期权交易致富的人。泰利斯生活在公元前 580年左右古希腊的米利塔斯市，位于今天土耳其的西南海岸。泰利斯运用自己的天文知识在冬季就预测到橄榄在来年春天将获得丰收。虽然没有什么钱，然而他用自己所有的积蓄在冬季淡季就以低价取得了春季旺季所有压榨机的使用权。当然，他支付的价格也很低，因为当时没有人认为有必要为了这些压榨机来竞价。当春天橄榄获得大丰收时，每个人都想找到压榨机。这时，泰利斯执行他的权利，将压榨机以高价出租，结果赚了一大笔钱。圣经故事、橄榄压榨机与荷兰郁金香 荷兰郁金香故事。在 17世纪 30年代的 “ 荷兰郁金香热 ”时期，郁金香的一些品种堪称欧洲最为昂贵的稀世花卉。1635年，那些珍贵品种的郁金香球茎供不应求，加上投机炒作，致使价格飞涨 20倍，成为最早有记载的泡沫经济。这股投机狂潮却开启了期权交易的大门。郁金香交易商向种植者收取一笔费用，授予种植者按约定最高价格向该交易商出售郁金香球茎的权利（卖权）。同时，郁金香交易商通过支付给种植者一定数额的费用，以获取以约定的最低价格购买球茎的权利（买权）。这种交易对于降低郁金香交易商和种植者的风险十分有用。圣经故事、橄榄压榨机与荷兰郁金香Chapter Overviewn What is an optionn Option payoff profilesn Combinations of optionsn The determinants of currency option valuesn Hedging with currency optionsA forward obligationSuppose a U.S. company has a forward obligation of 1 million due at time T in four months. Current spot and forward rates are S0$/ = FT$/ = $1.45/.n The expected amount due on this forward obligation isECFT$ = (ECFT )(EST$/ ) = (1,000,000)($1.45/) = $1,450,000.n If the actual exchange rate is $1.50/, then this 1 million obligation will costCFT$ = (CFT )(ST$/ ) = (1,000,000)($1.50/)= $1,500,000.q In this case, the U.S. company has an unexpected loss of $50,000. Underlying transaction-1,000,000Currency exposureV$/S$/A forward hedgen This forward exposure can be hedged by buying pound sterling in the forward market, which in this case means simultaneously selling dollars forward.n Buy 1 million in the forward market at the forward price F1$/ = $1.45/n The cash flow time line and the payoff profile of the forward contract are shown on the slide based on the forward rate of exchange is FT$/ = $1.45/. If the actual exchange rate is ST$/ = $1.50/, then purchasing 1,000,000 at the forward price of FT$/ = $1.45/ will save you $50,000 and offset your loss on the underlying exposure. Conversely, if the pound falls to $1.40/, you will gain $50,000 on the underlying obligation but lose $50,000 on the forward contract.A forward hedgen Wouldnt it be nice to own an insurance policy against a rise in the exchange rate without a corresponding loss if exchange rates fall?Long pound forward+1,000,000-$1,450,000Exposure of forward contractV$/S$/An option hedgen A currency option is like one-half of a forward contractq the option holder gains if pound sterling risesq the option holder does not lose if pound sterling fallsLong pound call(option to buypound sterling)S$/V$/An option hedgen Options are used for two purposes:- Hedging- SpeculationHedging is by far the more common use by corporate financial managers.n In this example, a call option on pound sterling acts as an insurance policy (a hedge) against a rise in the value of the pound. - If the actual exchange rate rises to ST$/ = $1.50/ at expiration, then the option provides a payoff of (1,000,000)($0.05/) = $50,000.- If the actual exchange rate falls to ST$/ = $1.40/, then the option is out-of-the-money and is not exercised. n Of course, this insurance policy does not come free. The cost of the option is called the option premium. The option holder pays the option premium when the option is purchased. Options Contracts: Preliminariesn A foreign currency option is a contract giving the option purchaser (the buyer) the right, but not the obligation, to buy or sell a given amount of foreign exchange at a fixed price per unit for a specified time period (until the maturity date).n The buyer of an option is termed the holder, while the seller of the option is referred to as the writer or grantor.n Every option has three different price elements:q The exercise or strike price the exchange rate at which the foreign currency can be purchased (call) or sold (put)q The premium the cost, price, or value of the option itselfq The underlying or actual spot exchange rate in the marketOptions Contracts: Preliminariesn An option gives the holder the right, but not the obligation, to buy or sell a given quantity of an asset in the future, at prices agreed upon today.n Calls vs. Putsq Call options gives the holder the right, but not the obligation, to buy a given quantity of some asset at some time in the future, at prices agreed upon today.q Put options gives the holder the right, but not the obligation, to sell a given quantity of some asset at some time in the future, at prices agreed upon today.Options Contracts: Preliminariesn European vs. American optionsq European options can only be exercised on the expiration date.q American options can be exercised at any time up to and including the expiration date.q Since this option to exercise early generally has value, American options are usually worth more than European options, other things equal.Options Contracts: Preliminariesn Intrinsic Valueq The difference between the exercise price of the option and the spot price of the underlying asset.n Speculative Valueq The difference between the option premium and the intrinsic value of the option.Option Premium =Intrinsic ValueSpeculative Value+Currency Options Marketsn PHLX(费城证券交易所 )n HKFE（香港期货交易所）n 20-hour trading day.n Options on the over-the-counter (OTC) market can be tailored to the specific needs of the firm but can expose the firm to counterparty risk.n Options on organized exchanges are standardized, but counterparty risk is substantially reduced.n OTC volume is much bigger than exchange volume.n Trading is in seven major currencies plus the euro against the U.S. dollar.PHLX Currency Option SpecificationsCurrency Contract SizeAustralian dollar AD50,000British pound 31,250Canadian dollar CD50,000Euro 62,500Japanese yen 6,250,000Swiss franc SF62,500Foreign Currency OptionsStatus of an optiona. In-the-moneyCall: Spot strikePut: Spot strikec. At-the-moneySpot = the strikeCurrency Futures Optionsn Are an option on a currency futures contract.n Exercise of a currency futures option results in a long futures position for the holder of a call or the writer of a put.n Exercise of a currency futures option results in a short futures position for the seller of a call or the buyer of a put.n Firms may purchase currency call options to n They may purchase currency call optionsq to hedge future payables;q to hedge potential expenses when bidding on projects; andq to hedge potential costs when attempting to acquire other firms.n Speculators may purchase call options on a currency that they expect to appreciate. Profit =selling (spot) price option premium buying (strike) pricen They may also sell (write) call options on a currency that they expect to depreciate.q Profit = option premium buying (spot) price+ selling (strike) priceThe functions of Call Optionn The purchaser of a call option will break even whenselling price =buying (strike) price + option premiumn The seller (writer) of a call option will break even whenn buying price = selling (strike) price+ option premiumBreakeven on Call OptionESTProfitlossc0 E + c0Long callESTProfitlossc0E + c0 short 1 calln Firms may purchase currency put options to hedge future receivables.n Speculators may purchase put options on a currency that they expect to depreciate. q Profit =selling (strike) price buying price option premiumn They may also sell (write) put options on a currency that they expect to appreciate. n Profit = option premium + selling price buying (strike) priceThe functions of Put OptionESTProfitloss p0 E p0long putE p0ESTProfitp0E p0short put E + p0Breakeven on Put OptionThe purchaser of a put option will break even whenbuy price =selling (strike) price - option premiumThe seller (writer) of a put option will break even whenselling price = buying (strike) price-option premiumPayoff profile of a call option at expirationLong call Short callST$/CallT$/KT$/ST$/-CallT$/KT$/In-the-moneyOut-of-the-moneyOut-of-the-moneyIn-the-moneyCurrency options are a zero-sum game; gains on one side are offset by losses on the other.Payoff profile of a put option at expirationShort putKT$/Long putST$/PutT$/ST$/-PutT$/KT$/In-the-moneyOut-of-the-moneyOut-of-the-moneyIn-the-moneyAs in the previous slide, options are a zero-sum game;gains on one side are offset by losses on the other.Forwards, puts, and callsA Forward by Any Other Namen A combination of a long call and a short put at the same exercise price and with the same expiration date results in a long forward position at that forward priceST$/CallT$/ FT$/-PutT$/ST$/ST$/Long call Short put Long forward+ =Forwards, puts, and callsA Forward by Any Other NameConversely, a short call and a long put with the same exercise price and expiration date is equivalent to a short forward position.ST$/-CallT$/ -FT$/PutT$/ST$/ST$/Short call Long put Short forward+ =A Forward by Any Other Name :Put-call parityLong forward=FT$/ST$/-PutT$/ST$/Short put+ST$/CallT$/Long call KT$/ST$/+Exercise priceKT$/Put-call parity relates call and put values to the value of a forward contract.nWhen we want to talk about the value (rather than changes in the value) of a long call and a short put, we need to adjust for the exercise price.The general case is called “put-call parity” and relates the value of a long call, a short put, the exercise price, and the forward price at expiration:CallTd/f - PutTd/f + Kd/f = FTd/fCombinations of options -A Straddle optionn One possible speculative strategy for volatile currencies is to purchase both a put option and a call option at the same exercise price. This is called a straddle. n Long straddle=a long call and a long put on the same underlying asset and with the same exercise price. n Short straddle=a short call and a short put on the same underlying asset and with the same exercise price. KT STSTKTVTVTLong straddle Short straddleCombinations of options -A Straddle optionn Heres an