Hedging Options 1 Brief History of Futures 1848

期貨與選擇權 Hedging & Options 1

Brief History of Futures 1848, CBOT (Chicago Board of Trade) 芝加哥交易所成立遠期契約，1860’s 期貨契約 grains → financial instruments, specious metals (金、銀、銅、石油) 商品期貨：農產品、金屬、能源、軟性 (咖啡、可可) 金融期貨：外匯、利率 (短期、長期)、股價指數、利率指數等 A futures contract is a legally binding commitment to make or take delivery of a standardized quantity and quality of a commodity at a price agreed upon in the trading pit or ring of a commodity exchange at the time the contract is executed. 2

Brief History of Futures（續） “forward contracts” v. s. （遠期契約） terms: amount, delibery date, quality, price are set in private by the buyers & sellers “futures contracts” （期貨契約） terms are standaredized with the exception of price ( price is discovered through public auction at an established exchange) Clearing Corporation – it assumes the *1. 標準化—交易標的物之定義 opposite side of each trade. 交易標的數量 契約到期日 交割方式 2. 消除違約風險（結算所背書保證） 3. 逐日結算 3

Hedging 避險期貨交易 “Hedge” means “protection”. Hedge：The buying and selling of offsetting positions in the futures（ 期貨） market in order to provide protection against an adverse change in price. Hedging → ↓price risk （If expect P↓→ sell futures contracts； expect P↑→ purchase futures contract ） The initiation of a futures position that is intended as a temporary substitute for the sale or purchase of the actual commodity. Usually, actual commodity does not change hands in the futures markets : The sale of futures contracts can be offset by the purchase of an equal number of futures contract's at a later date before the contract's delivery date. 4

l The Market Participants： 1. hedgers (避 險 交 易 者 ), include: farmers, country elevator operators, processors, livestock feeders, exporters, importers. To lock in a price and obtain protection against P↑ (buying futures)—“long” position（多頭） (bullish) P↓ (selling futures)—“short” position（空頭） (bearish) 風險轉移的原理： They seek protection against adverse price changes by initiating a position in the futures market as a temporary substitute for the sale or purchase of the actual commodity. 5

2. ”speculators”（投機者）- people who assume risk in antipation of profiting from a change in prices Speculation 有助於價格穩定. Speculators facilitate hedging by providing liquidity - the ability to enter and exit the market quickly & easily. To profit from P↑(buying futures); P↓(selling futures). They can realize a highly leveraged profit if they prove to be correct in anticipating the direction and timing of price changes. 3. Arbitrager （套利交易人）： 同時買賣現貨、期貨，以賺取無風險價差 6

保證金 “margin” – money that buyers and sellers of futures contracts must deposit with their brokers and that brokers in turn must deposit with the Clearing Corporation. – money deposit in case of losses happen “margin call” --- loss ↓, gain ↑ minimum amount ↑ until the open position is closed Deposit more money to maintain minimum margin requirement Clearing Corporation （結算所）assumes the opposite side of each open position and thereby assures the financial integrity of every futures contract traded at the CBOT. Hedge: the buying & selling of offsetting positions in order to provide protection against an adverse change in price. 7

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對沖交易 Hedge 避險期貨交易 Selling (short) hedge - 空頭避險 Buying (long) hedge – 多頭避險 避險功能 投機功能 價格發現功能 (price discovery) bearish 看跌→short； bullish 看漲（多）→long 有opening transaction, 一定要在到期日之前進行closing transaction = liquidation （平倉） 9

“basis” = cash price - futures price 基差 現貨價格 期貨價格 影響Basis之因素：transportation costs, storage costs, interests, S & D (local & overall market) 產地：cash price<future price "normal market" Gulf Coast：cash>future price "inverted market” + stronger ↑ 0 - + ↓weakening, ↑strengthening 0 weaker ↓ - ↑strengthening, ↓weakening 10

Hedging long hedge short hedge basis gain basis loss basis gain if basis weaken (cash falls more or rises less) if basis strengthens (cash falls less or rises more) 11

price $ futures price transportation cost carrying charges present convergence local cash price future time 12

Hedging利用期貨之價差來彌補現貨之價差。不避險時，面對 現貨市場價格波動，避險時面對兩市場間之基差波動（ basis risk）。因為期貨與現貨價格具高度相關性，互沖效果使基差 之波動小於現貨市場價格之波動，故hedging即以basis risk取代 price risk。 Usually, cash price and futures price move in the same direction. Basis fluctuations are usually smaller than cash price fluctuations. $ futures p. cash p. time 13

eg 1: short, futures gain, no basis change ( perfect hedge ) selling (short) hedges: a corn farmer wants to lock in corn price of $2. 20/bu. $0. 16/bu gain results: cash sale price $2. 04/bu + futures gain 0. 16 net selling price $2. 20/bu no change cash forward bid $2. 20/bu no basis change 0 net selling price $2. 20/bu 14

eg 2: short, futures loss, no basis change ( perfect hedge ) cash $2. 20 selling $2. 50 results: cash sale price 2. 50 futures loss - 0. 30 net selling price 2. 20 Ø futures sells $2. 45 buys $2. 75 $0. 30 loss basis $0. 25 under no basis change price objective $2. 20 no basis gain/loss 0 net selling price $2. 20 “perfect hedges ” : basis does not change between the time a hedge was placed and lifted 15

eg. 3 : short, basis weaken ( loss ) cash Sep price for new-crop corn $2. 20/bu Nov. sells 10, 000 bu corn at $2. 00/bu futures sells 2 Dec. corn contracts $2. 45/bu basis $0. 25 under Dec. buys 2 Dec. corn contracts at $2. 30/bu to offset initial short futures position $0. 30 under Dec. 0. 15/bu gain $0. 05 basis loss results: cash sale price $2. 00/bu price objective $2. 20/bu + futures gain 0. 15 - basis loss $0. 05/bu net selling price $2. 15/bu = net selling price $2. 15/bu 16

eg 4: short, basis strengthen ( gain ) Cash Sep $2. 20 sell Nov $2. 18 futures sell $2. 45 buy $2. 38 $0. 07/bu gain basis $0. 25 $0. 20 basis gain $0. 05 under results: cash sale price $2. 18/bu + futures gain 0. 07 net selling price 2. 25/bu price objective $2. 20 + basis gain $0. 05 $2. 25/bu 17

eg. 5: short, basis weaken ( loss ) A processor hedges to protect his soybean oil inventory against price ↓ cash futures May cash forward bid for soybean oil ￠ 18. 5/lb basis (60, 000 lbs each) sells 3 Sep. soybean oil contracts at ￠ 17. 5/lb ￠ 1. 00/lb over Sep. Aug sells 180, 000 lbs buys 3 Sep. soybean oil at ￠ 16. 25/lb contracts at ￠ 15. 5/lb to offset intial short futures position ￠ 2. 0/lb gain ￠ 0. 75/lb over Sep. ￠ 0. 25/lb basis loss results: cash sale 16. 25 + futures gain 2. 00 net selling price 18. 25 cents/lb cash forward bid 18. 50 - basis loss 0. 25 net selling price 18. 25 18

Buying (Long) Hedges: used to protect against ↑ in cash price. eg 1. Cash poultry producer Oct. cash price for soybean meal $148/ton Dec. buys soybean meal at $156/ton Futures (100 tons each) buys 1 Jan soybean meal contract at $153/ton sells 1 Jan soybean meal contract at $161/ton to offset initial long futures position $8/ton gain basis $5 under Jan $5 under Jan no change results: cash purchase price $156/ton price objective $148/ton - futures gain $ 8/ton no basis change 0 net purchase price $148/ton 19

eg 3. long, basis weaken ( gain ) cash futures basis Oct. cash price for soybean buys u Jan soybean meal $5 under Jan. meal $148/ton contract at $153/ton Dec. buys soybean meal at sells 1 Jan soybean meal $9 under Jan. $151/ton contract at $160/ton to offset initial long futures position $7/ton gain $4 basis gain results: cash purchase price $151/ton price objective $148/ton - futures gain $ 7/ton basis gain $4/ton net purchase price $144/ton 20

eg 4: long, basis strengthen ( loss ) cash Oct. cash price for soybean meals $148/ton Dec. buys soybean meal at $156/ton futures basis buys 1 Jan soybean meal contract at $153/ton $5 under Jan. sells 1 Jan soybean meal contract at $158/ton to offset initial long futures position $5/ton gain $2 under Jan. $3 basis loss results: cash purchase price $156/ton futures gain $ 5/ton net purchase price $151/ton price objective $148/ton + basis loss $ 3/ton net purchase price $151/ton 21

eg 5. long, basis weaken ( gain ) grain exporter cash futures basis July make commitment to sell buys 100 Dec. wheat $0. 10 over Dec. 1 million bu wheat at contract at $2. 62/bu $2. 72/bu Nov. buys 1 million bu wheat sells 200 Dec. wheat $0. 04 over Dec. at $2. 78/bu contract at $2. 74/bu to offset initial long futures position $0. 12/bu gain $0. 06 basis gain results: cash purchase price $2. 78/bu price objective $2. 72/bu - futures gain 0. 12/bu - basis gain $0. 06/bu net purchase price $2. 66/bu 22

Options ( 選擇權 ) Options: the right, but not the obligation, to buy or sell a futures contract at some predetermined price at anytime within a specific time period strike price Oct. 31, 1984 － soybeans Feb. 27, 1985 － corn + wheat, soybean oil, soybean meal etc. An option is a legally binding contract that gives the option buyer the right, but not the obligation, to buy or sell something under specific conditions in exchange for the payment of a premium. ( the price of an option ) 23

( It is the buyer's (holder) decision whether to exercise that right; only the seller (writer) of the option is obligated to perform. ) options “calls” – the right to buy 買權 “puts” – the right to sell 賣權 (not opposite side of the same transaction) 24

eg: Buy Nov. $8. 00 soybean put option before Nov. harvest. If at harvest, market price of soybean futures is $7. 00, you would certainly exercise your right to sell at $8. 00, or you would sell the option rights to someone else. If Nov. soybean futures at harvest are trading at $8. 50/bu, you would not exercise the right to sell at only $8. 00. You would simply let the option expire (and lose the premium) or sell it to someone else. And option buyer ( holders ) has several choices: 1. liquidate his option position by selling an identical option anytime prior to expiration 2. let the option expire 3. exercise his option Choices of writers: 1. before been noticed for exercise – buy an offsetting option 2. after been noticed – selling an offsetting futures contract 25

Options on Futures Contract The buyer of a call obtains protection against rising prices -similar to the protection of a long hedge with futures -- but without giving up the chance to benefit from rising prices. The buyer of a put obtains protection against declining prices -similar to the protection of a short hedge with futures of forward contracting -- but without giving up the chance to benefit from declining prices. 履約價格 Strike price -- the price at which the holder of a call (or put) may choose to exercise his right to purchase (or sell) the underlying futures contract. 26

內含價值 Intrinsic value : the difference between strike price & current market price call option: current futures price > strike price put option: current futures price < strike price An option is not worth exercising if it has no intrinsic value. In-the-money (worth exercising) -- an option that has intrinsic value Out-of-the-money -- an option that has no intrinsic value call option: current futures price < strike price put option: current futures price > strike price An option that is out-of-the-money at expiration will have no value, and the holder will allow it to expire worthless. At-the-money -- strike price = underlying futures price ( i. e. intrinsic value = 0 ) 27

Time value -- the amount that buyers are currently willing to pay for a given option over and above any intrinsic value, in anticipation that, over time, a change in the underlying futures price will cause the option to increase in value. time value 權利金 Option premiums -- time value + intrinsic value expiration time value the price of an option (the option buyer pays the option writer) Options are traded the same way futures contracts are traded, with the exception of margin requirements. Most option buyers and sellers elect to liquidate their option positions by an offsetting sale or purchase at or prior to expiration. 28

履約 Exercise: only an option buyer (holder) has the right to exercise an option when a call (put) is exercised, the holder will acquire a long (short) futures position at the strike price. Øfactors influencing premiums: 1. The length of time remaining until expiration 2. The volatility of the underlying futures price 3. The relationship of strike price and market price 4. Short-term risk-free interest rates 29

Strategies for buying and selling options • Buying put options: to establish a minimum price for sales A farmer might wish to purchase a put during the spring or summer in order to establish a minimum price for the sale of his crop at harvest. 30

eg 1: In May a soybean producer pays a premium of $0. 25 for a Nov. $7. 50 put. (This gives him the right to go short in the futures market at a price of $7. 50. The right continues for as long as he holds the option -- until he sells it, or exercise it, or until it expires in October) By harvest time, the Nov. futures price has declined to $6. 50 the put with a strike price of $7. 50 have an intrinsic value of $1. 00 31

Cash May. price for new-crop soybeans is $7. 25/bu Nov. sells 5, 000 bu soybeans at $6. 50/bu Option buy Nov. $7. 50 put at a premium of $0. 25/bu sells Nov. $7. 50 put to receive premium of $1. 00/bu and offset initial long option position + $0. 75 ($1. 00 - $0. 25). . option gain result : cash sale price + option gain $6. 50/bu $0. 75/bu net selling price $7. 25/bu 32

eg 2: cash May. price for new-crop soybeans is $7. 25 Nov. sells 5, 000 bu soybeans at $8. 00/bu options buys Nov. $7. 50 put at a premium of $0. 25/bu let option expire result: cash sale price $8. 00/bu - cost of option premium 0. 25/bu net selling price $7. 75/bu 33

• Buying call options: to sell the crops now (at harvest) and avoid storage costs (and P ↓), and also profit from P↑in winter or spring futures options Oct. May soybean futures buys May. $8. 00 call are $8. 00/bu at a premium of $0. 15/bu Apr. May soybean futures sells May $8. 00 call at a are $8. 50/bu premium of $0. 50/bu and offsets initial long option position result: gain from option position $0. 50/bu - cost of premium 0. 15/bu net gain $0. 35/bu 34

• Selling call options - to earn the option premium - when do not expect a substantial price increase "covered call" - write a call option against a commodity you own. - own commodity, cash market value of your commodity move with the same direction as the futures price "uncovered" or "naked" option - options not covered by having a cash or futures market position in the commodity 35

• Selling put options - to earn the option premium - puts are written by individuals who do not expect a substantial decrease in price 1. Buying put options for protection against lower prices. 2. Buying put options for "price insurance" when you store your crop. 3. Writing call options to achieve a higher effective selling price for a crop you are storing. 4. Buying call options at harvest to profit form a winter/spring price increase. 5. Buying call options for short-term protection against rising prices. 36

If futures price at expiration is: (basis maintains at – 0. 20) $6. 50 $7. 00 $7. 50 $8. 00 $8. 50 Your net return if you Write call with strike price of 0. 43 0. 30 0. 20 0. 13 Hedge or contra ct at $7. 50 $6. 73 $7. 23 $7. 48 6. 60 7. 10 7. 60 6. 50 7. 00 7. 50 7. 75 6. 43 6. 93 7. 43 7. 93 7. 30 $7. 25 $7. 50 $7. 75 $8. 00 premiums 8. 50 -0. 20+(7. 25 -8. 50)+0. 43 Buy put with $7. 50 strike price at a premium of $0. 30 Do nothi ng 7. 00 7. 50 8. 00 6. 30 6. 80 7. 30 7. 80 8. 30 6. 50 -0. 20+(7. 50 -6. 50)-0. 30 Futures price when you sell your crop – Local basis at the time you sell – Premium paid for option + Intrinsic value of option (if any) = Net return 37

net return $ do nothing buy put hedge or contract 7. 30 7. 00 7. 50 future price 38