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A derivative is an instrument whose value depends on the values of other more basic underlying variables 衍生性金融商品可以歸類為 ：

A derivative is an instrument whose value depends on the values of other more basic underlying variables 衍生性金融商品可以歸類為 ： 1. 遠期、 期貨 、交換 n 對於要以約定價格買進的那人，她 既是權利，也是義務 n 對於要以約定價格賣出的那人，她 既是權利，也是義務 除了7-11，大部份的生意，多少帶有些遠期交易特性. 2. 選擇權、認股權證 n 對於付出權利金，『握有』約定價格買進或是賣出『權』的那人，她 只享有權利， 並不需要擔負義務

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A derivative is an instrument whose value depends on the values of other more basic underlying variables 衍生性金融商品可以歸類為 ：

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  1. A derivative is an instrument whose value depends on the values of other more basic underlying variables衍生性金融商品可以歸類為： 1. 遠期、期貨、交換 n對於要以約定價格買進的那人，她既是權利，也是義務 n對於要以約定價格賣出的那人，她既是權利，也是義務 除了7-11，大部份的生意，多少帶有些遠期交易特性

  2. 2. 選擇權、認股權證 • n對於付出權利金，『握有』約定價格買進或是賣出『權』的那人，她只享有權利，並不需要擔負義務 • 對於收受權利金，任『對方』行使以約定價格買進或是賣出『權』的那人，她擔負義務，並不享有權利 • 買房屋先付訂金，就是一種買「選擇權」的例子，您為了這選擇權利付出的代價，就是所付訂金；對方收受訂金的同時，等於是賣「選擇權」。 • 參加保險，就是一種買「選擇權」的例子；保險公司很類似賣「選擇權」。 n

  3. Derivatives Markets • Exchange traded • Traditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic trading • Contracts are standard there is virtually no credit risk (交易所居於其間) • Over-the-counter (OTC) • A computer- & telephone-linked network of dealers at financial institutions, corporations, & fund managers • Contracts can be non-standard & there is some small amount of credit risk

  4. Ways Derivatives are Used • To hedge risks • To speculate (take a view on the future direction of the market) • To lock in an arbitrage profit • To change the nature of a liability • To change the nature of an investment without incurring the costs of selling one portfolio & buying another

  5. Forward (遠期) Contracts • A forward contract is an agreement to buy or sell an asset at a certain time in the future for a certain price (the delivery price) • It can be contrasted with a spot contract which is an agreement to buy or sell immediately • It is traded in the OTC market

  6. Foreign Exchange Quotes on Aug 16, 2001

  7. Forward Price • The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price) • The forward price may be different for contracts of different maturities

  8. Terminology • The party that has agreed to buyhas what is termed a long position • The party that has agreed to sell has what is termed a short position

  9. Example • On Aug. 16, 2001 the treasurer of a corporation enters into a long forward contract to buy £1 mil. in 6 months at an exchange rate of 1.4359 • This obligates the corporation to pay $1,435,900 for £1 mil. on Feb. 16, 2002 • What are the possible outcomes?

  10. Profit Price of Underlying at Maturity, ST Profit from aLong Forward Position K

  11. Profit Price of Underlying at Maturity, ST Profit from a Short Forward Position K

  12. Futures (期貨) Contracts • Agreement to buy or sell an asset for a certain price at a certain time • Similar to forward contract • Whereas a forward contract is traded OTC, a futures contract is traded on an exchange

  13. Examples of Futures Contracts • Agreement to: • 1. buy 100 oz. of gold @ US$300/oz. in December (COMEX) • 2. sell £62,500 @ 1.5000 US$/£ in March (CME) • 3. sell 1,000 bbl. of oil @ US$20/bbl. in April (NYMEX)

  14. 1. Gold: An Arbitrage Opportunity? • Suppose that: • The spot price of gold is US$300 • The 1-year forward price of gold is US$340 • The 1-year US$ interest rate is 5% per annum • Is there an arbitrage opportunity? (We ignore storage costs & gold lease rate)?

  15. 2. Gold: Another Arbitrage Opportunity? • Suppose that: • The spot price of gold is US$300 • The 1-year forward price of gold is US$300 • The 1-year US$ interest rate is 5% per annum • Is there an arbitrage opportunity?

  16. The Forward Price of Gold If the spot price of gold is S & the forward price for a contract deliverable in T years is F, then F = S(1+r)T where r is the 1-year (domestic currency) risk-free rate of interest. In our examples, S = 300, T = 1, & r =0.05 so that F= 300(1+0.05) = 315

  17. 1. Oil: An Arbitrage Opportunity? Suppose that: • The spot price of oil is US$19 • The quoted 1-year futures price of oil is US$25 • The 1-year US$ interest rate is 5% per annum • The storage costs of oil are 2% per annum • Is there an arbitrage opportunity?

  18. 2. Oil: Another Arbitrage Opportunity? • Suppose that: • The spot price of oil is US$19 • The quoted 1-year futures price of oil is US$16 • The 1-year US$ interest rate is 5% per annum • The storage costs of oil are 2% per annum • Is there an arbitrage opportunity?

  19. Exchanges Trading Options • Chicago Board Options Exchange • American Stock Exchange • Philadelphia Stock Exchange • Pacific Stock Exchange • European Options Exchange • Australian Options Market • and many more (see list at end of book)

  20. A call option is an option to buy a certain asset by a certain date for a certain price (the strike price) A put is an option to sell a certain asset by a certain date for a certain price (the strike price) Options

  21. Profit ($) 30 20 10 Terminal stock price ($) 30 40 50 60 0 70 80 90 -5 Long Call on Microsoft Profit from buying a European call option on Microsoft: option price = $5, strike price = $60

  22. Profit ($) 70 80 90 5 0 30 40 50 60 Terminal stock price ($) -10 -20 -30 Short Call on Microsoft Profit from writing a European call option on Microsoft: option price = $5, strike price = $60

  23. Profit ($) 30 20 10 Terminal stock price ($) 0 60 70 80 90 100 110 120 -7 Long Put on IBM Profit from buying a European put option on IBM: option price = $7, strike price = $90

  24. Profit ($) Terminal stock price ($) 7 60 70 80 0 90 100 110 120 -10 -20 -30 Short Put on IBM Profit from writing a European put option on IBM: option price = $7, strike price = $90

  25. Payoff Payoff K K ST ST Payoff Payoff K K ST ST Payoffs from OptionsWhat is the Option Position in Each Case? K = Strike price, ST = Price of asset at maturity

  26. Types of Traders • Hedgers • Speculators • Arbitrageurs Some of the large trading losses in derivatives occurred because individuals who had a mandate to hedge risks switched to being speculators

  27. 一. Hedging Examples • A US company will pay £10 million for imports from Britain in 3 months & decides to hedge using a long position in a forward contract • An investor owns 1,000 Microsoft shares currently worth $73 per share. A two-month put with a strike price of $65 costs $2.50. The investor decides to hedge by buying 10 contracts

  28. 二. Speculation Example • An investor with $4,000 to invest feels that Cisco’s stock price will increase over the next 2 months. The current stock price is $20 & the price of a 2-month call option with a strike of 25 is $1 • What are the alternative strategies?

  29. 三. Arbitrage Example • A stock price is quoted as £100 in London & $172 in New York • The current exchange rate is 1.7500 • What is the arbitrage opportunity?

  30. Futures Contracts • Available on a wide range of underlying assets • Exchange traded • Specifications need to be defined: • What can be delivered, • Where it can be delivered, • When it can be delivered • Settled daily

  31. Margins (保證金) • A margin is cash or marketable securities deposited by an investor with broker • The balance in the margin account is adjusted to reflect daily settlement • Margins minimize the possibility of a loss through a default on a contract

  32. 期合約的交易制度 n期貨合約的買、賣雙方均有交割之義務 n多為沖抵(Offset)的方式結平，現貨交割(Delivery)（真的送豬肚到你家）只佔少數 n某些金融商品無法實體交割 n設有最小跳動金額(依期貨的種類而不同) n部份有漲跌停板的限制 n公開競價的方式交易 買賣雙方均要設置保證金帳戶

  33. n保證金成數(依期貨的種類而不同) ~ 如保證金是契約價值的百分之十，等於拿一塊錢便可以交易價值十塊錢的商品。 n因此，期貨交易具有以小搏大的高槓桿特性。 n保證金分為「原始保證金」與「維持保證金」兩個層次 n交易人須於交易前繳交原始保證金至期貨商指定之銀行帳戶 如果行情不利於交易人，致使保證金水位低於維持保證金，則交易人須補足保證金至原始保證金水準。

  34. nMarked to Market [損益每日結平] ~ 為控制風險，遂有每天計算保證金是否足夠規定（此為期貨交易之另一個特性，又稱為「每日結算」）。 如果發現保證金不足，交易人須於期貨商規定的時間內補足保證金 否則期貨商有權結清交易人的部位。

  35. 【參考】

  36. 國內期貨市場保證金類型，分為「結算保證金」、「原始保證金」、與「維持保證金」國內期貨市場保證金類型，分為「結算保證金」、「原始保證金」、與「維持保證金」 「結算保證金」指期交所向結算會員收的保證金； 「原始保證金」為期貨經紀商向投資人收取的起始保證金；而當投資者保證金帳戶餘額低於「維持保證金」水準時，期貨經紀商會向投資人發出「補繳通知」（margin calls）。台灣期貨交易所會根據其風險控管機制，不定期公佈三種保證金的最低界線，

  37. 國內期貨市場保證金類型，分為「結算保證金」、「原始保證金」、與「維持保證金」國內期貨市場保證金類型，分為「結算保證金」、「原始保證金」、與「維持保證金」 期交所不准許期貨經紀商低收「原始保證金」與低設「維持保證金」水準。根據期交所三項保證金數據分析，「維持保證金」為「結算保證金」的1.15倍，「原始保證金」則為「結算保證金」的1.5倍 「結算保證金」是計算其它兩種保證金的基礎。

  38. 客戶保證金 • 「臺灣期貨交易所股份有限公司結算保證金收取方式及標準」中第四條：「股價指數類期貨契約結算保證金金額為各契約之期貨指數乘以指數每點價值乘以風險價格係數。前項所稱風險價格係數，係參考一段期間內指數變動幅度，估算至少可涵蓋一日指數變動幅度百分之九十九點七信賴區間之值。」 台灣期交所的「結算保證金」制定標準，是「涉險值」（value-at-risk、VaR）觀念的應用

  39. 市場風險敏感性係數： • 當市場投資組合的指數變動一單位時，投資組合價值變動百分比率，股票投資常常以貝他值 (Beta Coefficient)顯示其系統性風險，進而決定投資人要求的報酬率。如果投資人真的是充分分散投資標的，只有貝他值會影響他對於投資組合要求的報酬率。 • E(rx) = rf + b[E(rm) - rf] • 例如： E(rm) - rf = 0.08; rf = 0.03; - 全憑一個b係數在決定個股期望報酬 如 bx = 1.25 => E(rx) = .03 + 1.25(.08) • = 13%

  40. nMarked to Market [損益每日結平] ~ 為控制風險，遂有每天計算保證金是否足夠規定（此為期貨交易之另一個特性，又稱為「每日結算」）。 如果發現保證金不足，交易人須於期貨商規定的時間內補足保證金 否則期貨商有權結清交易人的部位。

  41. 如果結算系統靈敏, 可以計算 • 價差保證金 • 避險保證金 • 整戶保證金 (每客戶或是每交易帳戶, 以淨額計算其保證金) • 法人除期貨自營商, 只准許作避險, 目前主要是事後認定 • 期貨自營商可以作避險或是逐利交易

  42. Example of a Futures Trade • An investor takes a long position in 2 December gold futures contracts on June 5 • contract size is 100 oz. • futures price is US$400 • margin requirement is US$2,000/contract (US$4,000 in total) • maintenance margin is US$1,500/contract (US$3,000 in total)

  43. Other Key Points About Futures • They are settled daily • Closing out a futures position involves entering into an offsetting trade • Most contracts are closed out before maturity

  44. Delivery [交割] • If a contract is not closed out before maturity, it usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, & when it is delivered, the party with the short position chooses. • A few contracts (for example, those on stock indices & Eurodollars) are settled in cash

  45. Some Terminology • Open interest (未平倉合約): the total number of contracts outstanding • equal to number of long positions or number of short positions • Settlement price (最後成交價格): the price just before the final bell each day • used for the daily settlement process • Volume of trading: the number of trades in 1 day

  46. 【參考】 未平倉合約(Open Interest) 未平倉合約是指期貨交易收盤後未平倉的期貨契約單邊買或賣的數量。期貨市場買方或賣方可等待合約到期，或利用與先前買賣方向相反合約結束責任，稱為平倉。 未平倉合約是期貨交易特有資料，它表達商品現有在倉數量，也是商品走勢動能資料。在買賣期指合約及期權合約時，買賣方合約都會被計入未平倉合約數量。 期交所中交易之買賣方要存入保證金，參與者持有未平倉數量愈大，需支付保證金愈高，成本亦高，所以若他相信後市與之前所預測多空方向相反，他會進行平倉。

  47. 期貨市場名詞： 正價差 (期貨價格高於現貨價格時) 與 逆價差 (現貨價格高於期貨價格時)

  48. 逆價差與正價差 　權值股漲勢稍歇，期貨市場空單回補壓力暫紓解，多單追價意願降低，成交量略縮，台期指、電子類指與摩台指均維持價平與小幅逆價差，觀望氣氛濃。分析師表示台股短線漲幅已高，加上美科技類股回檔壓力，除非權值股漲勢重啟，下周四台指拉高結算行情恐落空。 　四大期指今表現乏善可陳，台指期貨欠缺昨台積電急拉軋空力道，空單回補不積極，多單短線漲幅已高，也不貿然追價。中信期貨表示，昨台指未平倉量降低，多方自希將堅守最後防線的空單逼出場，倘使權值股持續盤整，原信心岌岌可危的空單，將因盤整拖長逐步消化，周四預期拉高結算行情恐難現。 摩台指今走勢亦不若昨剽悍，雖與摩根現貨仍維持正價差，但僅維持強勢整理態勢，分析師研判外資回補台股趨勢未變，但買超幅應逐縮小，又近日費城半導體指數趨弱，恐降低外資買盤加碼意願。 - 摘錄自【期指動態】觀望 台期指狹幅震盪 中時晚報 920613 股市理財

  49. Convergence of Futures to Spot Futures Price Spot Price Futures Price Spot Price Time Time (a) (b)

  50. Regulation of Futures • Regulation is designed to protect the public interest • Regulators try to prevent questionable trading practices by either individuals on the floor of the exchange or outside groups

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