Mechanics of Options Markets

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1 Mechanics of Options Markets Chapter 8 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

2 何謂選擇權為衍生性商品, 是一種契約, 這個契約賦予你擁有的權利, 選擇或的權利, 而這項契約是可以買賣的交易人可以買選擇權, 也可以賣選擇權支付買進選擇權的代價稱為契約的持有者 ( 買方 ), 在支付權利金後, 擁有在未來一段時間內 or 某一特定時日, 以約定的價格 ( ) 買入或出售一定數量標的物的權利 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

3 選擇權與期貨的比較相同點 : 都是一種契約, 約定在未來以特定的價格買賣某一商品或金融資產相異點 : 1. Futures : 買方與賣方之權利與義務是對等的 Options : 有權利無義務, 有義務無權利 2. 履約價格訂定方式不同 Futures : 由買賣雙方透過決定 Options : 以在事先選定 3. 保證金的要求不同 Futures : 都有義務, 故都要繳交保證金 Options : 買方有權利無義務, 故保證金 ; 賣方有義務, 故保證金 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

4 Types of Options A is an option to buy A is an option to sell A can be exercised only at the end of its life ( 歐式 ) An can be exercised at any time ( 美式 ) (Bermudan option) 係介於歐式與美式選擇權之間, 可於契約到期日前之某些特定時點執行權利 (Asian option), 其與前者的差異係在於執行價格計算方式之不同, 亞洲式選擇權以契約存續期間內雙方所約定之數個時點的平均價格作為執行價格 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

5 Call option 買權賦予持有人權利, 可以在未來特定時點 ( 到期日 ) 以特定價格 ( 履約價格執行價格 ) 特定資產買權的買方在繳付權利金後, 有權利在到期日或到期日之前以約定之履約價格數量規格, 買進標的物, 買權的賣方則有義務依約賣出該標的物 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

6 Put option 賣權賦予持有人權利, 可以在未來特定時點 ( 到期日 ) 以特定價格 ( 履約價格執行價格 ) 特定資產賣權的買方有權利在到期日或到期日之前, 以約定的履約價格數量規格, 賣出該標的物賣權的賣方則有義務依約買進該標的物 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

7 Call & Put 比較交易者 Option Call 買權 Put 賣權買方擁有的權利擁有的權利賣方收取權利金, 並承受的義務收取權利金, 並承受的義務 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

8 Option Positions Long call Long put Short call Short put Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

9 Long Call on ebay (Figure 8.1, Page 252) Profit from buying one ebay European call option: option price = $5, strike price = $100, option life = 2 months Profit ($) Terminal stock price ($) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

10 買進買權 ( Long Call ) 權利金 = c, 履約價格 =K, 標的物之市價 =S S > K+c 時, S < K+c 時, ( 最大損失為 ) Profit ($) 損益平衡點 =K+c 0 -c K Terminal stock price ($) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

11 Example 買進買權 ( 買進 5 月到期履約買權 ) 情況 5 月 2 日期初 5 月 7 日到期前反向沖銷 5 月 17 日到期履約 5 月 17 日到期不履約結果履約價 :5300 支付權利金 : 115 點 50=5750 元賣出價 :59 點買權損失 :56 點損益 :(59-115) 50=-2800 元結算價 :5510 履約買權獲利 : =210 點損益 :( ) 50=4750 元結算價 :5250 買權不履約 : 因結算價低於履約價, 故不履約損益 :-115 點 50=-5750 元 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

12 選擇權是一場, 有人贏, 必有人輸 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

13 Short Call on ebay (Figure 8.3, page 256) Profit from writing one ebay European call option: option price = $5, strike price = $ Profit ($) Terminal stock price ($) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

14 賣出買權 (Short Call) 與買進買權恰好相反 ( 因為 : 選擇權是一場零合遊戲, 有人贏, 必有人輸 ) S < K+C:, 最大獲利為 S > K+C:, 且股價愈高, 損失愈大 c 0 Profit ($) 損益平衡點 =K+c K Terminal stock price ($) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

15 Long Put on IBM (Figure 8.2, page 254) Profit from buying an Oracle European put option: option price = $7, strike price = $ Profit ($) 損益平衡點 = Terminal stock price ($) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

16 買入賣權 (Long Put) 權利金 = p, 履約價格 =K, 標的物之市價 =S S > K-p 時, ( 最大損失為權利金 p ) S < K-p 時, Profit ($) 損益平衡點 =K-p 0 -p K Terminal stock price ($) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

17 Example 買進賣權 ( 買進 5 月到期履約買權 ) 情況 5 月 2 日期初 5 月 7 日到期前反向沖銷 5 月 17 日到期履約 5 月 17 日到期不履約結果履約價 :5300 支付權利金 : 100 點 50=5000 元賣出價 :120 點賣權獲利 :20 點損益 :( ) 50=1000 元結算價 :5250 履約賣權獲利 : =50 點損益 :50 點 50 元元 = 元結算價 :5510 賣權不履約 : 因結算價高於履約價, 故不履約損益 :-100 點 50=-5000 元 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

18 Short Put on IBM (Figure 8.4, page 256) Profit from writing an IBM European put option: option price = $7, strike price = $ Profit ($) Terminal stock price ($) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

19 選擇權到期日報酬圖損益買入買權 +Call 買入賣權 +Put 賣出買權 -Call 履約價履約價標的商品價格 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

20 選擇權到期日報酬圖損益 +Call +Put -Call 履約價履約價 -Put 標的商品價格 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

21 Payoffs from Options (1/2) What is the Option Position in Each Case? K = Strike price, S T = Price of asset at maturity Payoff Payoff K S T K S T Payoff Payoff K S T K S T Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

22 Payoffs from Options (2/2) S T : 標的物資產的 ( 到期時 ) K: 買權長部位之報償 : 賣權長部位之報償 : Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

23 Assets Underlying Exchange-Traded Options Page 標的物 1. 現貨 (Options on physical) Stocks Foreign Currency Stock Indices 2. 期貨 (Options on futures) Futures Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

24 Specification of Exchange-Traded Options Expiration date Strike price European or American Call or Put (option class) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

25 Terminology Moneyness : At-the-money option In-the-money option Out-of-the-money option Intrinsic value Time value Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

26 Terminology (continued) 價內 ( In-the-money ) 1. 價內是指有之選擇權, 也就是的選擇權無論是買權或賣權, IV > 0 的均稱為價內 2. 處於價內之選擇權買方如果執行權利有利可圖 3. IV 甚大的選擇權稱為, 該種選擇權買方執行權利時利益最大, 故最容易被履約 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

27 價外 ( Out-of-the-money ) 與價平 ( At-themoney ) 1. 價平 : 如果, 而且, 則稱為價平 2. 價外 : 如果, 標的物市價 < 履約價的買權, 或標的物市價 > 履約價的賣權, 稱為價外 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

28 整理 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

29 權利金 ( Premium ) 買方支付的金額即選擇權的價格, 其價格是透過市場之來決定權利金 P = + ( intrinsic value ) + ( time value ) = IV + TV 內含價值就是在合約有效期間的任何時點, 將選擇權履約所能獲利之利益 : 就買權而言 : S K 時, ( 當市價履約價格時 ) S > K 時, ( 當市價 > 履約價格時 ) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

30 就賣權而言 : S K 時, ( 當市價履約價格時 ) S < K 時, (IV = 履約價格 - 標的物市價 ) 時間價值 a. 代表交易者對於的期望價值交易者願意支付特定之金額以持有 Option, 並期望在一定時間內標的物的市價會變動到對其有利希望 b. 距到期日愈遠, 時間價值, 而在到期日時, 時間價值為 0, 某些目前沒有內含價值 ( IV = 0 ) 的選擇權會有人願意去買它, 就是因該合約尚未到期, 還有時間價值存在 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

31 選擇權的平倉買進一個賣權, 平倉時必須是一個賣出一個買權, 平倉時必須是一個賣出一個賣權, 平倉時必須是一個例如 : 買入一個 CBOT 十二月履約價 850 之 S & P 500 期貨買權, 平倉時必須賣出一個 CBOT 十二月履約價 850 之 S & P 500 期貨買權 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

32 造市者 (Market maker)(1/2) 為了迎合市場上所有交易者的需求, 當市場上有人願意出價買進或賣出時, 但卻找不到對應的賣方或買方時, 就應負責協助完成此筆交易造市者具有及的義務, 其主要功能在於提昇交易市場的價格密接性連續性穩定性及市場流動性, 並協助市場促成交易 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

33 造市者 (Market maker)(2/2) 同時提供某種選擇權的買價 (bid price) 與賣價 (offer price) Bid: 造市者願意支付的價位 Offer: 造市者所能接受的價位 Bid-offer spread( ): 賣價高於買價的部分 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

34 詢價與報價市場上有交易意願之參與者經由系統要求造市者提供報價詢價時須載明何種選擇權序列 ( 即商品代碼履約價格時間 ) 造市者在市場有詢價訊息產生時, 須依規定或主動提供報價採買賣雙邊報價 ( 價格 ) 及數量 ( 各不得低於五口 ) 報價將併入最佳五檔委託價量中揭示另單獨揭示市場最佳一檔報價資訊 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

35 Covered vs. Naked 有保護和未保護 ( Naked ) 之賣方 : 選擇權之如果, 稱為有保護的賣方, 例如某甲賣出玉米期貨買權, 若其左身擁有玉米期貨多頭部位, 則稱為有保護或有覆蓋 ( Covered ) 的賣方, 有覆蓋的賣方其反之, 如果選擇權之賣方未擁有相對的期貨部位 ( 或現貨部位 ), 則稱為未保護或稱無覆蓋之賣方, 例如某乙賣出玉米期貨買權, 手上無玉米期貨之多頭部位, 即是未保護之賣方, 若被要求履約, 其 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

36 Margins (Page 268) Margins are required when options are sold When a naked option is written the margin is the greater of: 1 A total of 100% of the proceeds of the sale plus 20% of the underlying share price less the amount (if any) by which the option is out of the money 2 A total of 100% of the proceeds of the sale plus 10% of the underlying share price For other trading strategies there are special rules Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

37 保證金 (Margin) 賣方賣出選擇權之後, 背負履約的義務, 為保證到期能履行義務, 故要求繳存一定金額之保證金保證金的最低限額由訂定, 通常以涵蓋一日可能損失的最大額度為原則需進行, 以控制違約風險 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

38 單一部位部位狀況保證金計收方式備註買進 call 買進 put 賣出 call 賣出 Put 1.A 值及 B 值依本公司公告之標準計算 2.call 價外值 : MAXIMUM(( 履約價格 - 標的指數價格 ) 契約乘數,0) 3.put 價外值 : MAXIMUM(( 標的指數價格 - 履約價格 ) 契約乘數,0) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

39 保證金收取收取保證金之部位買進單一部位 call 多頭價差 put 空頭價差買入跨式部位買入勒式部位收取保證金之部位賣出單一部位 call 空頭價差 put 多頭價差賣出跨式部位賣出勒式部位買進期貨並賣出 call 賣出期貨並賣出 put Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

40 例 1: 賣出價外之買權 A 值 =27,000 元 B 值 =14,000 元為例 ( 期交所將視市場行情隨時調整 A B 值 ) 情況 : 1 指數現貨價為 4,600 點 2 賣出履約價為 4,800 點之買權, 收取權利金 60 點保證金 : + =3,000+17,000 =NT$20,000 價外值 : (4,800 點 -4,600 點 )*50 元 / 點 =10,000 元 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

41 例 2: 賣出價內之買權情況 : 1 指數現貨價為 4,600 點 2 賣出履約價為 4,500 點之買權, 收取權利金 190 點保證金 : + =9,500+27,000 =NT$36,500 價外值 : 0 元 ( 因賣出履約價 4,500 元, 小於現貨價 4,600 點為價內之買權 ) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

42 例 3: 賣出價外之賣權情況 : 1 指數現貨價為 4,600 點 2 賣出履約價為 4,500 點之賣權, 收取權利金 70 點保證金 : + =3,500+22,000 =NT$25,500 價外值 : (4,600 點 -4,500 點 )*50 元 / 點 =5,000 元 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

43 例 2: 賣出價內之賣權情況 : 1 指數現貨價為 4,600 點 2 賣出履約價為 4,800 點之賣權, 收取權利金 240 點保證金 : + =12,000+27,000 =NT$39,000 價外值 :0 元 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

44 影響選擇權利金之因素 Notation c : European call option price p : European put option price S 0 : Stock price today K : Strike price T : Life of option σ: Volatility of stock price C : American Call option price P : American Put option price S T :Stock price at option maturity D : Present value of dividends during option s life r : Risk-free rate for maturity T with cont comp Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

45 Effect of Variables on Option Pricing (Table 9.1, page 284) Variable S 0 K T σ r D c p C P?? Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

46 影響選擇權利金之因素 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

47 選擇權之風險衡量 :delta (Δ) 是一個, 衡量對其的敏感程度, 即衡量標的資產價格變動一單位, 導致選擇權價格變動的幅度有多少 Delta 是在做無風險避險時, 買權的 Delta 為, 介於 0 到 1 之間賣權的 Delta 為, 介於 0 到 -1 之間 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

48 選擇權之風險衡量 :delta Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

49 選擇權之風險衡量 :delta 例如 : 標的物市價由 60 元上漲到 64 元, 買權權利金由 8 元上漲至 9.6 元則 Delta = = 因為買權的標的物市價與買權價格呈同方向變動, 故, 而賣權的標的物市價與買權價格呈反方向變動, 故 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

50 選擇權之風險衡量 :delta 例題 : 期貨賣權的 delta 為 -0.3, 表示在其他情況不變下, 期貨價格若下跌 1 元, 賣權價格會 (1) 上漲 0.7 元 (2) 下跌 0.7 元 (3) 上漲 0.3 元 (4) 下跌 0.3 元 Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull

51 選擇權之風險衡量 :delta 例題 : 假設 S&P500 指數期貨賣權之 delta= - 0.5, 若持有 1 單位指數期貨, 理論上需如何才能完全避險? 買入兩單位賣權賣權 P 2 + P Delta 0.5 S + S = = 0 0 δ= 0.5 S 上漲 1,P 下跌 0.5, 故, Fundamentals of Futures and Options Markets, 5 th Edition, Copyright John C. Hull P S =

Microsoft PowerPoint - Ch10 Trading Strategies Involving Options.ppt

Microsoft PowerPoint - Ch10 Trading Strategies Involving Options.ppt Notations Ch10 選擇權交易策略 Trading Strategies Involving Options S(T) : Stock price at time T C(,T) : the price of the call option with maturity T and strike price T1 < T2 < T3 < T4 1 < 2 < 3 < 4 出售備兌買權 (Writing