chapter16

Call Option Payoff PatternsTime 0 Time TPurchase call option,cash flow 0Between times 0 and T:Cash flow = 0 for European optionCash flow 0 for American optionWrite (I.e., issue) calloption,cash flow 0Pay terminal call payoff= - MaxST - X, 0 0Between times 0 and T:Cash flow = 0 for European optionCash flow 0 for American optionWrite (I.e., issue) calloption,cash flow 0Pay terminal call payoff= - MaxX - ST, 0 0在时间0和T之间:欧洲式看涨期权现金流量 = 0美国式看涨期权现金流量 0 出售（即发行）看涨期权,现金流量 0支付到期看涨期权清算= - MaxST - X, 0 0在时间0和T之间:欧洲式期权现金流量 = 0美国式期权现金流量 0 出售（即发行）看跌期权,现金流量 0支付到期看涨期权清算= - MaxX - ST, 0 0在时间0和T之间:欧洲式期权现金流量 = 0美国式期权现金流量 0 看涨期权购买者的现金流量看涨期权出售者的现金流量看跌期权购买者的现金流量看跌期权出售者的现金流量看涨期权清算模式看跌期权清算模式MOST ACTIVE OPTIONS, 3 OCTOBER 2006StockRank Symbol Name OptionexpirationOptionexercisepricePut orcall?1 HAL Halliburton 20-Apr-07 27.5 Put2 HAL Halliburton 19-Jan-07 27.5 Put3 HAL Halliburton 19-Jan-07 30.0 Put4 QQQQ Nasdaq 100 Index 20-Oct-06 40.0 Put5 HAL Halliburton 20-Apr-07 22.5 Put6 IWM Russell 2000 Index 17-Nov-06 70.0 Put7 QQQQ Nasdaq 100 Index 17-Nov-06 39.0 Put8 IWM Russell 2000 Index 20-Oct-06 72.0 Put9 SPY S&P Depository Receipts (Spider) 15-Dec-06 120.0 Put10 SPY S&P Depository Receipts (Spider) 15-Dec-06 139.0 Call11 SPY S&P Depository Receipts (Spider) 15-Dec-06 126.0 Put12 IWM Russell 2000 Index 20-Oct-06 71.0 Put13 QQQQ Nasdaq 100 Index 20-Oct-06 40.0 Call14 BMY Bristol-Myers Squibb 20-Oct-06 22.5 Call15 SPY S&P Depository Receipts (Spider) 20-Oct-06 125.0 Put16 S Sprint Nextel 17-Nov-06 17.5 Call17 IWM Russell 2000 Index 20-Oct-06 69.0 Put18 SPY S&P Depository Receipts (Spider) 20-Oct-06 137.0 Call19 QQQQ Nasdaq 100 Index 20-Oct-06 41.0 Put20 MMM MMM 20-Oct-06 85.0 PutVolume: Number of options traded on 4 Oct. 2006. Each option is for 100 shares, but price quotes are per share.Open interest: Number of open positions at end of day. A position is closed out (i.e., not open) if the option has been sold by day end.A B C D E F1234567891011121314151617181920212223242526StockclosingpriceOptionclosingpriceVolume OpenInterest26.75 3.025 60,945 7,305 -2.27526.75 2.450 59,767 61,121 -1.726.75 4.100 59,131 68,782 -0.8540.31 0.475 57,073 262,601 -0.47526.75 1.025 53,901 5,530 -1.02571.22 1.650 49,387 203,975 -1.6540.31 0.575 45,666 93,169 -0.57571.22 1.650 43,432 154,148 -0.87133.36 0.400 40,125 32,090 -0.4133.36 0.850 40,116 21,036 -0.85133.36 0.925 40,082 32,249 -0.92571.22 1.200 39,015 168,035 -1.240.31 0.875 37,502 196,355 -0.56524.82 2.325 31,989 10,934 -0.005133.36 0.075 31,964 25,569 -0.07516.97 0.525 31,350 9,078 -0.52571.22 0.600 30,777 111,620 -0.6133.36 0.125 30,199 6,261 -0.12540.31 0.975 29,881 94,955 -0.28574.03 11.000 25,732 6,364 -0.03MOST ACTIVE OPTIONS, 3 OCTOBER 2006Volume: Number of options traded on 4 Oct. 2006. Each option is for 100 shares, but price quotes are per share.Open interest: Number of open positions at end of day. A position is closed out (i.e., not open) if the option has been sold by day end.G H I J K L12345678910111213141516171819202122232425262006年10月3日最活跃的期权股票排名 符号 名称 期权的到期时间 期权的执行价格 看涨还是看跌1 HAL Halliburton 20-Apr-07 27.5 看跌2 HAL Halliburton 19-Jan-07 27.5 看跌3 HAL Halliburton 19-Jan-07 30.0 看跌4 QQQQ Nasdaq 100 Index 20-Oct-06 40.0 看跌5 HAL Halliburton 20-Apr-07 22.5 看跌6 IWM Russell 2000 Index 17-Nov-06 70.0 看跌7 QQQQ Nasdaq 100 Index 17-Nov-06 39.0 看跌8 IWM Russell 2000 Index 20-Oct-06 72.0 看跌9 SPY S&P Depository Receipts (Spider) 15-Dec-06 120.0 看跌10 SPY S&P Depository Receipts (Spider) 15-Dec-06 139.0 看涨11 SPY S&P Depository Receipts (Spider) 15-Dec-06 126.0 看跌12 IWM Russell 2000 Index 20-Oct-06 71.0 看跌13 QQQQ Nasdaq 100 Index 20-Oct-06 40.0 看涨14 BMY Bristol-Myers Squibb 20-Oct-06 22.5 看涨15 SPY S&P Depository Receipts (Spider) 20-Oct-06 125.0 看跌16 S Sprint Nextel 17-Nov-06 17.5 看涨17 IWM Russell 2000 Index 20-Oct-06 69.0 看跌18 SPY S&P Depository Receipts (Spider) 20-Oct-06 137.0 看涨19 QQQQ Nasdaq 100 Index 20-Oct-06 41.0 看跌20 MMM MMM 20-Oct-06 85.0 看跌成交量: 2006年10月4日交易的股票数量。每个期权100股，但以每股报价。未平仓量: 日末期权头寸的数量。如果期权在一天结束时早已卖出，头寸平仓 (也即，不开)。A B C D E F1234567891011121314151617181920212223242526股票的收盘价格期权的收盘价格 成交量 未平仓量26.75 3.025 60,945 7,305 -3.02526.75 2.450 59,767 61,121 -2.4526.75 4.100 59,131 68,782 -4.140.31 0.475 57,073 262,601 -0.16526.75 1.025 53,901 5,530 3.22571.22 1.650 49,387 203,975 -0.4340.31 0.575 45,666 93,169 0.73571.22 1.650 43,432 154,148 -1.65133.36 0.400 40,125 32,090 12.96133.36 0.850 40,116 21,036 -0.85133.36 0.925 40,082 32,249 6.43571.22 1.200 39,015 168,035 -0.9840.31 0.875 37,502 196,355 -0.56524.82 2.325 31,989 10,934 -0.005133.36 0.075 31,964 25,569 8.28516.97 0.525 31,350 9,078 -0.52571.22 0.600 30,777 111,620 1.62133.36 0.125 30,199 6,261 -0.12540.31 0.975 29,881 94,955 -0.97574.03 11.000 25,732 6,364 -112006年10月3日最活跃的期权成交量: 2006年10月4日交易的股票数量。每个期权100股，但以每股报价。未平仓量: 日末期权头寸的数量。如果期权在一天结束时早已卖出，头寸平仓 (也即，不开)。G H I J K L1234567891011121314151617181920212223242526HALLIBURTON JAN07 OPTIONS, PRICES ON 3OCT06Closing price of stock: 26.75, down 1.29Calls PutsExercisepriceClosingoptionpriceVolume OpeninterestClosingoptionpriceVolume Openinterest15.0 11.90 20 1,724 0.05 50 1,15317.5 12.70 23 9,449 0.05 140 3,31220.0 7.17 5 13,801 0.20 50 18,27722.5 5.00 339 4,595 0.60 49 15,24725.0 3.20 200 3,306 1.25 423 21,79327.5 1.85 571 3,918 2.50 53,267 61,12130.0 0.95 2,140 12,008 4.10 52,631 68,78232.5 0.55 810 10,527 6.00 216 21,56233.8 0.40 78 2,276 6.90 168 3,37835.0 0.30 231 69,727 8.10 142 20,25836.3 0.20 460 5,989 8.00 2 1,28037.5 0.15 1,249 78,762 9.10 5 5,53040.0 0.10 32 85,037 11.01 16 32242.5 0.05 170 24,439 15.70 135 1,92045.0 0.05 6 8,509 17.10 76 047.5 0.05 10 6,591 14.60 76 050.0 0.05 20 10,528 17.00 52 055.0 0.05 12 694 22.10 28 0A B C D E F G H123456789101112131415161718192021哈利伯顿公司07年1月期权, 06年10月3日价格股票收盘价格: 26.75, 下降 1.29看涨期权 看跌期权执行价格 期权收盘价格 成交量 未平仓量 期权收盘价格 成交量 未平仓量15.0 11.90 20 1,724 0.05 50 1,15317.5 12.70 23 9,449 0.05 140 3,31220.0 7.17 5 13,801 0.20 50 18,27722.5 5.00 339 4,595 0.60 49 15,24725.0 3.20 200 3,306 1.25 423 21,79327.5 1.85 571 3,918 2.50 53,267 61,12130.0 0.95 2,140 12,008 4.10 52,631 68,78232.5 0.55 810 10,527 6.00 216 21,56233.8 0.40 78 2,276 6.90 168 3,37835.0 0.30 231 69,727 8.10 142 20,25836.3 0.20 460 5,989 8.00 2 1,28037.5 0.15 1,249 78,762 9.10 5 5,53040.0 0.10 32 85,037 11.01 16 32242.5 0.05 170 24,439 15.70 135 1,92045.0 0.05 6 8,509 17.10 76 047.5 0.05 10 6,591 14.60 76 050.0 0.05 20 10,528 17.00 52 055.0 0.05 12 694 22.10 28 0A B C D E F G H I12345678910111213141516171819202122232425 J K L12345678910111213141516171819202122232425Page 427 dataPage 12Profit Patterns from GP Stock and OptionsInitial GP stock price 40Terminal GP stock price 70Profit from bought stock 30 - =B4-B3Profit from shorted stock -30 - =-B4+B3Call exercise price 40Call price, July 4Bought call profit 26 - =MAX(B3-B8,0)-B9Written call profit -26 - =+B9-MAX(B3-B8,0)Put exercise price 40Put price, July 2Bought put profit -2 - =MAX(B2-B13,0)-B14Written put profit 2 - =+B14-MAX(B2-B13,0)Terminalstock Bought Shorted Bought Writtenprice stock stock call call0 -40 40 -4 4 5 -35 35 -4 410 -30 30 -4 415 -25 25 -4 420 -20 20 -4 425 -15 15 -4 430 -10 10 -4 435 -5 5 -4 440 0 0 -4 445 5 -5 1 -150 10 -10 6 -655 15 -15 11 -1160 20 -20 16 -1665 25 -25 21 -2170 30 -30 26 -2675 35 -35 31 -31Page 427 dataPage 13Bought Writtenput put38 -3833 -3328 -2823 -2318 -1813 -138 -83 -3-2 2-2 2-2 2-2 2-2 2-2 2-2 2-2 2Page 427中文Page 14GP股票和期权的利润模型初始 GP股票价格 40到期 GP股票价格 70购买股票的利润 30 - =B4-B3卖空股票的利润 -30 - =-B4+B3看涨期权执行价格 407月看涨期权价格 4购买看涨期权利润 26 - =MAX(B3-B8,0)-B9出售看涨期权利润 -26 - =+B9-MAX(B3-B8,0)看跌期权执行价格 407月看跌期权价格 2购买看跌期权利润 -2 - =MAX(B2-B13,0)-B14出售看跌期权利润 2 - =+B14-MAX(B2-B13,0)到期股票 购买 卖空 购买 出售价格 股票 股票 看跌期权 看涨期权0 -40 40 -4 4 5 -35 35 -4 410 -30 30 -4 415 -25 25 -4 420 -20 20 -4 425 -15 15 -4 430 -10 10 -4 435 -5 5 -4 440 0 0 -4 445 5 -5 1 -150 10 -10 6 -655 15 -15 11 -1160 20 -20 16 -1665 25 -25 21 -2170 30 -30 26 -2675 35 -35 31 -31Page 427中文Page 15购买 出售看跌期权 看跌期权38 -3833 -3328 -2823 -2318 -1813 -138 -83 -3-2 2-2 2-2 2-2 2-2 2-2 2-2 2-2 2UN-10FPage 16S to c k P r o fit P a tte r n s8 07 06 05 04 03 02 01 00- 5 0- 4 0- 3 0- 2 0- 1 001 02 03 04 05 0T e r m in a l s to c k p r ic e , S T ($ ) Profit($)B o u g h t s to c k S h o rte d s to c kUN-10FPage 17股 票 利 润 模 型8 07 06 05 04 03 02 01 00- 5 0- 4 0- 3 0- 2 0- 1 001 02 03 04 05 0到 期 股 票 价 格 , ST ($) 利润($)购 买 股 票 卖 空 股 票UN-10GC a ll O p t io n P r o f it P a t t e r n s8 07 06 05 04 03 02 01 00- 4 0- 3 0- 2 0- 1 001 02 03 04 0T e r m in a l s to c k p r ic e , S T ($ )Profit($)B o u g h t c a ll W ritte n c a llUN-10G看 涨 期 权 利 润 模 式8 07 06 05 04 03 02 01 00- 4 0- 3 0- 2 0- 1 001 02 03 04 0到 期 股 票 价 格 , ST ($)利润($)购 买 看 跌 期 权 出 售 看 涨 期 权Page 430Page 20P u t O p t io n P r o f it P a t t e r n s8 07 06 05 04 03 02 01 00- 5 0- 4 0- 3 0- 2 0- 1 001 02 03 04 05 0T e r m in a l s to c k p r ic e , S T ($ )Profit($)B o u g h t p u t W ritte n p u tPage 430 中文Page 21看 跌 期 权 利 润 模 式8 07 06 05 04 03 02 01 00- 5 0- 4 0- 3 0- 2 0- 1 001 02 03 04 05 0到 期 股 票 价 格 , ST ($)利润($)购 买 看 跌 期 权 出 售 看 跌 期 权P r o t e c t iv e P u t P r o f it8 07 06 05 04 03 02 01 00- 5 0- 4 0- 3 0- 2 0- 1 001 02 03 04 05 0T e r m in a l s to c k p r ic e , S T ($ )Profit($)S to c kp ro fitP u tp ro fitP ro te c tiv ep u t p ro fit保 护 性 看 跌 期 权8 07 06 05 04 03 02 01 00- 5 0- 4 0- 3 0- 2 0- 1 001 02 03 04 05 0最 终 股 票 价 格 , ST ($)利润($)股 票 利 润 看 跌 期 权 利 润 保 护 性 看 跌 期 权 利 润Page 431 dataPage 24Profit Patterns from Protective PutInitial GP stock price = X 40Terminal GP stock price 30Put exercise price 40Put price, July 2Profit from stock, September -10 - =B3-$B$2Profit from put, September 8 - =MAX(B5-B3,0)-B6Protective put profit -2 - =B9+B8TerminalstockpriceStockprofitPutprofitProtectiveput profit- Data table header0 -40 38 -25 -35 33 -210 -30 28 -215 -25 23 -220 -20 18 -225 -15 13 -230 -10 8 -235 -5 3 -240 0 -2 -245 5 -2 350 10 -2 855 15 -2 1360 20 -2 1865 25 -2 2370 30 -2 28Page 431 dataPage 25- Data table headerPage 431 data中文Page 26保护性看跌期权利润模式初始GP股票价格 = X 40到期GP股票价格 30看涨看涨期权价格 407月看跌期权价格 29月来自股票的利润 -10 - =B3-$B$29月来自看跌期权的利润 8 - =MAX(B5-B3,0)-B6保护性看跌期权利润 -2 - =B9+B8到期股票价格 股票利润看跌期权利润保护性看跌期权利润- 模拟运算表头0 -40 38 -25 -35 33 -210 -30 28 -215 -25 23 -220 -20 18 -225 -15 13 -230 -10 8 -235 -5 3 -240 0 -2 -245 5 -2 350 10 -2 855 15 -2 1360 20 -2 1865 25 -2 2370 30 -2 28Page 431 data中文Page 27- 模拟运算表头P r o t e c t iv e P u t P r o f it8 07 06 05 04 03 02 01 00- 5 0- 4 0- 3 0- 2 0- 1 001 02 03 04 05 0T e r m in a l s to c k p r ic e , S T ($ )Profit($)S to c kp ro fitP u tp ro fitP ro te c tiv ep u t p ro fit保 护 性 看 跌 期 权8 07 06 05 04 03 02 01 00- 5 0- 4 0- 3 0- 2 0- 1 001 02 03 04 05 0最 终 股 票 价 格 , ST ($)利润($)S to c kp ro fitP u tp ro fitP ro te c tiv ep u t p ro fitPage 432 dataPage 30Profit Patterns from a SpreadCall price, X=40 4Call price, X=50 2Terminal stock price, ST 60Profit from written X = 50 call -8 - =-(MAX(B4-50,0)-B3)Profit from purchased X = 40 call 16 - =MAX(B4-40,0)-4Bull spread profit 8 - =B7+B6StockpricePurchasedcall, X=40Writtencall,X=50Spreadprofit- Data table header, hidden0 -4 2 -25 -4 2 -210 -4 2 -215 -4 2 -220 -4 2 -225 -4 2 -230 -4 2 -235 -4 2 -240 -4 2 -245 1 2 350 6 2 855 11 -3 860 16 -8 865 21 -13 870 26 -18 8Page 432 dataPage 31- Data table header, hiddenPage 432 data中文Page 32差价利润模型看涨期权价格, X=40 4看涨期权价格, X=50 2到期股票价格, ST 60出售X = 50看涨期权的利润 -8 - =-(MAX(B4-50,0)-B3)购买X = 40看涨期权的利润 16 - =MAX(B4-40,0)-4牛市差价利润 8 - =B7+B6股票价格购买看涨期权, X=40出售看涨期权,X=50 差价利润- 模拟运算表头隐藏0 -4 2 -25 -4 2 -210 -4 2 -215 -4 2 -220 -4 2 -225 -4 2 -230 -4 2 -235 -4 2 -240 -4 2 -245 1 2 350 6 2 855 11 -3 860 16 -8 865 21 -13 870 26 -18 8Page 432 data中文Page 33- 模拟运算表头隐藏UN-10JB u ll S p r e a d P r o f it C h a r t8 07 06 05 04 03 02 0- 1 0- 5051 01 52 02 53 0T e r m in a l s to c k p r ic e , S T ($ )Profit($)P u rc h a s e dc a ll, X = 4 0W ritte nc a ll, X = 5 0S p re a dp ro fitUN-10J牛 市 差 价 利 润 图8 07 06 05 04 03 02 0- 1 0- 5051 01 52 02 53 0到 期 股 票 价 格 , ST ($)利润($)购 买 看 涨 期 权 , X = 4 0 出 售 看 涨 期 权 , X = 5 0 差 价 利 润Proposition 1-Higher Lower Bounds for Call PricesCurrent stock price, S0 83Option time to maturity, T 0.5Option exercise price, X 80Interest rate, r 10%Naive minimum option price, Max(S0-X,0) 3Proposition 1 lower bound on option price, Max(S0 - Exp(-rT)X,0) 6.902A B12345678- =MAX(B2-B4,0)- =MAX(B2-EXP(-B5*B3)*B4,0)Proposition 1-Higher Lower Bounds for Call PricesC12345678定理 1-看涨期权定价的下界当前股票价格, S0 83期权到期时间, T 0.5期权执行价格, X 80利率, r 10%自然的最低期权价格, Max(S0-X,0) 3定理1 期权价格的下限, Max(S0 - Exp(-rT)X,0) 6.902A B12345678- =MAX(B2-B4,0)- =MAX(B2-EXP(-B5*B3)*B4,0)定理 1-看涨期权定价的下界C12345678Proposition 3-Lower Lower Bounds for Put PricesCurrent stock price, S0 55Option time to maturity, T 0.5Option exercise price, X 80Interest rate, r 10%Naive minimum put option price, Max(X- S0,0) 25Proposition 3 lower bound on put price, Max(Exp(-rT)X- S0,0) 21.098- =MAX(B4-B2,0)- =MAX(EXP(-B5*B3)*B4-B2,0)Proposition 3-Lower Lower Bounds for Put Prices定理 3-看跌期权定价的下限当前股票价格, S0 55期权内到期时间, T 0.5期权执行价格, X 80利率, r 10%自然的最低期权价格, Max(X- S0,0) 25定理 3 期权价格的下限, Max(Exp(-rT)X- S0,0) 21.098- =MAX(B4-B2,0)- =MAX(EXP(-B5*B3)*B4-B2,0)定理 3-看跌期权定价的下限Put-Call ParityCurrent stock price, S0 55Option time to maturity, T 0.5Option exercise price, X 60Interest rate, r 10%Call price, C0 3Put price, P0 5.0738 - =B6+B4*EXP(-B5*B3)-B2This spreadsheet uses put-call parity to derive the put price P0 from the callprice C0, the interest rate r, the time to maturityT, and the exercise price X.A B C123456789看跌-看涨期权平价当前股票价格, S0 55期权到期时间, T 0.5期权执行价格, X 60利率, r 10%看涨期权价格, C0 3看跌期权价格, P0 5.0738 - =B6+B4*EXP(-B5*B3)-B2该电子表使用看跌-看涨期权平价定理通过看涨期权价格C0,利率r,到期时间T,执行价格X来计算看跌期权的价格P0.A B C123456789