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TWO-DATE BINOMIAL OPTION PRICINGUp 1.40 Means that 5-year interest rate = 33.82%SP500 in 5 yearsGood state 2500 = Means that up = 66.67%Bad state 1200 = Means that down = -20.00%Positive return percentage 120%Payoff on BOWOWGood state 18Bad state 10Calculating 5-year state pricesSP500250015001200Bond, 5 years133.8226100133.8226State prices Check?qu 0.4641 SP 500 price today 1500qd 0.2832 Interest factor 33.82%At-the-money SP call1000464.06940To answer this question, note that BOBOWs payoff is $10 plus 1.2/1500 times an at-the-money SP call with T = 5.Value of an at-the-money SP call, using binomial model 464.06941.2/1500 times at-the-money SP call 0.3713PV($10) plus the above=? value of BOBOW 7.8438BEST OF BOTH WORLDS (BOBOW)两世最佳 (BOBOW)今天的成本 10今天的SP500 1500利率 6% =意味着5年期利率 = 33.82%5年后的SP500好的状态 2500 = 意味着 上涨 = 66.67%坏的状态 1200 = 意味着 下跌 = -20.00%收益为正的百分数 120%BOWOW上的现金流好的状态 18坏的状态 10计算5年后的状态价格SP500250015001200债券, 5年133.8226100133.8226状态价格 检查?qu 0.4641 SP 500 今天的价格 1500qd 0.2832利率因素 33.82%两平SP看涨期权1000464.06940回答这个问题,注意BOBOW的现金流是$10加上1.2/1500乘以一个SP两平看涨期权价格，该期权到期时间T = 5.SP实值看涨期权的价值, 用二项式模型 464.06941.2/1500乘以SP两平看涨期权价格 0.3713PV($10)加上上面=BOBOW的价值？ 7.8438两世最佳 (BOBOW)Exercise 10Page 72CONVERGENCE OF BINOMIAL TO BLACK-SCHOLESNote that this spreadsheet works for n =M A X (F 1 7 -E 5 ,0 ), n o , y e s )= M A X (q u * F 2 9 + q d * F 3 1 ,M A X (D 2 0 -E 4 ,0 )Illustration-Date 2 & 3 market values 0.0000.0000.0000.0000.0000.0000.000exercise 0.000PV 0.000= M A X (q u * H 2 6 + q d * H 2 8 ,M A X (F 1 7 -E 5 ,0 )= IF (q u * H 2 6 + q d * H 2 8 =M A X (F 1 7 -E 5 ,0 ), n o , y e s )TIME-DEPENDENT 执行价格S初始股票价格 50 执行价格s上涨 1.25 Date 1 55下跌 0.90 Date 2 113.3利率 1.06 Date 3 233.398状态价格qu 0.4313qd 0.5121Check1/(qu+qd) 1.06qu*上涨+qd*下跌 1股票价格 97.65678.12562.500 70.31350.000 56.25045.000 50.62540.50036.450Date 0 Date 1 Date 2 Date 3每个节点的价值 0.0000.0007.500 0.0003.235 0.0000.000 0.0000.0000.000提前执行?noyesnonono说明-第3天的现金流 0.00000.00000.00000.0000执行 0.000PV 0.000= IF (q u * H 2 6 + q d * H 2 8 =M A X (F 1 7 -E 5 ,0 ), n o , y e s )= M A X (q u * F 2 9 + q d * F 3 1 ,M A X (D 2 0 -E 4 ,0 )说明-第2 & 3天的市场价值 0.0000.0000.0000.0000.0000.0000.000执行 0.000PV 0.000= M A X (q u * H 2 6 + q d * H 2 8 ,M A X (F 1 7 -E 5 ,0 )= IF (q u * H 2 6 + q d * H 2 8 =M A X (F 1 7 -E 5 ,0 ), n o , y e s )PRICING THE BISCO STOCK DERIVATIVEUp, U 1.50Down, D 0.80 State pricesqu 0.3704Initial stock price 3 qd 0.5556Interest rate, R 1.08Exercise price 40Date 2 prices and security payoffsBisco moves: Biscoprice Securitypays off StatepriceUp, Up 6.75 268 - =MAX(B113-$B$7,0) 0.1372Up, Down 3.6 7 - =MAX(B123-$B$7,0) 0.4115Down, Down 1.92 0 - =MAX(B133-$B$7,0) 0.3086Value of Biscoderivative 39.440 - =SUMPRODUCT(C11:C13,E11:E13)Check- =(B6-B3)/(B6*(B2-B3) 1/(qu+qd) 1.08- =(B2-B6)/(B6*(B2-B3) qu*U+qd*D 1PRICING THE BISCO STOCK DERIVATIVE定价Bisco股票衍生物上涨, U 1.50下跌, D 0.80 状态价格qu 0.3704初始股票价格 3 qd 0.5556利率, R 1.08执行价格 40第 2 天价格和现金流Bisco运动: Bisco 价格 证券现金流 状态价格上涨, 上涨 6.75 268 - =MAX(B113-$B$7,0) 0.1372上涨, 下跌 3.6 7 - =MAX(B123-$B$7,0) 0.4115下跌, 下跌 1.92 0 - =MAX(B133-$B$7,0) 0.3086Bisco衍生物价值 39.440 - =SUMPRODUCT(C11:C13,E11:E13)检查- =(B6-B3)/(B6*(B2-B3) 1/(qu+qd) 1.08- =(B2-B6)/(B6*(B2-B3) qu*U+qd*D 1定价Bisco股票衍生物
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