第21章 期权定价 Option valuation 21-1
21-1 第21章 期权定价 Option Valuation
期权定价 Option valuation 21.1期权定价简 21.2期权价值的限制 21.3二项式期权定价模型 21.4布莱克-斯克尔斯期权定价 21.5布莱克-斯克尔斯公式的运用 21.6经验证明 21-2
21-2 期权定价 Option Valuation 21.1 期权定价简介 21. 2 期权价值的限制 21.3 二项式期权定价模型 21.4 布莱克-斯克尔斯期权定价 21.5 布莱克-斯克尔斯公式的运用 21.6 经验证明
期权定价 Option Values ■内在价值一立即执行该期权能获的收入 Intrinsic value-profit that could be made if the option was immediately exercised 看涨期权:股票价格一执行价格 Call: stock price-exercise price 看跌期权:执行价格-股票价格 Put: exercise price-stock price ■时间价值一期权价格与内在价值间的差异 Time value -the difference between the option price and the intrinsic value 21-3
21-3 期权定价 Option Values 内在价值 – 立即执行该期权能获的收入 Intrinsic value - profit that could be made if the option was immediately exercised – 看涨期权: 股票价格 – 执行价格 Call: stock price - exercise price – 看跌期权: 执行价格 - 股票价格 Put: exercise price - stock price 时间价值 – 期权价格与内在价值间的差异 Time value - the difference between the option price and the intrinsic value
期权的时间价值:看涨期权 Time Value of Options: Call 期权价值 Option value 看涨期权价值 Value of call 内在价值 时间价值 Intrinsic value Time value 股票价格 Stock price
21-4 期权的时间价值 ：看涨期权 Time Value of Options: Call 期权价值 Option value X 股票价格Stock Price 看涨期权价值 Value of Call 内在价值 时间价值 Intrinsic Value Time value
影响看涨期权价值的因素 Factors Influencing Option Values: Calls 因素 Factor 对价值的作用 Effect on value 股票价格 Stock price Increases 执行价格 EXercise price decreases 股票价格的波动 Volatility of stock price increases 到期 Time to expiration ncreases 利息率 nterest rate Increases 股利 Dividend rate decreases 21-5
21-5 影响看涨期权价值的因素 Factors Influencing Option Values: Calls 因素 Factor 对价值的作用 Effect on value 股票价格 Stock price increases 执行价格 Exercise price decreases 股票价格的波动Volatility of stock price increases 到期 Time to expiration increases 利息率 Interest rate increases 股利 Dividend Rate decreases
二项式期权定价模型:举例 Binomial Option Pricing Text EXample 200 5 100 50 0 股票价格 Stock price 看涨期权价值 Call optionⅤalue X=125 21-6
21-6 二项式期权定价模型：举例 Binomial Option Pricing: Text Example 100 200 50 股票价格Stock Price C 75 0 看涨期权价值 Call Option Value X = 125
二项式期权定价模型:举例 Binomial Option pricing Text Example 另一个组合 Alternative portfolio 150 买1股100元的股票借$4630 8%的利率)净支出是$537053.70 Buy 1 share of stock at $100 Borrow $46. 30(8% Rate) 0 Net outlay $53.70 收入 Payoff 收入结构正好是看涨期 Value of stock 50 200 权的2倍 Repay loan 50-50 Payoff structure is exactly 2 times the call Net Payoff 0150 21-7
21-7 二项式期权定价模型：举例 Binomial Option Pricing: Text Example 另一个组合Alternative Portfolio 买1股100元的股票借$46.30 8%的利率）净支出是$53.70 Buy 1 share of stock at $100 Borrow $46.30 (8% Rate) Net outlay $53.70 收入Payoff Value of Stock 50 200 Repay loan - 50 -50 Net Payoff 0 150 53.70 150 0 收入结构正好是看涨期 权的2倍 Payoff Structure is exactly 2 times the Call
项式期权定价模型:举例 Binomial Option Pricing: Text EXample 150 5 53.70 0 0 2C=S53.70 C=$2685 21-8
21-8 二项式期权定价模型：举例 Binomial Option Pricing: Text Example 53.70 150 0 C 75 0 2C = $53.70 C = $26.85
收入和期权价值的另一种观点 Another View of replication of Payoffs and option values 另一个组合-1股股票和两个售出的看涨期权的组合恰 好被套期保值 Alternative Portfolio - one share of stock and 2 calls written (X=125) Portfolio is perfectly hedged 股票价值 Stock value 50 200 两个售出的看涨期权的义务 Ca‖ Obligation 150 净收入 Net payoff 50 50 Hence100-2C=46.30oC=2685 219
21-9 收入和期权价值的另一种观点 Another View of Replication of Payoffs and Option Values 另一个组合 – 1股股票和两个售出的看涨期权的组合恰 好被套期保值 Alternative Portfolio - one share of stock and 2 calls written (X = 125) Portfolio is perfectly hedged 股票价值 Stock Value 50 200 两个售出的看涨期权的义务 Call Obligation 0 -150 净收入 Net payoff 50 50 Hence 100 - 2C = 46.30 or C = 26.85
布莱克-斯科尔斯期权定价模型 Black-Scholes Option valuation Co=Se8TN(d1)-×eN(d d1=[n(S。)+(r-δ+σ2/2)/(oT12 d2=d1-(oT12) 式中 Where C。=当前看涨期权的价值 Current call option value S。=当前股票价格 Current stock price N(d)=随机的偏离标准正态分布的概率小于d probability that a random draw from a normal dist will be less than d
21-10 布莱克-斯科尔斯期权定价模型 Black-Scholes Option Valuation Co = Soe -dTN(d1 ) - Xe-rTN(d2 ) d1 = [ln(So /X) + (r – d + s 2 /2)T] / (s T1/2) d2 = d1 - (s T1/2) 式中 where Co = 当前看涨期权的价值Current call option value. So = 当前股票价格 Current stock price N(d) = 随机的偏离标准正态分布的概率小于d probability that a random draw from a normal dist. will be less than d