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