ch21期權定價(存儲版)
【正文】 k 50 200Repay loan 50 50Net Payoff 0 1501500收入結(jié)構正好是看漲期權的 2倍Payoff Structure is exactly 2 times the Call218二項式期權定價模型：舉例Binomial Option Pricing: Text Example1500C7502C = $C = $219收入和期權價值的另一種觀點Another View of Replication of Payoffs and Option Values 另一個組合 – 1股股票和兩個售出的看漲期權的 組合恰好被套期保值 Alternative Portfolio one share of stock and 2 calls written (X = 125) Portfolio is perfectly hedged股票價值 Stock Value 50 200兩個 售出的看漲期權的義務 Call Obligation 0 150凈收入 Net payoff 50 50 Hence 100 2C = or C = 2110布萊克 斯科爾斯期權定價模型BlackScholes Option ValuationCo = SoedTN(d1) XerTN(d2)d1 = [ln(So/X) + (r – d + s2/2)T] / (s T1/2)d2 = d1 (s T1/2)式中 whereCo = 當前 看漲期權的價值 Current call option value.So = 當前股票 價格 Current stock priceN(d) = 隨機的偏離標準正態(tài)分布的概率小于 d probability that a random draw from a normal dist. will be less than d.2111布萊克 斯科爾斯期權定價模型BlackScholes Option Valuation X = 執(zhí)行價格 Exercise price.d = 標的股票的年股利收益率 Annual dividend yield of underlying stocke = , 自然對數(shù)函數(shù)的底數(shù) the base of the nat. log.r = 無風險利率 Riskfree interest rate (annualizes continuously pounded with the same maturity as the option.2112布萊克 斯科爾斯期權定價模型BlackScholes Option Valuation T = 期權到期前的時間（以年為單位） time to maturity of the option in years.ln = 自然對數(shù) Natural log functions = 股票連續(xù)復利年收益率的標準差 Standard deviation of annualized cont. pounded rate of return on the stock2113標準 正態(tài)曲線 布萊克 斯科爾斯看漲期權舉例Call Option Example股票價格 So = 100 執(zhí)行價格 X = 95利率 r = .10 到期時間 T = .25 (quarter)標準差 s = .50 股利收益率 d = 0d1 = [ln(100/95)+(.100+(.5 2/2))]/(.5 .251/2) = .43 d2 = .43 ((.5)( .251/2) =
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