ch21期權(quán)定價(jià)-全文預(yù)覽
【正文】 d yield of underlying stocke = , 自然對(duì)數(shù)函數(shù)的底數(shù) the base of the nat. log.r = 無(wú)風(fēng)險(xiǎn)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(quán)定價(jià)模型BlackScholes Option Valuation T = 期權(quán)到期前的時(shí)間（以年為單位） time to maturity of the option in years.ln = 自然對(duì)數(shù) Natural log functions = 股票連續(xù)復(fù)利年收益率的標(biāo)準(zhǔn)差 Standard deviation of annualized cont. pounded rate of return on the stock2113標(biāo)準(zhǔn) 正態(tài)曲線 布萊克 斯科爾斯看漲期權(quán)舉例Call Option Example股票價(jià)格 So = 100 執(zhí)行價(jià)格 X = 95利率 r = .10 到期時(shí)間 T = .25 (quarter)標(biāo)準(zhǔn)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) = .182114正態(tài)分布的概率Probabilities from Normal Dist.N (.43) = .6664Table d N(d) .42 .6628 .43 .6664 添寫(xiě) Interpolation .44 .67002115正態(tài)分布的概率Probabilities from Normal Dist.N (.18) = .5714Table d N(d) .16 .5636 .18 .5714 .20 .57932116看漲期權(quán)價(jià)值Call Option ValueCo = SoedTN(d1) XerTN(d2)Co = 100 X .6664 95 e .10 X .25 X .5714 Co = 隱含波動(dòng)性 Implied Volatility用 布萊克 斯科爾斯公式和實(shí)際期權(quán)價(jià)格來(lái)解決 波動(dòng)性Using BlackScholes and the actual price of the option, solve for volatility.隱含波動(dòng)性是否與股票具有一致性？Is the implied volatility consistent with the stock?2117看跌期權(quán)價(jià)值：布萊克 斯科爾斯Put Option Value: BlackScholesP=XerT [1N(d2)] S0edT [1N(d1)] 用上例的數(shù)據(jù) Using the sample dataP = $95e()() $100 ()P = $2118看跌期權(quán)定價(jià)：用看漲 看跌期權(quán)平價(jià)關(guān)系Put Option Valuation: Using PutCall ParityP = C + PV (X) So = C + XerT SoUsing the example dataC = X = 95 S = 100r = .10 T = .25P = + 95 e X .25 100P = 2119用布萊克 斯科爾斯公式Using the BlackScholes Formula 套期：套期保值率或 d 系數(shù) Hedging: Hedge ratio or delta 股票價(jià)格需要套期保值防范所持有期權(quán)的價(jià)格變化風(fēng)險(xiǎn) The number of stocks requi
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