定價(jià)策略black-scholesoptionpricingformula(1)(文件)
【正文】 t have n(2?1) ? ? ?T 4n?(?1) ?2 ??T This can be acplished by setting ? = 189。 ?2C/?S2 ?2(S,t)]dt + [?C/?S ?(S,t)]dz Consider a portfolio P, bination of S and C to eliminate uncertainty: P = C + ?C/?S S , the dynamics of P is dP = dC + ?C/?S dS, dP = [?C/?S ?(S,t) + ?C/?t + 189。 ?2C/?S2 ?2(S,t)]dt / [ C + ?C/?S S] = r dt, rearranging terms leads to the well known BS partial differential equation: ?C/?t + r S?C/?S + 189。(d1)eqT/(S?T1/2) Theta with respect to a decrease in maturity ?c=SN39。s ? is its partial derivative with respect to a change in the continuously pounded interest rate. Specifically, the call option pricing formula (Black and Scholes) is c=SN(d1)XerTN(d2) where d1=[ln(S/X)+(r+?2/2)T]/(?T1/2), d2=d1?T1/2 It follows that ?c/?r = XTerTN(d2) and (?c/?r)/c = (X/c)TerTN(d2)0 The total differential of the call option can be written as dc = ?c/?r dr + ?c/?S dS Dc=(dc/dr)/c =(?c/c)/?r ?c/?S (dS/dr)= = (X/c)TerTN(d2)(S/c)N(d1)Ds Consider a call option with strike price of $70 and maturity of 53 days (53/365= years). The current stock price is $, the annual standard deviation of %. The risk free rate of interest () is10%. d1=, N(d1)=, d2=, N(d2)= c= Thus Dc = (70/)* +()**Ds =+*Dc If Ds, then Dc is positive. 靜夜四無(wú)鄰，荒居舊業(yè)貧。 00:58:1400:58:1400:58Sunday, February 12, 2023 1乍見(jiàn)翻疑夢(mèng)，相悲各問(wèn)年。 2023年 2月 12日星期日 12時(shí) 58分 14秒 00:58:1412 February 2023 1做前，能夠環(huán)視四周；做時(shí)，你只能或者最好沿著以腳為起點(diǎn)的射線向前。 :58:1400:58Feb2312Feb23 1世間成事，不求其絕對(duì)圓滿，留一份不足，可得無(wú)限完美。 2023年 2月 上午 12時(shí) 58分 :58February 12, 2023 1少年十五二十時(shí)，步行奪得胡馬騎。 00:58:1400:58:1400:582/12/2023 12:58:14 AM 1越是沒(méi)有本領(lǐng)的就越加自命不凡。 :58:1400:58:14February 12, 2023 1意志堅(jiān)強(qiáng)的人能把世界放在手中像泥塊一樣任意揉捏。 上午 12時(shí) 58分 14秒 上午 12時(shí) 58分 00:58: MOMODA POWERPOINT Lorem ipsum dolor sit, eleifend nulla ac, fringilla purus. Nulla iaculis tempor felis amet, consectetur adipiscing elit. Fusce id urna blanditut cursus. 感謝您的下載觀看 專家告訴 。 2023年 2月 上午 12時(shí) 58分 :58February 12, 2023 1業(yè)余生活要有意義，不要越軌。 00:58:1400:58:1400:58Sunday, February 12, 2023 1知人者智，自知者明。 上午 12時(shí) 58分 14秒 上午 12時(shí) 58分 00:58: 楊柳散和風(fēng)，青山澹吾慮。 :58:1400:58:14February 12, 2023 1意志堅(jiān)強(qiáng)的人能把世界放在手中像泥塊一樣任意揉捏。 , February 12, 2023 很多事情努力了未必有結(jié)果，但是不努力卻什么改變也沒(méi)有。 2023年 2月 12日星期日 上午 12時(shí) 58分 14秒 00:58: 1比不了得就不比，得不到的就不要。 00:58:1400:58:1400:582/12/2023 12:58:14 AM 1以我獨(dú)沈久，愧君相見(jiàn)頻。(d1)?eqT/(2T1/2) qSN(d1)eqT+rXerTN(d2) Vega: with respect to an increase in volatility ?c=?p=ST1/2N39。 ?2)(Tt), ?(Tt)1/2) c=SeqTN(d1)XerTN(d2) p=XerTN(d2)SeqTN(d1) where d1=[ln(S/X)+(rq+?2/2)T]/(?T1/2), d2=d1?T1/2 Example: X=$70, Maturity date = June 27 (Evaluate on May 5: T=53/365 = ) ______________________________________________ S= X= T= r= . = q = European option prices: Call = Put = ? Implied volatility The volatility that makes the model price equal its market price. Assume that the call and put options in the above example are traded at and , respectively. Call i
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