eva · 2024年04月02日
NO.PZ2020021205000010
问题如下：
A stock price is currently 40. At the end of six months it will be either 36 or 44. The risk-free rate is 5% per annum with continuous compounding. What is the value of a six month European put option with a strike price of 40?
解释：
In this case, u = 44/40 = 1.1 and d = 36/40 = 0.9
so that:
p==0.6266
and the value of the option is
(0.6266 X 0 + 0.3734 x 4) x= 1.4568
6months为何r不用除2，不是应该2.5%？
NO.PZ2020021205000010 问题如下 A stopriis currently 40. the enof six months it will either 36 or 44. The risk-free rate is 5% per annum with continuous compounng. Whis the value of a six month Europeput option with a strike priof 40?p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 7.5px Helveticcolor: #444047}span.s1 {color: #664f47}span.s2 {color: #466b}span.s3 {color: #3a3035} In this case, u = 44/40 = 1.1 an= 36/40 = 0.9p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e44}span.s1 {color: #757374}span.s2 {font: 10.0px Helvetica}so that:p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #585458}p=e0.05∗0.5−0.91.1 − 0 .9\frac{e^{0.05\ast0.5}-0.9}{1.1\;-\;0\;.9}1.1−0.9e0.05∗0.5−0.9=0.6266anthe value of the option isp.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484046}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #534f}span.s1 {color: #6b5547}(0.6266 X 0 + 0.3734 x 4) xe−0.05∗0.5e^{-0.05\ast0.5}e−0.05∗0.5= 1.4568p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #534f}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #3f393f} In this case, u = 44/40 = 1.1 an= 36/40 = 0.9
NO.PZ2020021205000010问题如下A stopriis currently 40. the enof six months it will either 36 or 44. The risk-free rate is 5% per annum with continuous compounng. Whis the value of a six month Europeput option with a strike priof 40?p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 7.5px Helveticcolor: #444047}span.s1 {color: #664f47}span.s2 {color: #466b}span.s3 {color: #3a3035} In this case, u = 44/40 = 1.1 an= 36/40 = 0.9p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e44}span.s1 {color: #757374}span.s2 {font: 10.0px Helvetica}so that:p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #585458}p=e0.05∗0.5−0.91.1 − 0 .9\frac{e^{0.05\ast0.5}-0.9}{1.1\;-\;0\;.9}1.1−0.9e0.05∗0.5−0.9=0.6266anthe value of the option isp.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484046}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #534f}span.s1 {color: #6b5547}(0.6266 X 0 + 0.3734 x 4) xe−0.05∗0.5e^{-0.05\ast0.5}e−0.05∗0.5= 1.4568p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #534f}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #3f393f}老师这道题不是说either 44 or 36 那么每个结果不应该各占50%概率么
老师好。问一下 In this case, u = 44/40 = 1.1 an= 36/40 = 0.9 是怎么来的
