问一道题：NO.PZ2020021205000030 [ FRM I ]

NO.PZ2020021205000030 问题如下 The futures priof asset is US20, anthe volatility of the futures priis 30%. Calculate the value of a put option to sell futures in three months for US22. The risk-free rate is 4%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463f46}span.s1 {color: #4b5768}span.s2 {color: #6b5147} In this case F0 = 20, K = 22, r = 0.04, u = 0.3,p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4134}span.s1 {font: 8.5px Helvetica}span.s2 {font: 5.5px Helvetica}span.s3 {color: #696b}span.s4 {font: 9.5px Helvetica}span.s5 {color: #675248}T = 0.25, anEquation (15.13) gives=ln⁡(20/22)  +  (0.32/2)  X  0.250.30.25\frac{\ln(20/22)\;+\;(0.3^2/2)\;X\;0.25}{0.3\sqrt{0.25}}0.30.25​ln(20/22)+(0.32/2)X0.25​= -0.5604p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a4449}span.s1 {color: #6b6b6b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 5.5px Helveticcolor: #4c474span.s1 {font: 8.5px Helvetica}span.s2 {font: 8.0px Helvetica}span.s3 {font: 8.0px Helveticcolor: #a29f9e} =ln⁡(20/22)  −  (0.32/2)  X  0.250.30.25\frac{\ln(20/22)\;-\;(0.3^2/2)\;X\;0.25}{0.3\sqrt{0.25}}0.30.25​ln(20/22)−(0.32/2)X0.25​= -0.7104p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4c474p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a444b}put =22*EXP(-4%*0.25)*N(0.7104)-20*EXP(-4%*0.25)*N(0.5604)=2.48p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a444b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4e464c}span.s1 {color: #373a}span.s2 {color: #777377}span.s3 {color: #636b73}span.s4 {font: 5.0px Helvetic 老师，如题，是我哪里理解错了吗

NO.PZ2020021205000030问题如下 The futures priof asset is US20, anthe volatility of the futures priis 30%. Calculate the value of a put option to sell futures in three months for US22. The risk-free rate is 4%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463f46}span.s1 {color: #4b5768}span.s2 {color: #6b5147} In this case F0 = 20, K = 22, r = 0.04, u = 0.3,p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4134}span.s1 {font: 8.5px Helvetica}span.s2 {font: 5.5px Helvetica}span.s3 {color: #696b}span.s4 {font: 9.5px Helvetica}span.s5 {color: #675248}T = 0.25, anEquation (15.13) gives=ln⁡(20/22)  +  (0.32/2)  X  0.250.30.25\frac{\ln(20/22)\;+\;(0.3^2/2)\;X\;0.25}{0.3\sqrt{0.25}}0.30.25​ln(20/22)+(0.32/2)X0.25​= -0.5604p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a4449}span.s1 {color: #6b6b6b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 5.5px Helveticcolor: #4c474span.s1 {font: 8.5px Helvetica}span.s2 {font: 8.0px Helvetica}span.s3 {font: 8.0px Helveticcolor: #a29f9e} =ln⁡(20/22)  −  (0.32/2)  X  0.250.30.25\frac{\ln(20/22)\;-\;(0.3^2/2)\;X\;0.25}{0.3\sqrt{0.25}}0.30.25​ln(20/22)−(0.32/2)X0.25​= -0.7104p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4c474p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a444b}put =22*EXP(-4%*0.25)*N(0.7104)-20*EXP(-4%*0.25)*N(0.5604)=2.48p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a444b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4e464c}span.s1 {color: #373a}span.s2 {color: #777377}span.s3 {color: #636b73}span.s4 {font: 5.0px Helvetic为什么考虑R但是计算P价格的时候要考虑R

NO.PZ2020021205000030问题如下The futures priof asset is US20, anthe volatility of the futures priis 30%. Calculate the value of a put option to sell futures in three months for US22. The risk-free rate is 4%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463f46}span.s1 {color: #4b5768}span.s2 {color: #6b5147} In this case F0 = 20, K = 22, r = 0.04, u = 0.3,p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4134}span.s1 {font: 8.5px Helvetica}span.s2 {font: 5.5px Helvetica}span.s3 {color: #696b}span.s4 {font: 9.5px Helvetica}span.s5 {color: #675248}T = 0.25, anEquation (15.13) gives=ln⁡(20/22)  +  (0.32/2)  X  0.250.30.25\frac{\ln(20/22)\;+\;(0.3^2/2)\;X\;0.25}{0.3\sqrt{0.25}}0.30.25​ln(20/22)+(0.32/2)X0.25​= -0.5604p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a4449}span.s1 {color: #6b6b6b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 5.5px Helveticcolor: #4c474span.s1 {font: 8.5px Helvetica}span.s2 {font: 8.0px Helvetica}span.s3 {font: 8.0px Helveticcolor: #a29f9e} =ln⁡(20/22)  −  (0.32/2)  X  0.250.30.25\frac{\ln(20/22)\;-\;(0.3^2/2)\;X\;0.25}{0.3\sqrt{0.25}}0.30.25​ln(20/22)−(0.32/2)X0.25​= -0.7104p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4c474p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a444b}p=22 /spe−0.04∗0.25 /spe^{-0.04\ast0.25} /spe−0.04∗0.25N(O.71O4)p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4e464c}span.s1 {color: #373a}span.s2 {color: #777377}span.s3 {color: #636b73}span.s4 {font: 5.0px Helvetica}- 20 spe−0.04∗0.25 spe^{-0.04\ast0.25} spe−0.04∗0.25N(O.56O4) = 2.48p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4a444b}答案后两行是乱码，请老师更正。