问一道题：NO.PZ2020021205000045 [ FRM I ]

NO.PZ2020021205000045 问题如下 A trar wants to create synthetically a nine-month Europeput futures option on 1 million times inx. The futures priis US2,500, the strike priis US2,400, the risk-free rate is 2%, anthe volatility of the futures priis 20%. Whposition shoulthe trar take in futures contracts initially? How es this ffer from the position the trar woultake if he or she were heing the same nine-month Europeput futures option on 1 million times the inx?p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #473f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484045}span.s1 {color: #303b5f}span.s2 {color: #6b5547}span.s3 {color: #434c63}span.s4 {color: #695147} The lta of a long position in a put option on a futures priis e-rT[N( ) - 1]. In this case:=ln⁡(2,500/2,400)  +  (0.22/2)  X  0.750.20.75\frac{\ln(2,500/2,400)\;+\;(0.2^2/2)\;X\;0.75}{0.2\sqrt{0.75}}\\0.20.75​ln(2,500/2,400)+(0.22/2)X0.75​= 0.3223p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}anlta ise−o.o2xo.75e^{-o.o2xo.75}\\e−o.o2xo.75[N(0.3223) - 1] = -0.368The trar shoulshort futures contracts on 368,000 times the inx initially to matthe lta of the position this sire If the trar were heing 1 million put futures contracts he or she woultake a long position in futures contracts on 368,000 times the inx.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474347}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4a4449}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e42}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4031}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484349}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4c454c}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463e46}span.s1 {color: #4b586c}span.s2 {color: #635b63}span.s3 {font: 6.0px Helveticcolor: #515f7b}span.s4 {color: #7b7b7b}span.s5 {color: #777373}span.s6 {font: 6.0px Helvetica}span.s7 {color: #565663}span.s8 {color: #4a5465}span.s9 {color: #665047}span.s10 {color: #354067} 如标题

NO.PZ2020021205000045 问题如下 A trar wants to create synthetically a nine-month Europeput futures option on 1 million times inx. The futures priis US2,500, the strike priis US2,400, the risk-free rate is 2%, anthe volatility of the futures priis 20%. Whposition shoulthe trar take in futures contracts initially? How es this ffer from the position the trar woultake if he or she were heing the same nine-month Europeput futures option on 1 million times the inx?p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #473f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484045}span.s1 {color: #303b5f}span.s2 {color: #6b5547}span.s3 {color: #434c63}span.s4 {color: #695147} The lta of a long position in a put option on a futures priis e-rT[N( ) - 1]. In this case:=ln⁡(2,500/2,400)  +  (0.22/2)  X  0.750.20.75\frac{\ln(2,500/2,400)\;+\;(0.2^2/2)\;X\;0.75}{0.2\sqrt{0.75}}\\0.20.75​ln(2,500/2,400)+(0.22/2)X0.75​= 0.3223p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}anlta ise−o.o2xo.75e^{-o.o2xo.75}\\e−o.o2xo.75[N(0.3223) - 1] = -0.368The trar shoulshort futures contracts on 368,000 times the inx initially to matthe lta of the position this sire If the trar were heing 1 million put futures contracts he or she woultake a long position in futures contracts on 368,000 times the inx.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474347}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4a4449}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e42}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4031}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484349}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4c454c}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463e46}span.s1 {color: #4b586c}span.s2 {color: #635b63}span.s3 {font: 6.0px Helveticcolor: #515f7b}span.s4 {color: #7b7b7b}span.s5 {color: #777373}span.s6 {font: 6.0px Helvetica}span.s7 {color: #565663}span.s8 {color: #4a5465}span.s9 {color: #665047}span.s10 {color: #354067} futures inx指的是股票指数吗

NO.PZ2020021205000045 问题如下 A trar wants to create synthetically a nine-month Europeput futures option on 1 million times inx. The futures priis US2,500, the strike priis US2,400, the risk-free rate is 2%, anthe volatility of the futures priis 20%. Whposition shoulthe trar take in futures contracts initially? How es this ffer from the position the trar woultake if he or she were heing the same nine-month Europeput futures option on 1 million times the inx?p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #473f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484045}span.s1 {color: #303b5f}span.s2 {color: #6b5547}span.s3 {color: #434c63}span.s4 {color: #695147} The lta of a long position in a put option on a futures priis e-rT[N( ) - 1]. In this case:=ln⁡(2,500/2,400)  +  (0.22/2)  X  0.750.20.75\frac{\ln(2,500/2,400)\;+\;(0.2^2/2)\;X\;0.75}{0.2\sqrt{0.75}}\\0.20.75​ln(2,500/2,400)+(0.22/2)X0.75​= 0.3223p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}anlta ise−o.o2xo.75e^{-o.o2xo.75}\\e−o.o2xo.75[N(0.3223) - 1] = -0.368The trar shoulshort futures contracts on 368,000 times the inx initially to matthe lta of the position this sire If the trar were heing 1 million put futures contracts he or she woultake a long position in futures contracts on 368,000 times the inx.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474347}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4a4449}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e42}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4031}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484349}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4c454c}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463e46}span.s1 {color: #4b586c}span.s2 {color: #635b63}span.s3 {font: 6.0px Helveticcolor: #515f7b}span.s4 {color: #7b7b7b}span.s5 {color: #777373}span.s6 {font: 6.0px Helvetica}span.s7 {color: #565663}span.s8 {color: #4a5465}span.s9 {color: #665047}span.s10 {color: #354067} 我查表了，N()是0.6255，那么lta put应该是-0.3745。可是答案写lta put是-0.368？

NO.PZ2020021205000045问题如下 A trar wants to create synthetically a nine-month Europeput futures option on 1 million times inx. The futures priis US2,500, the strike priis US2,400, the risk-free rate is 2%, anthe volatility of the futures priis 20%. Whposition shoulthe trar take in futures contracts initially? How es this ffer from the position the trar woultake if he or she were heing the same nine-month Europeput futures option on 1 million times the inx?p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #473f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484045}span.s1 {color: #303b5f}span.s2 {color: #6b5547}span.s3 {color: #434c63}span.s4 {color: #695147}The lta of a long position in a put option on a futures priis e-rT[N( ) - 1]. In this case:=ln⁡(2,500/2,400)  +  (0.22/2)  X  0.750.20.75\frac{\ln(2,500/2,400)\;+\;(0.2^2/2)\;X\;0.75}{0.2\sqrt{0.75}}\\0.20.75​ln(2,500/2,400)+(0.22/2)X0.75​= 0.3223p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}anlta ise−o.o2xo.75e^{-o.o2xo.75}\\e−o.o2xo.75[N(0.3223) - 1] = -0.368The trar shoulshort futures contracts on 368,000 times the inx initially to matthe lta of the position this sire If the trar were heing 1 million put futures contracts he or she woultake a long position in futures contracts on 368,000 times the inx.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474347}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4a4449}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e42}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4031}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484349}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4c454c}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463e46}span.s1 {color: #4b586c}span.s2 {color: #635b63}span.s3 {font: 6.0px Helveticcolor: #515f7b}span.s4 {color: #7b7b7b}span.s5 {color: #777373}span.s6 {font: 6.0px Helvetica}span.s7 {color: #565663}span.s8 {color: #4a5465}span.s9 {color: #665047}span.s10 {color: #354067}答案中368000是怎么来的

NO.PZ2020021205000045问题如下A trar wants to create synthetically a nine-month Europeput futures option on 1 million times inx. The futures priis US2,500, the strike priis US2,400, the risk-free rate is 2%, anthe volatility of the futures priis 20%. Whposition shoulthe trar take in futures contracts initially? How es this ffer from the position the trar woultake if he or she were heing the same nine-month Europeput futures option on 1 million times the inx?p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #473f46}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484045}span.s1 {color: #303b5f}span.s2 {color: #6b5547}span.s3 {color: #434c63}span.s4 {color: #695147}The lta of a long position in a put option on a futures priis e-rT[N( ) - 1]. In this case:=ln⁡(2,500/2,400)  +  (0.22/2)  X  0.750.20.75\frac{\ln(2,500/2,400)\;+\;(0.2^2/2)\;X\;0.75}{0.2\sqrt{0.75}}\\0.20.75​ln(2,500/2,400)+(0.22/2)X0.75​= 0.3223p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}anlta ise−o.o2xo.75e^{-o.o2xo.75}\\e−o.o2xo.75[N(0.3223) - 1] = -0.368The trar shoulshort futures contracts on 368,000 times the inx initially to matthe lta of the position this sire If the trar were heing 1 million put futures contracts he or she woultake a long position in futures contracts on 368,000 times the inx.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474347}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4a4449}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #443e42}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #474445}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4031}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #484349}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #4c454c}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #463e46}span.s1 {color: #4b586c}span.s2 {color: #635b63}span.s3 {font: 6.0px Helveticcolor: #515f7b}span.s4 {color: #7b7b7b}span.s5 {color: #777373}span.s6 {font: 6.0px Helvetica}span.s7 {color: #565663}span.s8 {color: #4a5465}span.s9 {color: #665047}span.s10 {color: #354067}请一步步写下这个题目要求干啥，解题步骤可以吗？跟任何例题也靠不上？多谢了