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Archie · 2022年05月07日

这一章内容

NO.PZ2020021205000045

问题如下:

A trader wants to create synthetically a nine-month European put futures option on 1 million times an index. The futures price is USD 2,500, the strike price is USD 2,400, the risk-free rate is 2%, and the volatility of the futures price is 20%. What position should the trader take in futures contracts initially? How does this differ from the position the trader would take if he or she were hedging the same nine-month European put futures option on 1 million times the index?

解释:

The delta of a long position in a put option on a futures price is e-rT[N(d1 ) - 1]. In this case:

d1=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}}\\= 0.3223

and delta is

eo.o2xo.75e^{-o.o2xo.75}\\[N(0.3223) - 1] = -0.368

The trader should short futures contracts on 368,000 times the index initially to match the delta of the position that is desired. If the trader were hedging 1 million put futures contracts he or she would take a long position in futures contracts on 368,000 times the index.

期货的delta啥的在哪里哦

1 个答案

李坏_品职助教 · 2022年05月07日

嗨,从没放弃的小努力你好:


这个题目是把期权定价的BSM和期权delta结合起来了。可以看一下讲义Delta Hedging那部分,P518:

这里的△就是delta的意思。delta的含义是当股票价格变动1%时,期权价格变动百分之多少。

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努力的时光都是限量版,加油!

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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

2024-03-16 12:15 3 · 回答

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2023-06-08 11:47 1 · 回答

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2023-03-31 22:29 1 · 回答

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2023-03-11 15:35 2 · 回答