开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

呜啦啦 · 2024年09月05日

long call=long stock+卖bond借钱

  1. CFA II
  2. Derivative

NO.PZ2023020101000023

问题如下：

Cummins states that long-/short-hedge fund managers seek to identify and exploit any mispricing that may exist between the price of an option and the price of its underlying stock, utilizing a replicating strategy. Cummins asks Spelding to assess the three scenarios outlined in Exhibit 2, based on the information in Exhibit 1 and assuming that the price of a one-year European-style call option is $19.25.

Exhibit 1: Binomial Model Variables and Values

Exhibit 2: Scenarios and Replicating Strategies

With respect to the replicating strategies, which scenario is most likely correct:

选项：

A.

Scenario 1.

B.

Scenario 2.

C.

Scenario 3.

解释：

The $19.25 price of the call option exceeds its value of $15.44, as calculated based on both the no-arbitrage approach and the expectations approach. Accordingly, the replicating strategy per 100 shares is to (1) sell 1 option, (2) buy h shares, and (3) borrow h * (up/down factor price + up/down call payoff).

The call option calculations follow:

• No-arbitrage approach:

Hedge ratio

h=c+−c−S+−S−=35−0135−75=3560=0.5833h=\frac{c^+-c^-}{S^+-S^-}=\frac{35-0}{135-75}=\frac{35}{60}=0.5833

Call Option value

c=hS+PV(−hS−+c−=0.5833∗100+(−75∗0.5833)1.02+0=$15.44c=hS+PV(-hS^-+c^-=0.5833\ast100+\frac{{(-75\ast0}{.5833)}}{1.02}+0=\$15.44

• Expectations approach:

Probability of an up move π=0.45

Call Option value

c=35∗0.45+01+0.02=$15.44c=\frac{35\ast0.45+0}{1+0.02}=\$15.44

如果说long call=long stock+卖bond借钱，那现在需要short call为什么仍然是buy stock，而不是short呢

添加评论
1 个答案
已采纳答案

李坏_品职助教 · 2024年09月05日

嗨，努力学习的PZer你好：


本题的意思是，当前真实的option市场价格是19.25，而虚拟的option的理论价值（No-arbitrage approach）是15.44，所以为了进行套利，需要卖出被高估的真实option（以19.25的价格卖出），同时买入被低估的虚拟option。


买入被低估的虚拟option，也就是要用buy h shares + borrow去构造一个虚拟的option。


----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

  • 1

    回答

  • 0

    关注

  • 121

    浏览
相关问题

NO.PZ2023020101000023 问题如下 Cummins states thlong-/short-hee funanagers seek to intify anexploit any mispricing thmexist between thepriof option anthe priof its unrlying stock, utilizing areplicating strategy. Cummins asks Spelng to assess the three scenariosoutlinein Exhibit 2, baseon the information in Exhibit 1 anassuming thatthe priof a one-yeEuropean-style call option is $19.25.Exhibit1: BinomiMol Variables anValuesExhibit2: Scenarios anReplicating StrategiesWith respeto the replicatingstrategies, whiscenario is mostlikely correct: A.Scenario1. B.Scenario2. C.Scenario3. The$19.25 priof the call option excee its value of $15.44, calculateaseon both the no-arbitrage approaanthe expectations approach.Accorngly, the replicating strategy per 100 shares is to (1) sell 1 option, (2)buy h shares, an(3) borrow h * (up/wn factor pri+ up/wn call payoff).Thecall option calculations follow:• No-arbitrage approach:Hee ratio h=c+−c−S+−S−=35−0135−75=3560=0.5833h=\frac{c^+-c^-}{S^+-S^-}=\frac{35-0}{135-75}=\frac{35}{60}=0.5833h=S+−S−c+−c−​=135−7535−0​=6035​=0.5833Call Option value c=hS+PV(−hS−+c−=0.5833∗100+(−75∗0.5833)1.02+0=$15.44c=hS+PV(-hS^-+c^-=0.5833\ast100+\frac{{(-75\ast0}{.5833)}}{1.02}+0=\$15.44c=hS+PV(−hS−+c−=0.5833∗100+1.02(−75∗0.5833)​+0=$15.44 • Expectations approach:Probability of up move π=0.45 Call Option valuec=35∗0.45+01+0.2=$15.44c=\frac{35\ast0.45+0}{1+0.2}=\$15.44c=1+0.235∗0.45+0​=$15.44 C=hS0- PV(bonIf we are buying synethic call, isn't it buy h shares of stoanshort bonwhiis lenmoney.I having a hartime unrstanng the the + an- sign of the PV term.

2023-10-14 02:05 2 · 回答

NO.PZ2023020101000023 问题如下 Cummins states thlong-/short-hee funanagers seek to intify anexploit any mispricing thmexist between thepriof option anthe priof its unrlying stock, utilizing areplicating strategy. Cummins asks Spelng to assess the three scenariosoutlinein Exhibit 2, baseon the information in Exhibit 1 anassuming thatthe priof a one-yeEuropean-style call option is $19.25.Exhibit1: BinomiMol Variables anValuesExhibit2: Scenarios anReplicating StrategiesWith respeto the replicatingstrategies, whiscenario is mostlikely correct: A.Scenario1. B.Scenario2. C.Scenario3. The$19.25 priof the call option excee its value of $15.44, calculateaseon both the no-arbitrage approaanthe expectations approach.Accorngly, the replicating strategy per 100 shares is to (1) sell 1 option, (2)buy h shares, an(3) borrow h * (up/wn factor pri+ up/wn call payoff).Thecall option calculations follow:• No-arbitrage approach:Hee ratio h=c+−c−S+−S−=35−0135−75=3560=0.5833h=\frac{c^+-c^-}{S^+-S^-}=\frac{35-0}{135-75}=\frac{35}{60}=0.5833h=S+−S−c+−c−​=135−7535−0​=6035​=0.5833Call Option value c=hS+PV(−hS−+c−=0.5833∗100+(−75∗0.5833)1.02+0=$15.44c=hS+PV(-hS^-+c^-=0.5833\ast100+\frac{{(-75\ast0}{.5833)}}{1.02}+0=\$15.44c=hS+PV(−hS−+c−=0.5833∗100+1.02(−75∗0.5833)​+0=$15.44 • Expectations approach:Probability of up move π=0.45 Call Option valuec=35∗0.45+01+0.2=$15.44c=\frac{35\ast0.45+0}{1+0.2}=\$15.44c=1+0.235∗0.45+0​=$15.44 我看了之前老师回答的答案，【根据无套利组合，每卖出1份call，需要long Δ份股票，因此我们long0.58份股票】无套利组合是啥，这是李老师在哪里讲的知识点？为什么不能用C+K=P+S？我最开始尝试用这个思考，发现算不出来。我也用了老师讲的等式，如下图，推出的是卖出看涨期权【也就是题目所求的操作内容】，等于买空股票加买入债券，发现答案没有我的这个。请老师指出我错在哪里呢？

2023-10-04 17:01 3 · 回答

NO.PZ2023020101000023 问题如下 Cummins states thlong-/short-hee funanagers seek to intify anexploit any mispricing thmexist between thepriof option anthe priof its unrlying stock, utilizing areplicating strategy. Cummins asks Spelng to assess the three scenariosoutlinein Exhibit 2, baseon the information in Exhibit 1 anassuming thatthe priof a one-yeEuropean-style call option is $19.25.Exhibit1: BinomiMol Variables anValuesExhibit2: Scenarios anReplicating StrategiesWith respeto the replicatingstrategies, whiscenario is mostlikely correct: A.Scenario1. B.Scenario2. C.Scenario3. The$19.25 priof the call option excee its value of $15.44, calculateaseon both the no-arbitrage approaanthe expectations approach.Accorngly, the replicating strategy per 100 shares is to (1) sell 1 option, (2)buy h shares, an(3) borrow h * (up/wn factor pri+ up/wn call payoff).Thecall option calculations follow:• No-arbitrage approach:Hee ratio h=c+−c−S+−S−=35−0135−75=3560=0.5833h=\frac{c^+-c^-}{S^+-S^-}=\frac{35-0}{135-75}=\frac{35}{60}=0.5833h=S+−S−c+−c−​=135−7535−0​=6035​=0.5833Call Option value c=hS+PV(−hS−+c−=0.5833∗100+(−75∗0.5833)1.02+0=$15.44c=hS+PV(-hS^-+c^-=0.5833\ast100+\frac{{(-75\ast0}{.5833)}}{1.02}+0=\$15.44c=hS+PV(−hS−+c−=0.5833∗100+1.02(−75∗0.5833)​+0=$15.44 • Expectations approach:Probability of up move π=0.45 Call Option valuec=35∗0.45+01+0.2=$15.44c=\frac{35\ast0.45+0}{1+0.2}=\$15.44c=1+0.235∗0.45+0​=$15.44 老师，1）options tra / stotra/ Financing 分别是什么？2）如何做这个套利？

2023-08-30 20:55 1 · 回答

NO.PZ2023020101000023 问题如下 Cummins states thlong-/short-hee funanagers seek to intify anexploit any mispricing thmexist between thepriof option anthe priof its unrlying stock, utilizing areplicating strategy. Cummins asks Spelng to assess the three scenariosoutlinein Exhibit 2, baseon the information in Exhibit 1 anassuming thatthe priof a one-yeEuropean-style call option is $19.25.Exhibit1: BinomiMol Variables anValuesExhibit2: Scenarios anReplicating StrategiesWith respeto the replicatingstrategies, whiscenario is mostlikely correct: A.Scenario1. B.Scenario2. C.Scenario3. The$19.25 priof the call option excee its value of $15.44, calculateaseon both the no-arbitrage approaanthe expectations approach.Accorngly, the replicating strategy per 100 shares is to (1) sell 1 option, (2)buy h shares, an(3) borrow h * (up/wn factor pri+ up/wn call payoff).Thecall option calculations follow:• No-arbitrage approach:Hee ratio h=c+−c−S+−S−=35−0135−75=3560=0.5833h=\frac{c^+-c^-}{S^+-S^-}=\frac{35-0}{135-75}=\frac{35}{60}=0.5833h=S+−S−c+−c−​=135−7535−0​=6035​=0.5833Call Option value c=hS+PV(−hS−+c−=0.5833∗100+(−75∗0.5833)1.02+0=$15.44c=hS+PV(-hS^-+c^-=0.5833\ast100+\frac{{(-75\ast0}{.5833)}}{1.02}+0=\$15.44c=hS+PV(−hS−+c−=0.5833∗100+1.02(−75∗0.5833)​+0=$15.44 • Expectations approach:Probability of up move π=0.45 Call Option valuec=35∗0.45+01+0.2=$15.44c=\frac{35\ast0.45+0}{1+0.2}=\$15.44c=1+0.235∗0.45+0​=$15.44 Accorngly, the replicating strategy per 100 shares is to (1) sell 1 option, (2) buy h shares, an(3) borrow h * (up/wn factor pri+ up/wn call payoff).算出来的15,44我懂，怎么操作我没理解

2023-07-09 16:09 2 · 回答