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Stella · 2024年07月28日

这道题能不能更简单的通过题干得到答案?

NO.PZ2022062601000025

问题如下:

Investor John evaluated the U-fund, which is a convertible bond strategy. In order to gain a more accurate understanding of fund investment styles, John studied various trading examples used by U fund managers to generate alpha. Exhibit 1 provides data on recent transactions in which managers have been involved.

Exhibit 1

U-Fund Convertible Bond Arbitrage Position

Based on the data in Exhibit 1, what strategy is the most likely to be implemented by the portfolio manager of Fund U?

选项:

A.

Taking advantage of option mispricing

B.

Profiting from extreme market volatility

C.

Going long a put on the equity net of hedging

解释:

A is correct. In order to obtain and extract relatively cheap embedded options in convertible securities, the manager hedged other risks embedded in convertible securities. These risks include interest rate risk, credit risk, and market risk. These risks can be hedged through a combination of interest rate derivatives, credit default swaps, and short selling the appropriate Delta adjusted amount of the underlying stock, or by purchasing put options.

B is incorrect because convertible arbitrage strategies perform best in moderate volatility. Heightened volatility would suggest a period of illiquidity and widening credit spreads.

C is incorrect because purchasing convertible bonds and Delta hedging positions do not equate to long put positions.

知识点考察:Convertible Bond Arbitrage


首先看到表格中红框的这几项,联想到Convertible Bond Arbitragelong CB short stock,同时使用杠杆。然后表格中剩下的没有红框的内容是是针对convertible arbitrage strategy中的convertible securityinterest rate risk, credit risk of the corporate issuer, and market risk进行对冲,相应的对冲工具也是表格中的内容interest rate derivatives, credit default swaps, and short sales of an appropriate delta-adjusted amount of the underlying stock or, alternatively, the purchase of put options

所以判断是Convertible Bond Arbitrage。然后这个策略实际就是利用Convertible Bond由于新发行时交易量小,债券的复杂性导致其内嵌的option波动低,因此其交易价格低于其自身价值,也就是被低估,所以做多Convertible Bond。这正是选项ATaking advantage of option mispricing。所以选择A


问题一:因为题干已经说了是convertible bond strategy,所以就直接选a呢?表格信息反而算是有些干扰了?

问题二:表格中put option on stock的rational中“only in place of delta hedge”是什么意思?

2 个答案
已采纳答案

伯恩_品职助教 · 2024年07月28日

嗨,从没放弃的小努力你好:


好的,只是对于希腊字母还是有点不太清楚,框架图中也没有整理的模式,虽然是二级学习的内容,但三级涉及的还是多,请问助教老师有没有整理好的希腊字母总结?——

1,Delta


Delta值(δ),又称对冲值。反映了期权价格相对于标的价格的敏感程度,衡量标的资产价格变动时,期权价格的变化幅度。


用公式表示:Delta=期权价格变化/标的资产现货价格变化。期权的delta值介于-1到1之间。


例如:认购期权 Delta值=0.5,代表标的资产价格上涨1元,认购期权价格上涨0.5元。


对于看涨期权来说,Dleta为正值,其波动范围在0到1之间。看涨期权的实值程度越高,Delta值越大。平值看涨期权的Delta值接近0.5,当看涨期权处于深度实值状态时,Delta趋近于1,处于深度虚值状态时,Delta则趋近于0。


Delta的几个重要特性: 1、标的合约的Delta 值恒为1; 2、看涨期权的Delta 值在(0,1) 之间; 3、看跌期权的Delta 值在(-1,0) 之间; 4、平值的看涨期权的Delta在0.5附近,平值的看跌期权在-0.5 附近; 5、一对到期日和行权价相同的看涨期权和看跌期权,二者Delta 的绝对值之和为1;


2,Gamma


Gamma(γ)值= Delta的变化量/标的价格的变化量。从数学推导上,Gamma 其实就是Delta 的斜率, 所以Gamma 的特征和Delta 密切相关。


Gamma是反映标的物价格变动1%,delta变动的幅度。例如:某一期权合约的delta为0.6,gamma值为0.05,则表示标的价格上升1%,所引起delta增加量为0.05。delta将从0.6增加到0.65


平值期权的gamma值最大,深实值或深虚值期权的gamma值则趋近于0。gamma值越大,表明delta的变化速度愈快。


同一行权价,看涨期权与看跌期权的Gamma值一样。买入期权的gamma为正,卖出期权的gamma为负。


Gamma的运用:


• 当标的资产价格变化一个单位时,新的delta值便等于原来的delta值加上或减去 Gamma值。因此Gamma值越大,Delta值变化越快。进行Delta中性套期保值,Gamma绝对值越大的头寸,风险程度也越高,因为进行中性对冲需要调整的频率高;相反,Gamma绝对值越小的头寸,风险程度越低。


3,Vega


• Vega(ν):衡量标的资产价格波动率变动时,期权价格的变化幅度,是用来衡量期货价格的波动率的变化对期权价值的影响。公式为:Vega=期权价格变化/波动率的变化。如果某期权的Vega为0.15,若价格波动率上升(下降)1%,期权的价值将上升(下降)0.15


Vega值是期权对标的资产价格波动率变动的敏感度,它反映当波动率变化一个单位时(通常用1%来衡量),期权价格理论上的变化,Vega值永远都是正数,值越大,投资者面对波动率变化的风险便越大。


• 当期权类型和剩余到期期限相同的情况下,平值期权对波动率变化最为敏感,所以比实值和虚值期权具有更高的Vega;


• 相同的合约规格,更长的剩余时间以为波动率有更多的时间产生影响,长期期权比短期期权的波动率更为敏感,因此长期期权Vega 更大;


4,Theta


•Theta(θ)是用来测量时间变化对期权理论价值的影响。表示时间每经过一天,期权价值会损失多少。公式为[1]:Theta=期权价格的变化/流逝时间的长短变化(passage of time)。一般用负来表示,以提醒期权持有者,时间是敌人。


• 其他因素相同,相同行权价的看涨期权和看跌期权的Theta 相同;


• 期权的多头头寸Theta 值为负,期权的空头头寸Theta 值为正;


• Gamma 和Theta 不仅符合总是相反的,二者大小也相互关联,高正值Gamma通常对应高负值Theta,高负值Gamma 通常对应高正值Theta 同时出现;平值期权的Gamma 随着到期日临近会加速变大,Theta 值会加速衰减,这一点尤其要注意。


5,Rho


Rho衡量了利率变化对期权价格的影响,即利率变化成一个单位,期权价格产生的变化。认购期权的Rho是正值,认沽期权的Rho是负值。


Rho的相关公式为:


新期权价格=原期权价格+Rho×利率变化


同上例:有某股票认购期权合约,期权价格为0.2282元,Rho为0.094,目前无风险利率为2.5%。


在其他条件不变的情况下,如果无风险利率变为3.5%,即增加了1%,则期权理论价格=0.2282+0.094×1%=0.2291元。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

伯恩_品职助教 · 2024年07月28日

嗨,从没放弃的小努力你好:


问题一:因为题干已经说了是convertible bond strategy,所以就直接选a呢?表格信息反而算是有些干扰了?——如果说是做题技巧是可以的,但是题目说的很清楚是根据表格1

问题二:表格中put option on stock的rational中“only in place of delta hedge”是什么意思?——仅仅是用作CB中的call的delta hedge,不是为了获取其PUT因股价下跌的盈利

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努力的时光都是限量版,加油!

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