NO.PZ202208100100000102
问题如下：
With respect to Company A, which of Navarro’s statements to Patel is most likely correct?
选项：
A.Statement 1 B.Statement 2 C.Statement 3解释：
Solution
B is correct. Statement 2 is correct. The short stock/long call position is long vega and will benefit from increased volatility, whereas the short stock/short put position is short vega and will benefit from reduced volatility. Statement 1 is incorrect. The delta of her short position is –500. The call delta is 500 × 0.439 = 219.5. The delta of the combined position is –280.5. The short put delta is 0.199.5 = 500 × –(–0.399). The delta of the combined position is –300.5. Thus, both positions are bearish, but the put delta position is more bearish. Statement 3 is incorrect. The theta of the short stock/long call position is negative and is exposed to time decay. The theta for the short stock/short put position is positive [= –(–0.028)] and benefits from time decay.
A is incorrect. Statement 1 is incorrect. The delta of her short position is –500. The call delta is 500 × 0.439 = 219.5. So, the stock + call position delta is –280.5. The short put delta is 500 × –(–0.399) = 199. So, the stock + short put position delta is –300.5. Thus, while both positions are bearish, the stock + short put delta position is more bearish.
C is incorrect. Statement 3 is incorrect. The theta of the short stock/long call position is negative and is exposed to time decay. The theta for the short stock/short put position is positive [= –(–0.028) and benefits from time decay.
中文解析：
本题考察的是希腊字母delta，vega和theta.
表述1：该表述讨论的是关于delta的内容。
Short 500份的stock，其delta=-500*1= -500；long 5份的call，其delta = 5*100*0.439=219.5；short 5份的put，其delta = - 5*100*（-0.399）=199.5.（这里可以理解一份期权对应100份股票，所以在计算期权的delta的时候，要用合约的份数先乘以100再乘以期权的delta值）。
Short stock和long call构成的头寸其delta等于-500+219.5 = -280.5；short stock和short put构成的头寸，其delta等于-500+199.5 = -300.5.
Delta为负数，说明当标的资产价格上涨的时候，整个策略是亏钱的，因此是bearish的，且delta负数的绝对值越大，对市场更加是bearish。所以该表述错误。
表述2：该表述讨论的是关于vega的内容。
Vega衡量的是volatility对期权价格的影响。现货头寸没有vega；买期权就是在买入vega，即看涨波动率；而卖期权就是在卖出vega，即看跌波动率。
因此Short stock和long call构成的头寸是在看涨波动率，在波动率上涨时获利；而short stock和short put构成的头寸是在看跌波动率，在波动率下降时获利。该表述正确。
表述3：该表述讨论的是关于theta的内容。
Theta衡量的是逝去的时间对期权价格的影响，又叫做time decay。Theta为负数，说明逝去的时间越长，期权越不值钱。
现货头寸不考虑theta。因此Short stock和long call构成的头寸，其theta值由 long call来决定，是负数，说明遭受时间衰减（time decay）的影响；而short stock和short put构成的头寸，其theta值由short put来决定，是正数，即不会受到时间衰减（time decay）的影响（put option的theta为负数，short put的theta就位正数）。因此该表述错误。
为什么short put theta是正的就不受时间流逝影响了？theta正的不就是时间流逝对我来说是好事吗
