NO.PZ202208100100000703
问题如下：
If the client executes Fillizola’s suggested strategy at the current price, her position delta will most likely be the same as the position delta of a portfolio that is:
选项：
A.
long 2,000 shares and short forward 980 shares.
B.
long 1,020 shares and short forward 980 shares.
C.
long 2,000 shares and short forward 1,020 shares.
解释：
Solution
C is correct. The delta for the February 2020 $140 call strike option on Company A is 0.51. The delta for a long position in one share of Company A is 1. She is long 2,000 shares of Company A. The position delta for the covered call is (1 – 0.51) × 2,000 = 980. This position delta can be replicated by going long 2,000 shares and taking a short forward position in 1,020 shares. Forwards have deltas of 1.0 for non-dividend-paying stocks. Position delta for Option C = (2,000 – 1,020) = 980.
A is incorrect. The position delta for a portfolio that is long 2,000 shares and short forward 980 shares is (2,000 × 1) – (980 × 1) = 1,020. The position delta for the covered call is 980. The delta for the call option on Company A is 0.51. The delta for a long position in one share of Company A is 1. She is long 2,000 shares of company A. The position delta for the covered call is (1 – 0.51) × 2,000 = 980.
B is incorrect. The position delta for a portfolio that is long 1,020 shares and short forward 980 shares is 1,020 × 1 – 980 × 1 = 40. The position delta for the covered call is (1 – 0.51) × 2,000 = 980.
中文解析：
本题考察的是delta hedge。
如果按照Fillizola的建议卖出看涨期权，构成covered
call头寸，其中持有2000份的股票头寸（股票的delta=1），对应的delta=2000；short call的delta为2000*（-0.51）= -1020，注意一般默认1 contract
option相当于对应着100张的看涨期权，其中每一张期权对应一只股票，所以write 20 contracts call option的delta=20*100*（-0.51）= -1020。
因此covered call头寸的delta = 2000-1020
=980.
又因为short forward的delta为-1，所以long 2000份股票同时short 1020份的forward合约，构成的头寸的delta为2000-1020=980，等于covered call头寸的delta，选C。
A选项构成的头寸，delta=1020；B选项构成的头寸，delta=40。
请解释下这道题的算法
