NO.PZ2023091802000155
问题如下：
Portfolio manager Sally has a position in 100 option contracts with the following position Greeks: theta = +25,000; vega = +330,000 and gamma = -200; ie., positive theta, positive vega and negative gamma. Which of the following additional trades, utilizing generally at-the-money (ATM) options, will neutralize (hedge) the portfolio with respect to theta, vega and gamma?
选项：
A.Sell short-term options + sell long-term options (all roughly at-the-money)
B.Sell short-term options + buy long-term options (~ ATM)
C.Buy short-term options + sell long-term options (~ ATM)
D.Buy short-term options + buy long-term options (~ ATM)
解释：
For ATM options, vega and theta are increasing funtions with
maturity; and gamma is a decreasing function with matutity.
To buy short-term options + sell long-term
options ≥ negative position thera, negative position vega, and positive
position gamma.
In regard to (A), sell short-term + sell
long-term options ≥ positive thera, negative vega; negative gamma.
In regard to (B), sell short-term + buy
long-term options ≥ positive thera, positive vega; and negative gamma.
In regard to (D), buy short-term + buy
long-term ≥ negative thera, positive vega; and positive gamma.
Note: the above are approximately actual
number for 100 option contracts.
(100 options each = 10,000 options) with the
following properties: Strike = Stock = $100; volatility = 15.0%, risk-free rate
= 4.0%; term = 1.0 year. Under these assumptions:
a) 1-year term: percentage theta =
-5.0, vega = +37, gamma = +0.025
b) 10-year term:percentage theta =
-2.5, vega = +70, gamma = +0.005
解析完全没看懂，可以再解释下吗？
