P1.T4.204. Option Greeks
204.1. North Dealer, a market maker, has written (sold) a contract of 100 put options when the (percentage) delta of each put is -0.40 and the gamma is 0.090. North Dealer now wants add two positions in order to render the portfolio, including all three positions, both delta and gamma neutral. The two trades must involve call options and shares, when the call options have a delta of +0.60 and gamma of 0.050. Which trades cumulatively neutralize the portfolio's delta and gamma?
- Buy (long) 180 call options and sell (short) 148 shares
- Sell (short) 180 call options and buy (long) 148 shares
- Buy (long) 90 call options and sell (short) 52 shares
- Sell (short) 90 call options and buy (long) 52 shares
204.2. Portfolio Manager Sally has a position in 100 option contracts with the following position Greeks: theta = +25,000, vega = +330,000 and gamma = -200; i.e., 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?
- Sell short-term options + sell long-term options (all roughly at-the-money)
- Sell short-term options + buy long-term options (~ ATM)
- Buy short-term options + sell long-term options (~ ATM)
- Buy short-term options + buy long-term options (~ ATM)
204.3. In regard to option Greeks, each of the following is true EXCEPT:
- In a delta-neutral option portfolio, positive position theta implies negative position gamma
- For long at-the-money (ATM) positions, both position vega and position theta increase as maturity increases
- For short at-the-money (ATM) positions, both position vega and position theta decrease as maturity increasing
- For at-the-money (AMT) positions, position gamma increases with maturity for a long position but decreases with maturity for a short position