Explanation:
C is correct. Although gamma is similar to vega in that it is greatest for an option that is at-the-money and approaches zero as the option moves deep-in-the-money or deep-out-of-the-money, one important difference is that while vega increases as the time to maturity increases, gamma decreases.
Since the 1-month option has a lower vega and a higher gamma than the 4-month option, a portfolio with a short position in the 1-month and a long position in the 4-month will have positive vega and negative gamma. Adding this to the original portfolio would reduce the gamma and increase the vega of the original portfolio.
This combination effectively reduces the overall gamma while increasing the overall vega of the portfolio.
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An options trader wants to hedge the gamma and vega risks of a portfolio of several options on a single non-dividend paying stock. The portfolio currently has a positive gamma and a negative vega. There are two at-the-money call options available on this stock, one with a 1-month expiration and the other with a 4-month expiration. Which combination of transactions in these two options would reduce the gamma and increase the vega of the current portfolio?
A
Buy both the 1-month and the 4-month options.
B
Buy the 1-month option and sell the 4-month option.
C
Sell the 1-month option and buy the 4-month option.
D
Sell both the 1-month and the 4-month options.
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