Explanation

To understand this question, we need to analyze the Greek sensitivities:

Gamma (Γ): Measures the rate of change of delta with respect to changes in the underlying asset price. Gamma is highest for at-the-money options and decreases as options move away from the money. Gamma also decreases as time to expiration decreases.

Vega (ν): Measures sensitivity to changes in volatility. Vega is higher for longer-dated options and decreases as expiration approaches.

Key relationships:

• 1-month option: Higher gamma, lower vega
• 4-month option: Lower gamma, higher vega

Analysis of options:

• Option C (Sell 1-month, Buy 4-month):
  • Selling the 1-month option reduces gamma (since short-term options have higher gamma)
  • Buying the 4-month option increases vega (since long-term options have higher vega)
  • This combination achieves both objectives: reducing gamma and increasing vega

Other options:

• A: Buying both increases both gamma and vega
• B: Buying 1-month increases gamma, selling 4-month decreases vega
• D: Selling both decreases both gamma and vega

Therefore, Option C is the correct choice.