Explanation

This question involves hedging an option portfolio that has:

• High unfavorable sensitivity to increases in implied volatility (negative vega)
• Significant daily losses with the passage of time (negative theta)

Key Analysis:

1. Vega Exposure:

• The portfolio has negative vega (unfavorable sensitivity to volatility increases)
• To hedge negative vega, we need to buy volatility (positive vega)
• Buying options gives positive vega

2. Theta Exposure:

• The portfolio has negative theta (time decay losses)
• To hedge negative theta, we need to sell time value (positive theta)
• Selling options gives positive theta

3. Calendar Spread Strategy:

• Short-dated options have higher theta decay (more time value erosion)
• Long-dated options have higher vega sensitivity (more volatility exposure)

4. Correct Hedge:

• Buy short-dated options: Provides positive vega to offset negative vega, but has high theta cost
• Sell long-dated options: Provides positive theta to offset negative theta, but has negative vega
• The combination creates a calendar spread that balances the vega and theta exposures

Why Option B is correct:

• Buying short-dated options adds positive vega to hedge the negative vega
• Selling long-dated options adds positive theta to hedge the negative theta
• This creates a net hedge against both risks

Why other options are incorrect:

• A: Selling short-dated and buying long-dated would increase negative vega exposure
• C: Selling both would increase negative vega and negative theta
• D: Buying both would increase negative theta exposure

The calendar spread in Option B effectively hedges both the vega and theta risks simultaneously.