Explanation

To hedge the portfolio's Greeks:

Current Position:

• Theta = +25,000 (positive theta means the position benefits from time decay)
• Vega = +330,000 (positive vega means the position benefits from increased volatility)
• Gamma = -200 (negative gamma means the position is short gamma, sensitive to large price movements)

Hedging Strategy Analysis:

Option A: Sell short-term options + sell long-term options

• Selling options gives negative theta (benefits from time decay)
• Selling options gives negative vega (benefits from volatility decrease)
• Selling options gives positive gamma (opposite to current negative gamma)

Option B: Sell short-term options + buy long-term options

• Selling short-term options: negative theta, negative vega, positive gamma
• Buying long-term options: positive theta, positive vega, negative gamma

Matching the Greeks:

• The portfolio needs negative theta to offset +25,000 theta
• The portfolio needs negative vega to offset +330,000 vega
• The portfolio needs positive gamma to offset -200 gamma

Option B provides the correct combination:

• Selling short-term options gives strong negative theta and negative vega
• Buying long-term options gives positive gamma (to offset the negative gamma)
• The combination can be balanced to achieve the desired neutralization

Therefore, Option B is correct because it allows for creating a position with negative theta, negative vega, and positive gamma to offset the current portfolio's positive theta, positive vega, and negative gamma.