You purchase put options on a stock index, and wish to trade shares of the underlying stock index to establish a delta-neutral position. To maintain a delta neutral position, you will need to:

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Question restatement: You buy put options on a stock index and want to trade shares of the underlying index to establish a delta-neutral position. To maintain delta neutrality, you will need to:

Option 1: Buy more shares of the index as the stock index rises.
- Why this is not correct: When the index rises, the delta of long put options becomes less negative (moves toward zero). To keep the overall delta neutral, you would not want to increase positive delta further just because prices rose; this would push you away from neutrality rather than toward it.
- Conceptual takeaway: Increasing positive delta (buying more index shares) is not the appropriate reaction to an index rise when you hold puts with negative delta.

Option 2: Buy more shares of the index as the stock index falls.
- Why this is correct: Long puts carry negative delta. If the index falls, the put delta becomes more negative (the magnitude increases). To offset this added negative delta and restore neutrality, you add positive delta by buying more shares of the index. This rebalance moves the overall position back toward zero net delta.
- Conceptual takeaway: Delta hedging with long puts typically involves adding positive exposure (buying the index) when the underlying falls, to offset the increasing negative delta from the puts.

Option 3: No need to rebalance the initial position in shares of the index.
- Why this is not correct: Delta hedging is dynamic; as the underlying moves, the delta of the options changes. Failing to rebalance means the portfolio will drift off delta-neutral as market moves occur.
- Conceptual takeaway: Delta neutrality requires ongoing adjustments in response to market movements, not a static, one-time hedge.

Option 4: Close your position in index shares and hold Treasury bills.
- Why this is not correct: Closing the index position eliminates the hedge you’re using to maintain delta neutrality. Replacing with Treasury bills removes the delta exposure entirely, but also defeats the purpose of actively hedging with the underlying. It’s not a delta-neutral management strategy for a position comprised of puts.
- Conceptual takeaway: A hedge typically involves maintaining some positive delta exposure to offset negative delta, not entirely removing exposure or flipping to a cash-like substitute.

Summary of reasoning: The delta of long put options is negative; to maintain a delta-neutral stance, you offset that negative delta by adding positive delta exposure through the underlying. When the index falls and puts become more negatively deltas, you offset by buying more shares of the index. The other options propose reactions that would not preserve neutrality under rising or falling markets or misconstrue the hedging objective and mechanics.

2025FallDYN-T-FIN530-86763-86762 Quiz 6 - "Black-Scholes-Merton Model and Dynamic Hedging"

You purchase put options on a stock index, and wish to trade shares of the underlying stock index to establish a delta-neutral position. To maintain a delta neutral position, you will need to:

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