You buy call 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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Reframing the scenario helps: you own call options on a stock index, which have positive delta. To maintain a delta-neutral position, you need to offset that positive delta with an equivalent negative delta position, typically by shorting the underlying index.

Option: 'Sell more shares of the index as the stock index rises.' This aligns with delta-hedging logic: when the index price increases, the delta of your long calls generally rises (becomes more positive). By selling more shares, you increase the negative delta exposure, offsetting the increased positive delta from the calls and keeping the overall position near delta neutrality.

Why this makes sense in practice: delta hedging is dynamic; as the underlying moves, you adjust the hedge size to keep net delta close to zero. If you did not adjust (e.g., kept a static hedge), the position would drift away from neutrality as the calls’ delta changes with price changes and movement in implied volatility.

Note about the missing other options: the provided options list appears to contain a single choice. In a typical delta-neutral hedging scenario, you would also consider adjustments for changes in volatility and time decay, but the core action following a rise in the index is to implement additional negative delta via selling more index shares. Therefore, the given statement correctly captures the primary hedging action in this scenario.

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

You buy call 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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