You are an option trader, and you just sold a
European call option on a given underlying. You decide to delta hedge your position. Which of the following statements is correct?

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BlackTom AI · Accepted Answer

Question restatement: You are an option trader who has sold a European call option and decides to delta hedge. Which statement is correct?

Option a: 'Delta hedging implies that you will need to buy the underlying asset initially. Later, you will incrementally buy some additional shares of the underlying asset as the delta of the option changes.' This option says you buy initially and then only buy more as delta changes. Since you sold (shorted) the call, your initial delta exposure is negative. To hedge a negative delta, you would typically take a long position in the underlying to offset that negative exposure, so buying initially is correct in concept. However, the second part states you will only buy more shares as delta changes, implying you never sell any shares during adjustments. In delta hedging, as the option’s delta evolves, you may need to both buy and sell shares to maintain a delta-neutral position, especially if the underlying moves and the option’s delta moves in a way that requires rebalancing. Hence this option is incomplete or misleading because it excludes the possibility of selling shares during rebalancing.

Option b: 'Delta hedging implies that you will need to buy the underlying asset initially. Later, you will incrementally buy or sell some additional shares of the underlying asset as the delta of the option changes.' This aligns with the standard delta-hedging approach for a short call: you offset the negative delta by buying the underlying at the outset. As the delta of the option changes with movements in the underlying (and with time decay), you adjust the hedge by trading additional shares in either direction (buy or sell) to maintain delta neutrality. This captures both the initial action and subsequent dynamic hedging steps.

Option c: 'Delta hedging implies that you will need to sell the underlying asset initially. Later, you will incrementally buy or sell some additional shares of the underlying asset as the delta of the option changes.' Since the trader sold a call, the initial delta exposure is negative. Selling the underlying would increase the negative delta exposure, worsening the hedge. The correct initial action for a short option is typically to buy the underlying, not sell.

Option d: 'Delta hedging implies that your position, after delta hedging, will have no exposure to price fluctuations.' Delta hedging aims to neutralize first-order exposure (delta) to price movements, but it does not eliminate all risk. Gamma, theta, vega, and other factors still expose you to price movements and changes in delta itself, especially since hedges must be rebalanced as conditions change. Therefore, stating that there will be no exposure after hedging is incorrect.

Summary of reasoning across options: The core idea is that a short call needs an initial long underlying position to offset negative delta, and then dynamic adjustments are made by trading the underlying as the option’s delta changes. Options A, C, and D either misstate the initial action, ignore the possibility of bidirectional rebalancing, or claim complete risk elimination, respectively. Option B correctly reflects the initial hedging step and the subsequent need to adjust by buying or selling as delta evolves."

FINS3635-Options, Futures & Risk Mgmt - T3 2025

You are an option trader, and you just sold a European call option on a given underlying. You decide to delta hedge your position. Which of the following statements is correct?

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