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You are long a call option on a stock and you are delta hedged. The stock crashes in price. How do you adjust your delta, do you buy or sell stock?

Could answers please be quantitative (i am getting signs the wrong way round probably) as well as qualitative.

Note: I do not understand the solution in Heard on the Street Question 2.7.

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To hedge your long call option (which as a delta between 0 and 1), you had to short sell some stock. If the stock price crashes the option you are long of is less in the money (or further out of the money). Therefore you are overhedged by your short stock position and need to buy back some stock.

You can also think in terms of gamma. Your long vanilla option is long gamma (gamma positive): its delta increases as the spot rises and decreases as the spot falls. Since your delta is lower on your long option (less positive on a call or more negative on a put), you must buy back some stock.

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