medium · FRM Part 1 Valuation and Risk Models

If an underlying asset's volatility (σ) increases, how does this typically affect the Γ of an at-the-money (ATM) option?

1. Γ remains unchanged because it only depends on the stock price and the strike.
2. Γ increases because the option becomes more sensitive to price changes.
3. Γ decreases because the probability of the option staying ATM over a small price move is reduced.
4. Γ becomes negative for long positions as volatility 'destabilizes' the hedge.

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