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?
- Gamma remains fixed since it depends only on the current stock price and the option's strike.
- Gamma increases because higher volatility makes the option more sensitive to price swings near expiration.
- Γ decreases because the probability of the option staying ATM over a small price move is reduced.
- Gamma turns negative for long option positions since rising volatility destabilizes the delta-hedge ratio.
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