Why Do Options Deep OTM/ITM Have Low Gamma Regardless of Implied Volatility?
Options deep Out-of-the-Money (OTM) or In-the-Money (ITM) have very low Gamma because their Delta is already stable, close to 0 or 1/-1, respectively. The option is either highly unlikely or highly likely to expire ITM.
Changes in implied volatility primarily affect the uncertainty around the strike price (ATM options), not the certainty of deep OTM/ITM options. Therefore, their Delta is already saturated, and Gamma is near zero.
Glossar
Deep ITM
Depth ⎊ In cryptocurrency options and financial derivatives, a Deep In-The-Money (ITM) position signifies an option contract where the strike price is significantly below the current market price of the underlying asset for calls, or substantially above for puts.
Deep Otm Options
Position ⎊ Deep OTM Options are contracts where the strike price is significantly far from the current spot price, possessing minimal intrinsic value but substantial extrinsic value, often used for speculative bets or complex hedging strategies.
Deep OTM Option
Exposure ⎊ A Deep OTM Option represents a position with a very low probability of finishing in-the-money at expiration, resulting in minimal immediate directional exposure.
Low Gamma
Exposure ⎊ Low gamma describes a state in an options portfolio where the delta changes minimally in response to movements in the underlying asset's price.