Does Inventory Risk Change Based on the Option’s Time to Expiration?

Yes, inventory risk is dynamic and changes with time to expiration. Options with a longer time to expiration generally carry higher inventory risk because they have higher Vega (volatility risk) and the market maker's hedge needs to be maintained for a longer period.

As an option approaches expiration, Gamma and Theta increase, requiring more frequent and costly hedging, thus changing the nature of the risk.