How Does Implied Volatility Affect the Premium of a Put Option?

Implied volatility (IV) is a market's forecast of the likely movement in the underlying asset's price. Since a put option is a hedge against a price drop, higher implied volatility increases the probability of a large price move, making the option more valuable.

Therefore, a higher implied volatility directly leads to a higher option premium, as the risk of the option writer having to pay out is perceived as greater.