How Does the Volatility of the Underlying Asset Affect the Cost of Delta Hedging?

Higher volatility increases the cost of delta hedging. This is because high volatility causes the option's Delta to change more rapidly (higher Gamma), requiring more frequent and larger rebalancing trades in the underlying asset.

Each rebalancing trade incurs transaction costs and potentially slippage. Therefore, the higher the volatility, the more expensive the dynamic adjustment process becomes for the option writer.