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.
Glossar
Cost of Delta Hedging
Cost ⎊ The cost of delta hedging represents the aggregate expenses incurred by a market participant to maintain a neutral delta position in an options portfolio.
Cost of the Underlying
Cost ⎊ The cost of the underlying asset represents the expenses incurred when holding the asset that an option contract is based upon.