What is one of the primary issues with delta hedging?

Delta hedging is a risk management strategy that involves adjusting a portfolio's position in the underlying asset to maintain a neutral delta, which is a measure of the sensitivity of an option's price to changes in the price of the underlying asset. One of the primary issues with delta hedging is indeed that delta changes as the price of the underlying asset changes or as time passes. This characteristic of delta, known as "delta gamma," means that the effectiveness of a delta hedge can fluctuate due to changes in the underlying asset's price or the passage of time.

As the price of the underlying security moves, the delta of an option will typically change, reflecting a new price sensitivity. This requires continuous adjustments to the hedge, resulting in increased transaction costs and potential risk if the hedge is not adjusted in time. Additionally, as options approach expiration, their delta can become more volatile, further complicating the hedging process.

This dynamic nature of delta is crucial for traders and risk managers to understand, as it directly impacts the stability and performance of a delta hedge strategy.