Definition
Delta hedging involves taking offsetting positions in the underlying asset proportional to the option's delta to neutralize price risk. As delta changes with price (due to gamma), the hedge must be continuously rebalanced. Market makers routinely delta-hedge their option books. The cost of delta hedging is related to the option's theta and gamma—gamma creates the rebalancing need while theta is the cost.
lightbulb Example
A market maker sells 100 call options with delta 0.50 and hedges by buying 5,000 shares (100 × 50 delta). If the stock rises and delta increases to 0.55, the maker buys 500 more shares. Daily rebalancing captures the gamma profit/loss.
verified_user Key Points
- Continuously adjusts hedge ratio to maintain delta neutrality
- Gamma drives rebalancing frequency and cost
- Theta decay funds the hedging cost for option sellers
- Foundation of option market making