What is Delta Hedging? Neutralizing Directional Risk in Options

Delta hedging is a strategy used by market makers to reduce the risk associated with price movements in an underlying asset by balancing the delta.

In derivatives trading, Delta Hedging is the process of maintaining a delta-neutral position to eliminate directional risk. The delta ($\Delta$) of an option represents the rate of change of the option's price with respect to changes in the underlying asset's price. If a trader sells a call option with a delta of 0.60, they are effectively 'short' 60 shares for every 100 shares the option represents. To hedge this, the trader must buy 60 shares of the underlying stock.

The mathematical definition is $\Delta = \frac{\partial V}{\partial S}$. For a European call option in the Black-Scholes-Merton model framework, $\Delta = N(d_1)$. Because $\Delta$ changes as the stock price moves and time passes, a hedge must be rebalanced frequently. This is known as dynamic hedging. If a market maker does not rebalance, they are exposed to Gamma Risk, which is the sensitivity of delta to the underlying price.

Market makers at firms like Citadel Securities or Susquehanna use delta hedging to profit from the bid-ask spread rather than betting on stock direction. If a market maker buys a put option (negative delta), they will buy the underlying stock (positive delta) to reach a net delta of zero. In 2021, the 'meme stock' short squeezes were amplified by market makers buying underlying shares to hedge call options sold to retail traders, a phenomenon known as a gamma squeeze.