What is Gamma Scalping? Profiting from Option Convexity

Gamma scalping is a delta-neutral strategy used to capture profits from price swings. Learn the math of rehedging and how to monetize option gamma.

Gamma scalping converts option convexity into systematic profit through disciplined delta rebalancing. What is Gamma Scalping? It is a sophisticated trading technique used by option market makers and volatility traders to profit from the movement of an underlying asset while maintaining a delta-neutral position.

When you are long an option, you are long Gamma ($\Gamma$), which is the second derivative of the option price with respect to the underlying: $\Gamma = \frac{\partial^2 V}{\partial S^2}$. This represents the rate at which your Delta ($\Delta$) changes. In gamma scalping, as the stock price rises, your delta becomes more positive, requiring you to sell shares to stay neutral. Conversely, as the price falls, your delta becomes more negative, requiring you to buy shares. This 'buy low, sell high' process is the essence of the scalp.

Gamma scalping is not free money. To be long Gamma, you must pay Theta ($\theta$), which is the time decay of the option. The profit from your scalps must exceed the daily theta bleed to be profitable. This relationship is captured in the simplified Black-Scholes-Merton model PDE for a delta-neutral portfolio: $\Theta + \frac{1}{2}\sigma^2 S^2 \Gamma = rV$. If the realized volatility $\sigma$ is higher than the implied volatility used to price the option, the gamma gains will outweigh the theta losses.

1. Long Straddle/Strangle: You buy both a call and a put to become long Gamma. 2. Delta Hedging: You sell or buy the underlying to bring the total portfolio $\Delta$ to 0. 3. Price Movement: The stock moves, changing the $\Delta$. 4. The Scalp: You trade the underlying to return to $\Delta = 0$, locking in a small profit.

A quant system must monitor the 'Hedge Error' continuously. If the underlying price moves from $S_1$ to $S_2$, the required adjustment in shares is approximately $\Gamma \cdot (S_2 - S_1)$.