Gamma Scalping

Gamma scalping is a technique in which a trader buys options, hedges away their directional exposure with the underlying asset, and then repeatedly adjusts that hedge as the price moves. Because of the way a long option position behaves, each adjustment sells the underlying after it has risen or buys it after it has fallen. The small gains from these trades are set against the daily loss in value of the options held.

The technique is a way of trading volatility, not direction. It makes money when the underlying moves around more than the option prices implied when the position was opened, and loses when the market is quieter than that. It is used by option market makers and volatility funds, and despite the name it has little in common with ordinary scalping of small price moves.

The trader starts with a long option position, often a straddle, and trades the underlying until the combined position is delta neutral. A long option position has positive gamma, which means its delta rises as the price rises and falls as the price falls.

Suppose the price goes up. The position's delta turns positive, so the trader sells some of the underlying to bring it back to zero. If the price then falls back, the delta turns negative and the trader buys the underlying back, at a lower price than it was sold. The round trip has produced a profit, and the position is where it began. A fall followed by a recovery works the same way in reverse. The process of rebalancing is delta hedging, and with positive gamma it always means selling high and buying low.

These gains are not free. An option loses value as time passes, an effect measured by theta. Every day the long options decay, whether or not the price has moved. Gamma scalping is profitable only if the hedging gains exceed that decay.

The gain from one price move, for a position that was delta neutral beforehand, is approximately:

and the daily move at which this gain equals one day's time decay is approximately:

• $\Gamma$ is the gamma of the whole position.
• $\Delta S$ is the change in the underlying price.
• $S$ is the underlying price and $\sigma$ is the annual implied volatility at which the options were bought.
• 252 is the usual count of trading days in a year.

A share trades at $100. A trader holds options on 1,000 shares with a gamma of 0.039 per share, so the position gamma is 39. The options were bought at an implied volatility of 20 percent. The break-even daily move is 100 × 0.20 ÷ √252 = 20 ÷ 15.87 = $1.26.

A move of $1.26 earns 0.5 × 39 × 1.26² = 0.5 × 39 × 1.59 = about $31, which is roughly what the options lose to time decay in a day. If the share instead moves $2, the gain is 0.5 × 39 × 4 = $78, and the day's net result is about 78 − 31 = +$47. If the share moves only $0.50, the gain is 0.5 × 39 × 0.25 = about $5, and the net result is about −$26.

The example shows the general result. A daily move of 1.26 percent corresponds to annual volatility of 20 percent, the level implied by the option price. Gamma scalping therefore earns a profit when realized volatility over the life of the trade is above the implied volatility paid, and makes a loss when it is below. This makes it a basic tool of volatility trading and volatility arbitrage.

The position also has vega. If implied volatility rises while the trade is open, the options gain value, and if it falls they lose. A trader can be right about realized volatility and still lose money because implied volatility dropped.

The trader must decide when to rebalance. Hedging at fixed times, such as the close each day, is simple. Hedging whenever the price has moved a set amount, or the delta has drifted beyond a band, captures swings within the day. Rebalancing too often gives away the gains in transaction costs and cuts short moves that would have continued. Rebalancing too rarely risks the price returning to its starting point with nothing locked in.

The main risk is a quiet market. If the underlying sits still, there is nothing to scalp, and the position loses its time decay every day. Option buyers have historically paid more in implied volatility than was later realized on average, a gap known as the volatility risk premium, so a long gamma position starts at a disadvantage in most markets and depends on choosing the occasions when options are cheap.

The loss on a long option position is limited to the premium paid, which makes long gamma scalping less dangerous than its mirror image. The reverse trade, selling options and hedging them, collects time decay and loses on every rebalance. It earns steady small profits in calm periods and can lose heavily in a sudden large move. Neither side offers a reliable profit, and both require low trading costs and constant attention.