It's no easy task to profit from short-term trading on small market movements. However, there is a strategy that option traders can use to attempt to potentially increase their chances of trading profitably if they keep a close eye on volatility. It involves buying calls or puts, then hedging the position, and finally using a couple of tools that measure changes in options pricing to try to close profitable trades.

It's known as gamma scalping, an advanced trading approach that requires experience and a studied viewpoint of how volatility could affect an underlying stock. It often involves complicated work that takes precision, experience and requires close attention to account management.

Understanding the workings of gamma scalping—often referred to as gamma or delta-neutral hedging—is part of a thorough risk education that begins with brushing up on the greeks—specifically, the role that delta and gamma play in calculating the price of an options contract.

Let’s look at the financial metrics that affect the pricing of an options contract (aka the greeks), an overview of what gamma scalping is, and examples of gamma scalping.

## Options risk basics

All options have delta, which is an estimate of how much the price of the option will theoretically increase or decrease relative to price changes in the underlying stock. When implementing this strategy, it may also be helpful for traders to think of delta as the number of shares of the underlying stock they'd need to own for the stock to behave like the option. The reason for this is that each transaction is designed to re-align the offsetting stock and options positions to neutralize the net delta.

If you're not familiar with the greeks, they're theoretical measures of the sensitivity of an option’s price to changes in external factors like its underlying stock price, implied volatility, time until expiration, and interest rates.

Delta tells us how much an option’s value might be expected to change given a $1 move in the underlying. Gamma, on the other hand, provides insight into how much an option’s delta will change, theoretically, given a $1 move in the underlying.

For example, 40 shares of stock typically behave the same as a long call option with a .40 delta. With all aspects of the model being equal, if the stock price increases $1, the options premium should increase in price by $0.40 ($40 in value), and the 40 stock shares will also gain $40 in value.

Options also have gamma, which measures the generally expected speed of change of the delta relative to a $1 change in the underlying stock price. For example, suppose an option had a delta of .40 and a gamma of .15. The options premium would theoretically increase $0.40, from its delta, with the first $1 increase in the underlying security. This moved the call option closer to being in the money (ITM), and delta moved closer to 1.00. On the second $1 increase, the options premium would theoretically increase $0.55: the sum of delta (.40) and gamma (.15). Because delta cannot exceed 1.00, gamma decreases as the option gets further ITM.

One way to think of a long options position is that it's essentially a long gamma position. A long option is a gamma-positive position, meaning volatility can be beneficial because rising volatility typically increases the value of both calls and puts. By contrast, a long options position is more likely to lose money in times of falling volatility. Gamma tends to be lower on stocks with relatively high implied volatility and higher on stocks with relatively low implied volatility.

## How gamma scalping works

Gamma scalping involves short-term stock trading based on movements in the delta of an options position.

If a trader thinks implied volatility is too low, they may be able to profit by buying long calls and combining them with a short position in the underlying stock. They could also buy long puts and combine them with a long position in the underlying stock. The number of stock shares they trade should be relative to the delta of the option. This is **not** the same as when they trade 100 stock shares for each options position, commonly called a protective call or protective put position.

When the number of stock shares reflects the delta, it's called **delta-neutral trading** or **gamma scalping**.

Gamma scalping is a strategy most often used by professional traders and transaction costs can be high. Please consider the economic impact of transaction costs, including commissions, fees, margin interest, and taxes before using this strategy.

For regular, exchange-traded options, the delta of the option will generally increase when the underlying stock increases in value, and vice versa. If a trader is long calls and short the stock, or long puts and long the stock, they will acquire more delta when the stock increases in price. And conversely, if the stock decreases in price, they will get shorter more delta.

It doesn't matter whether they're long put or call options because the delta should increase (call options increase from 0.00 to 1.00; put options increase from –1.00 to 0.00). While calls have a positive delta and puts have a negative delta, both calls and puts have a positive gamma. Positive gamma is where opportunity comes from.

To understand gamma scalping, try thinking of the stock, on a per share basis, as an option with a 1.00 delta and a 0.00 gamma. The goal in gamma scalping is to earn a profit by remaining delta-neutral but gamma-positive. To do this, a trader will need to sell shares in the underlying stock as it increases in price and buy shares when the stock decreases in price. If they do this whenever the price of the stock changes, the trader is seeking to end up buying the shares lower and selling them higher.

The reason options have gamma is because there is always an assumption that a stock will have a certain amount of volatility. It's an assumption effectively built into the price of the options. If the swings in the stock and the subsequent gamma-scalping gains outweigh the aggregate premiums paid for the options—put another way, if the stock is more volatile than the volatility implied by the gamma—the strategy should be profitable (all else being equal).

If the market remains relatively flat and the stock is less volatile than gamma implies, a trader will probably lose money faster through time-value erosion—known as theta or time decay—than they'll gain from gamma scalping.

## Gamma scalping examples

Now that we've gone over what gamma scalping is and why traders use this strategy, let's review two trading scenarios that demonstrate how gamma scalping works.

*Example 1: Long call and short stock*

A trader buys 10 April 520 calls for $12 per contract on ABCD with a delta of .29 and a gamma of .005.

They hedge the options position by short selling 290 shares of ABCD at $475 per share. At this point, they're long 290 delta (from their 10 long calls) and short 290 delta (from their 290 shares short ABCD)—aka they're delta neutral. However, they're net long a total of .05 gamma (.005 x 10 options). In other words, they've neutralized the directional price movement in the near term, but they remain sensitive to overall volatility (nondirectional price movement). Again, this example relies on all aspects of the model being equal and it's worth repeating a reminder that greeks are strictly theoretical measures for the way options pricing will react to real-life market conditions.

If ABCD increases by about 1% in one day to $480, the delta of each of the 520 calls will theoretically increase to .32, up by approximately the gamma amount of .025 (.005 x 5 points). Because the trader is long calls, they'll now have to short sell 30 more shares of ABCD at $480 to remain delta neutral.

After selling 30 shares, the trader will be long 320 delta (from their 10 long calls) and short 320 delta (from their 320 shares short ABCD)—still delta neutral. Now if ABCD falls back to its previous price of $475, the delta on the calls will drop back to .29 again, and the trader will buy back 30 shares of ABCD at $475 to remain delta neutral.

Because the selling price of $480 was about 1% higher than the purchase price of $475, the trader should gain about 1%, or $5 per share, on 30 shares of ABCD (approximately $150).

Gamma scalp completed.

The gain happened because the trader was long gamma. If this process can occur enough times before the options expire, the gains from the gamma scalps will eventually exceed the aggregate time erosion of the options (see the table below).

## Detailed breakdown of gamma scalping

Source: Schwab Center for Financial Research

The strategy of buying low and selling high works the same if the stock falls first and then rises. If this happens, a trader could buy back shares as they decrease in price and then sell them again if the price rises. It doesn't matter which order they do this if they sell high and buy low.

*Example 2: Long put and long stock*

A trader buys 10 April 60 puts for $0.65 per contract on BNB with a delta of –.31 and a gamma of .094, hedging the options position by buying 310 shares of BNB at $62.

At this point, the trader is short 310 delta (from their 10 long puts) and long 310 delta (from their 310 shares long BNB)—which makes the trade delta neutral. However, the trader is net long .94 gamma (.094 x 10 options).

If BNB decreases 2% in one day to $60.76, the delta of each of the 60 puts will theoretically decrease to –.43, down by approximately the gamma amount of 0.116 (.094 x 1.24 points) to 0.43. Because the trader is long puts, they'll now have to buy 120 more shares of BNB at $60.76 to remain delta neutral. After buying 120 more shares, they'll be short 430 delta (from their 10 long puts) and long 430 delta (from their 430 shares of BNB)—which is still delta neutral. Now if BNB rises back to its previous price of $62, the delta on the puts will increase back to –.31 again, and the trader could sell 120 shares of BNB at $62 to remain delta neutral.

Because the selling price of $62 was 2% higher than the purchase price of $60.76, the trader should gain about 2%, or $1.24 per share, on 120 shares of BNB (approximately $148). As mentioned above, if this process can happen enough times before the options expire, the total gains from the gamma scalps will exceed the aggregate time erosion of the options.

And remember, it doesn't matter which way the stock moves first as long as a trader sells high and buys low. This example would be similar if BNB rose first and the trader sold shares, and then it fell, and they bought back shares.

## Reverse gamma scalping or negative gamma scalping

Gamma scalping has a flip side known as** **negative gamma scalping or reverse gamma scalping. If a trader believes implied volatility is too high, they can do the strategy in reverse by selling calls and buying stock long or selling puts and shorting stock.

However, this means they'll be selling stock when it drops in price and buying more as it increases. This will likely result in a loss on that trader's stock transactions. But if the actual volatility is less than expected, the trader may still finish profitably. That's because the time erosion on their short options position may exceed the losses on their stock trades (see the table below).

## Detailed breakdown of negative gamma scalping

Source: Schwab Center for Financial Research

For more information about gamma scalping, or for help using Schwab's options trading tools and platforms, please call a Schwab Trading Specialist at **800-435-9050**.

Options carry a high level of risk and are not suitable for all investors. Certain requirements must be met to trade options through Schwab. Please read the options disclosure document titled Characteristics and Risks of Standardized Options before considering any options transaction. Call Schwab at 1-800-435-4000 for a current copy. Supporting documentation for any claims or statistical information is available upon request.

Supporting documentation for any claims will be provided upon request.

Commissions, taxes and transaction costs are not included in this discussion, but can affect final outcome and should be considered. Please contact a tax advisor for the tax implications involved in these strategies.

Short selling is an advanced trading strategy involving potentially unlimited risks, and must be done in a margin account. [There is no guarantee the brokerage firm can continue to maintain a short position for any period of time. Your position may be closed out by the firm without regard to your profit or loss.]

The information provided here is for general informational purposes only and should not be considered an individualized recommendation or personalized investment advice. The investment strategies mentioned here may not be suitable for everyone. Each investor needs to review an investment strategy for his or her own particular situation before making any investment decision.

All expressions of opinion are subject to change without notice in reaction to shifting market conditions. Data contained herein from third-party providers is obtained from what are considered reliable sources. However, its accuracy, completeness, or reliability cannot be guaranteed.

Examples provided are for illustrative purposes only and not intended to be reflective of results you can expect to achieve. Supporting documentation for any claims or statistical information is available upon request.

The Schwab Center for Financial Research is a division of Charles Schwab & Co., Inc.

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