# Gamma Scalping and a Crash Course on the Greeks

I have many traders come to me looking to learn one specific options-trading strategy: gamma scalping. A lot of traders are called by the siren song of a completely non-directional trade in which any movement in either direction, even back-and-forth movements can result in profits -- even big ones. It's interesting. It's alluring. It's sexy.

But gamma scalping as a trading strategy is not for everyone. In fact, of all the traders who have asked me to teach them gamma scalping, I've turned most of them down. As a market maker on the floor of the CBOE, I was a gamma scalper every day of my trading career. But for non-professional traders, only and handful qualify for this sort of trading. Only traders who are very well capitalized, very knowledgeable and experienced, and who have retail portfolio margining should even consider gamma scalping.

Though only some traders should actually engage themselves in gamma scalping, it is essential to understand how it works. The gamma scalping of market makers is the fly rod in the machine that prices volatility. And, after all, volatility is the source of edge for retail traders. Therefore, it behooves traders to learn how it works. To understand gamma scalping, traders must understand how options traders trade the greeks.

** The Greeks: A Crash Course **

The so-called option greeks are metrics that measure the affect of the influences on an option's value, such as the underlying asset price, time and volatility. Each influence has its own metric. Delta

Delta is the rate of change of an option's value relative to a change in the underlying asset.

Delta is stated as a percent, written in decimal form. Calls have positive deltas, puts have negative deltas. So for example if an option as a delta of 0.45, it moves 45 percent as much as the underlying stock. If the stock rises by one dollar, the 0.45-delta call rises by 45 cents.

Traders can think of delta as effectively how many shares of the underlying they have. Imagine a trader has a call (representing the rights on 100 shares) that has a 0.45 delta. Because it moves 45% as much as the underlying, it is as if the trader owns 45 shares of the underlying stock.

At-the-money options have deltas close to 0.50. The farther an option is in-the-money, the greater its delta, up to 1.00. The farther an option is out-of-the-money, the smaller its delta, down to 0.

**Gamma **

Gamma is the rate of change of an option's delta relative to a change in the underlying asset.

As discussed, the more in-the-money an option, the bigger the delta and the more out-of-the-money, the smaller the delta. As the underlying stock price changes, options are constantly getting more in- or out-of-the-money. Consequently, their deltas are in a constant state of change. Sometimes this change can have a profound effect on the trader's P&(L). It is very important to understand how changes in delta will affect the trader's P&(L). Thus, gamma is important.

Gamma is stated in terms of deltas. If an option has a gamma of 0.10, the option will gain 0.10 deltas as the underlying stock rises, and lose 0.10 deltas as the underlying stock falls.

Long options (both calls and puts) have positive gamma. Short options have negative gamma. Positive gamma helps traders. It leads to them making more on their winners and losing less on their losers than delta would indicate. Negative gamma hurts traders.

**Theta **

Theta is the rate of change of an option's value relative to a change in the time to expiration.

As time passes, options get worth less (all other pricing influences held constant). Theta measures how much value an option loses as one day passes. Theta is measured in dollars and cents. An option that has a theta of 0.04 loses four cents as each day passes, attributable to time decay.

Long options have negative theta, that is, they are adversely affected by time passing. Short options positions have positive theta -- they benefit from time passing.

Theta and gamma are inversely related. The benefit that long options have because of positive gamma is countered by the detriment of negative theta. The positive theta benefit of short option positions is countered by the negative gamma detriment.

**Vega **

Vega is the rate of change of an options value relative to a change in implied volatility.

Implied volatility is the volatility component embedded in an option's price. The higher the implied volatility the higher the option price; the lower the implied volatility, the lower the option price. Implied volatility changes. The impact of these changes on the value of the option is measured by vega.

Vega is stated in dollars and cents in the same way as theta. If an option has a vega of 0.06, it gains six cents for each one-point rise in implied volatility and loses six cents for each one-point fall in implied volatility.

**Starting Delta Neutral **

When traders set out to gamma scalp, they create a delta-neutral position. They do so by placing an option trade and they offset the delta of the option trade by selling stock.

For example, imagine a trader, Jill, buys 100 XYZ calls that each have a 0.45 delta. The position delta would be 45 -- the delta of each option (0.45) times the number of options (100). Based on the previous discussion of delta, that means the call position would function as if it were a stock position of 4,500 shares. Thus, Jill could offset her immediate directional sensitivity by selling short 4,500 shares of XYZ stock.

**Scalping Gamma **

If XYZ rises or falls, Jill's delta won't remain flat. It will change because of gamma. Jill has long options (calls) so she has positive gamma. So gamma will benefit her; delta will change in her favor. Her delta will get shorter as XYZ falls and longer as XYZ rises.

This recalibrating of delta as a result of gamma gives rise to an opportunity for Jill. She'll hedge as her delta changes resulting in scalping the stock. When the stock falls (and her delta gets short) she'll buy stock. Then when XYZ rises and her delta gets long, she'll sell stock. These scalping transactions of buying stock when it's low and selling it when it's high create a cash flow.

**The Theta Problem **

Recall that the trade off of positive gamma is negative theta. Jill's position loses value in the amount of theta each day. Imagine her theta is 0.02 per call. On the 100 contracts, her theta would be 2.00 -- that's $200 of cash per day. That's real money. Therefore in order for Jill's gamma scalping to be profitable, she needs to scalp more than $200 a day in order to break even.

**Vega and Theta **

Theta is a function of implied volatility. Recall that the higher the implied volatility, the higher the value of the options. Options of greater value must, logically, have higher thetas. That means when implied volatility is high, gamma scalpers must scalp for more profit to cover the higher theta.

** How Gamma Scalping Factors into Volatility Pricing **

Market makers (exchange members who provide liquidity) are major players in the gamma-scalping arena. As they take the other side of public trades, they hedge the deltas and subsequently scalp gamma of long option positions.

When market makers find they cannot cover their theta by gamma scalping because the underlying stock is not experiencing enough actual price oscillation, they are incented to try and sell their options to get out of the losing trade. They lower their bids and offers some to try and attract buyers. If that doesn't work, they lower them more. All the while, this lowers the options' implied volatility.

In a way, the gamma scalping of market makers links together implied and historical volatility. If the stock isn't moving enough (i.e., historical volatility is too low) for market makers to cover theta, they lower their markets (i.e., they lower implied volatility).

**Take Aways **

A typical retail trader will never gamma scalp (maybe some, perhaps--the elite). But understanding how it fits into volatility pricing is essential in understanding the mechanics of volatility. Traders can use this insight to trade use implied volatility with foresight and mastery. Most importantly, traders can use knowledge of implied volatility to gain edge on option trades.

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