Gamma is a second derivative of an option’s price that measures the rate of change in delta over time.
Since delta values shift with the underlying asset’s price, gamma is applied and used to measure the rate of change in delta based on a $1 move in the underlying security. It’s a gauge of the velocity of potential change in delta. The larger the gamma, the faster the option’s delta is going to move.
Similar to delta, gamma is constantly changing with the underlying stock’s movements. The values of gamma are generally highest for at-the-money and soon-to-expire options, and they are lowest for out-of-the-money options. The exception is options that are deep in the money or out of the money, which have gamma values closer to 0.
Additionally, it’s important to remember that all long options have a positive gamma, while all short options have a negative gamma to account for direction easily.
Still mixed up?
Think of these metrics in a way that is related to physics acting on a car. The car is traveling at a speed of 50 miles per hour (delta), and requires accelerating by 10 miles per hour (gamma) to reach the new speed it is needed to be traveling at.
In other words, the speed the car is currently traveling is also known as delta, and the acceleration or deceleration it will experience to change the speed is known as gamma.
Another way to think of gamma is by a measure of the stability of an option’s probability. If delta represents the probability of being in the money at expiration, gamma represents the stability of that probability over time.
Example of Gamma
Suppose Apple (AAPL) is the car in the above example, and is currently trading at $100. Meanwhile, the 105-strike call option is priced at $5. Now, let’s assume it has a delta of 0.50 (the speed of the car) and a gamma of 0.10 (the acceleration of the car).
If the stock price moves up by $1 to $101, then the new option price is $5.50, based on its delta of 0.50. At this point, the new delta would increase by 0.10 to 0.60, based on the value of gamma.
How Time Impacts Gamma
As expiration nears, the gamma of at-the-money options will rise in value, while the gamma of in-the-money and out-of-the-money options will fall.
Gamma is an important metric because it corrects for convexity issues of delta based on the move in the underlying equity, and lets you know how much an option’s delta should change as the stock price changes.
1. Gamma is smallest for deep out-of-the-money and deep-in-the-money options.
2. Gamma is highest when the option gets near the money.
3. Gamma is positive for long options and negative for short options.
There are riskier options strategies that seem more like gambling as they can open you up to a significant amount of risk than more traditional options trades, like buying calls and puts. Two of these higher risk strategies are uncovered calls and puts.
And if you want to sell naked options, you’ll be required to have the top level of clearance from your broker, as well as a margin account. Most brokers require a minimum $2,000 balance to maintain a margin account.
Trading on margin can be a risky proposition. If your losses exceed your account, you still have to pay back the balance. And with short calls and puts that are uncovered, these can accumulate quickly. In fact, your loss potential is theoretically unlimited for naked calls, and extensive until the stock hits $0 for puts.
Let’s take a closer look at these high-risk, low-reward strategies.
When a trader sells calls, they are making a bearish bet. The position gains value when the stock stays put or declines.
An uncovered call means you are selling a call on a stock you do not own. The profit potential is capped on the trade at the premium collected, but the risk is not — if the stock price jumps above the strike price, and the call is exercised, you will be responsible for buying the stock on the open market and then selling it at the strike price to cover your portion of the contract.
In other words, you could be subject to heavy losses.
Let’s say RBLL stock gapped below $10 recently, and you think this round-number level will serve as a short-term ceiling for the stock. You decide to sell a 10-strike call for $3, or $300 (accounting for 100 shares).
This is also the most you stand to gain on the trade, should the shares remain below the strike through expiration.
However, what happens if the stock gaps sharply higher, and gaps all the way to $30? Losses can accumulate quickly once the option moves into the money. Considering your breakeven price is $13 (strike plus net credit collected) you’d be staring at a loss of $23 (30 – 23), or $2,300. This loss would only grow the higher the stock climbs.
A short put is also called an uncovered put or naked put, and is initiated by selling a put. Unlike the option buyer, the put seller collects a premium, and this premium represents the maximum potential profit on the trade.
A short put play is neutral to bullish because by selling the put, the trader believes the stock price will remain above the strike price through expiration. If the stock stays above the strike, the option will expire worthless, and the speculator gets to pocket the full premium. However, if the stock price falls below the strike price, the put seller faces significant losses.
Because the put seller is required to purchase the shares of the underlying stock at the strike price if the put buyer exercises the option. What happens if the company goes bankrupt, and the shares go to zero? Well, those put options would become really expensive.
Take a look at RBLL stock, which has been holding above short-term support near $10. You think this round-number mark will continue to serve as a floor for the shares, so you sell a 10-strike put for $3, or $300 (accounting for 100 shares).
This net credit received is the most the put writer stands to gain on the trade, should RBLL stay above the strike price through expiration.
What if the stock gaps below support at $10? Losses will accumulate quickly once the option moves into the money. Let’s say RBLL falls all the way down to $2. Considering your breakeven price of $7 (strike price less net credit), you’d be staring at a loss of $5 (7-2), or $500.
Writing options without being hedged is extremely dangerous and you should stray away from it when you’re first learning to trade options. For those that do choose to short uncovered calls and puts, they will need a margin account and clearance from their broker.
They will also need to choose their strike prices carefully to avoid assignment, and look for higher levels of implied volatility, since this boosts options prices — and in turn, the net credit they collect.