Gamma is a second derivative of an optionâ€™s price that measures the rate of change in delta over time.

Since delta values shift with the underlying assetâ€™s price, gamma is applied and used to measure the rate of change in delta based on a $1 move in the underlying security. Itâ€™s a gauge of the velocity of potential change in delta. The larger the gamma, the faster the optionâ€™s delta is going to move.

Similar to delta, gamma is constantly changing with the underlying stockâ€™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, itâ€™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 optionâ€™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, letâ€™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.

Wrapping Up
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 optionâ€™s delta should change as the stock price changes.

Remember:

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, youâ€™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.

Letâ€™s take a closer look at these high-risk, low-reward strategies.

Naked Calls

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.

Letâ€™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) youâ€™d be staring at a loss of $23 (30 – 23), or $2,300. This loss would only grow the higher the stock climbs.

Naked Puts

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.

Why?

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. Letâ€™s say RBLL falls all the way down to $2. Considering your breakeven price of $7 (strike price less net credit), youâ€™d be staring at a loss of $5 (7-2), or $500.

Wrapping Up

Writing options without being hedged is extremely dangerous and you should stray away from it when youâ€™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.

Options are financial tools that are called derivatives.

Derivatives are based on the value of underlying securities, such as stocks.Â Â

What is an option contract?

Gives an investor the right, but not the obligation, to buy or sell a stock at an agreed upon price.

Gives an investor the obligation to buy or sell a stock at an agreed upon price.

Gives an investor the right, but not the obligation, to buy or sell a stock at any price.

Gives an investor the obligation to buy or sell a stock at any price.Â Â

Answer: A

Notes: A stock option gives an investor the right, but not the obligation, to buy or sell a stock at an agreed upon price.

What is a call option?

Call options offer the writerÂ the opportunity to buy the underlying asset at the strike price.

Call options offer the writerÂ the opportunity to sell the underlying asset at the current market price.

Call options offer the buyer the opportunity to buy the underlying asset at the strike price.

Call options offers the buyer the opportunity to sell the underlying asset at the current market price.

Answer : C

What is a put option?

Put options offer the writer the opportunity to sell the underlying asset at the strike price.

Put options offer the buyer the opportunity to sell the underlying asset at the strike price.Â Â

Put options offer the buyer the opportunity to buy the underlying asset at the current market price..

Put options offer the writer the opportunity to buy the underlying asset at the current market price.

Answer: B

What are weekly contracts?

Options contracts that expire on every second Friday of the month.

Options contracts that expire on every third Thursday of the month.

Options contracts that expire on Friday of every week.

Options contracts that expire on Saturday of every week.

Answer : C

What are standard monthly contracts?

Options contracts that are issued with 9 month expirations and expire on the Saturday following the 3rd Friday of every month at 11:59pm EST.

Options contracts that are issued with 12 month expirations and expire on the Sunday following the 2nd Friday of every month at 11:50pm EST.

Options contracts that are issued with 6 month expirations and expire on the Friday following the 2nd Friday of every month at 11:59 EST.

Options contracts that are issued with 9 months of expiration and expire on the Saturday of the 2nd Friday of every month at 11:59pm EST.

Answer: A

What does the OCC stand for?

Options Clearing Company

Options Clearing Committee

Options Conference Committee

Options Concile Company

Answer : B

What are Listed Stock Options?

Listed Options are futures options that are a put or call that is traded on a national options exchange, and have a fixed strike price and a fixed expiration date.

Listed Options are a put or call that is traded on a national options exchange, and have variable strike prices and fixed expiration dates

Listed Options are a put or call that is traded on a regional options exchange only, and have variable strike prices and variable expiration dates.

Listen Options are a put or call that is traded on a national options exchange, and have a fixed strike price and a fixed expiration date.

Answer : D

What is the underlying security for stock options?

The stock that can be purchased or sold upon exercise of options contracts

The future that can be purchased or sold upon exercise of options contracts

The stock that can be purchased or sold without exercise of options contracts

The future that can be purchased or sold without exercise of options contracts

Answer : A

What does it mean to exercise an option?

To implement the right for the option holder to buy (for a call) or sell (for a put) the underlying security at the market price.

To implement the right for the option holder to sell (for a call) or buy (for a put) the underlying security at the listed strike price.

To implement the right for the option seller to sell (for a call) or buy (for a put) the underlying security at the listed strike price.

To implement the right for the option holder to buy (for a call) or sell (for a put) the underlying security at the listed strike price.

Answer : D

Notes:

Options are typically exercised when they are in the money.

When do listed equity options settle?

Settle â€śnon-regular wayâ€ť, or two business days from the expiration date

Settle â€śregular wayâ€ť, or four business days from the expiration date

Settle â€śregular wayâ€ť, or three business days from the expiration date

Settle â€śnon-regular wayâ€ť, or four business days from the expiration date

Answer : C

What is the strike price of an option?

The price at which the holder of an option can buy (for a call) or sell (for a put) the underlying security when the option is exercised.

The price at which the seller of an option can sell (for a call) or buy (for a put) the underlying security when the option is exercised.

The price at which the holder of an option can buy (for a call) or sell (for a put) the underlying security before the option is exercised.

The price at which the seller of an option can buy (for a call) or sell (for a put) the underlying security before the option is exercised.

Answer : A

How is options premium calculated?

Option Premium = Intrinsic Value + Extrinsic Value

Option Premium = Intrinsic Value – Extrinsic Value

Option Premium = Intrinsic Value + Extrinsic Value + Strike Price

Option Premium = Intrinsic Value – Extrinsic Value + Strike Price

Answer : A

How is Intrinsic Value calculated?

Difference between the strike price and market price of the underlying security.Â Â

Difference between the market price and the current option priceÂ

Difference between the current option price and At-the-Money (ATM) option price

Difference between the At-The-Money (ATM) option price and the market price of the underlying security

Answer: A

Notes:Â Intrinsic Value = Strike Price – Market Price of security

How is Extrinsic Value calculated?

The sum of the strike price of an option and the intrinsic price minus the market price, also known as its premium.

The difference between the market price of an option, also known as its premium, and its intrinsic price.

The difference between the market price of an option, also known as its premium, and its strike price.Â Â

The difference between the strike price of an option and the intrinsic price plus premium

Answer: B

Notes:

Extrinsic Value = premium – intrinsic price

Extrinsic Value is also known as time value

What are the types of options?

Calls and Puts

Strikes and Market price

Calls only

Puts only

Answer : A

What is an options class?

Every Call or every Put of an underlying stock, regardless of expiration month and strike price.

Every Call or every Put of an underlying stock, in the same expiration month and same strike price.

Every Call of an underlying stock, regardless of expiration month and strike price.

Every Put of an underlying stock, regardless of expiration month and strike price.

Answer : A

What is an option expiration?

The day after the final date on which the derivatives contract is valid

The final date on which the derivatives contract is valid

The day prior the final date on which the derivatives contract is valid

Two days prior the final date on which the derivatives contract is valid

Answer : B

Notes:

All contracts have a specified life cycle and expire on a specific date.Â

What does Out of the Money (OTM) of a call refer to?

Â call is â€śOut-of-the-Moneyâ€ť (OTM) when the market price is higher than strike price.

A call is â€śOut-of-the-Moneyâ€ť (OTM) when it has only intrinsic value and no extrinsic value.

A call is â€śOut-of-the-Moneyâ€ť (OTM) when the market price is equal to the strike price.

A call is â€śOut-of-the-Moneyâ€ť (OTM) when the market price is lower than strike price.

Answer : D

What does Out-of-the-Money (OTM) of a put refer to?

A put is â€śOut-of-the-Moneyâ€ť (OTM) when it has only intrinsic value and no extrinsic value.

A put is â€śOut-of-the-Moneyâ€ť (OTM) when the market price is equal to the strike price.

A put is â€śOut-of-the-Moneyâ€ť (OTM) when the market price is higher than the strike price.

A put is â€śOut-of-the-Moneyâ€ť (OTM) when the market price is lower than the strike price.

Answer : C

What does In The Money (ITM) of a call refer to?

A call is â€śin the moneyâ€ť when the market price is lower than the strike price.

A call is â€śin the moneyâ€ť when the market price is higher than the strike price.

A call is â€śin the moneyâ€ť when the market price is equal to the strike price.

A call is â€śin the moneyâ€ť when the option possesses extrinsic value and no intrinsic value.

Answer : B

Notes:

A call option is in the money (ITM) if the market price is above the strike price.

ITM options only possess intrinsic value, and no extrinsic value

What does In The Money (ITM) of a put refer to?

A put is â€śin the moneyâ€ť when the market price is lower than the strike price.

A put is â€śin the moneyâ€ť when the market price is higher than the strike price.

A put is â€śin the moneyâ€ť when the market price is equal to the strike price.

A put is â€śin the moneyâ€ť when the option possesses extrinsic value and no intrinsic value.

Answer : A

Notes:Â Â

A put option is in the money if the market price is below the strike price.

ITM options only possess intrinsic value, and no extrinsic value

What does At The Money (ATM) refer to?

When an option’s strike price is less than the market price of the underlying security.

When an optionâ€™s strike price is greater than the market price of the underlying security.

When an optionâ€™s strike price is equal to the market price of the underlying security.

When the market price of the underlying security is equal to the optionâ€™s strike price plus breakeven price

Answer : C

How do you calculate the breakeven price of a long call?

Breakeven = Strike Price + Market Price

Breakeven = Cost – Strike Price

Breakeven = Cost + Strike Price

Breakeven = Strike Price – Market Price

Answer : C

How do you calculate the breakeven price of a long put?

Breakeven = Strike Price + Market Price

Breakeven = Cost – Strike Price

Breakeven = Cost + Strike Price

Breakeven = Strike Price – Market Price

Answer : B

How do you calculate the breakeven price of a covered call?

Breakeven = call option premium – market price of stock at initiation

Breakeven = call option premium + market price of stock at initiation

Breakeven = call option premium – current market price

Breakeven = call option premium – strike price

Answer : A

How do you calculate the breakeven price of a protective put?

Breakeven = current price of stock – premium paid

Breakeven = purchase price of stock – premium paid

Breakeven = current price of stock + premium paid

Breakeven = purchase price of stock + premium paid

Answer : DÂ

What are the 4 factors that impact options premium?

implied volatility, intrinsic value, time remaining until expiration

historical volatility, intrinsic value, time remaining until expiration

implied volatility, intrinsic value, time remaining until expiration, interest rates

historical volatility, extrinsic value, time remaining until expiration, interest rates

Answer : C

What is Implied Volatility?

IV is a metricthat captures the market’s view of the likelihood of changes in a given security’s price

IV is a metric that captures the marketâ€™s view of the likelihood of a change in a given securityâ€™s delta

IV is a metric that captures the marketâ€™s view of the likelihood of a change in a given securityâ€™s time value

IV is a metric that captures the marketâ€™s view of the likelihood of a change in a given securityâ€™s historical volatility

Answer : A

What are the 5 common options greeks?

Delta, Gamma, Theta, Vega, Rho

Vomma, Volta, Surge, Speed, Delta

Delta, Theta, Rho, Volga, Vomma

Gamma, Delta, Vola, Volga, Theta

Answer : A

Notes: Option greeks us a term used to describe the different dimensions of risk involved in taking an options position

What does the greek, Delta, represent?

Represents the rate of change between the options price and $4 change in the underlying assetâ€™s price.

Represents the rate of change between the theta and $3 change in the underlying assetâ€™s price.

Represents the rate of change between the gamma and $2 change in the underlying assetâ€™s price.

Represents the rate of change between the options price and $1 change in the underlying assetâ€™s price.

Answer : D

Notes: Calls have a positive delta, between 0 and 1.Â Puts have a negative delta, between 0 and -1

What does the greek, Gamma, represent?

Represents the rate of change between the options theta and the underlying asset price.

Represents the rate of change between the options delta and the underlying asset price

Represents the rate of change between the options vega and the underlying asset price.

Represents the rate of change between the options rho and the underlying asset price.

Answer : B

Notes:

Second order derivative

Indicates the amount the delta would change given a $1 move in underlying assetâ€™s price

What does the greek, Theta, represent?

Represents the rate of change between the options price and historical volatility, or options volatility sensitivity

Represents the rate of change between the options implied volatility and time, or options vomma sensitivity

Represents the rate of change between the options price and time, or options time sensitivity

Represents the rate of change between the options price and delta, or options dollar sensitivity

Answer : C

Notes:

Also known as optionâ€™s time decay

Theta increases when options are At the money

Theta decreases when options are In the money or Out-of-the-money

As options near expiration, Theta will increase significantly

What does the greek, Vega, represent?

Represents the rate of change between the underlying market price and implied volatility.

Represents the rate of change between an optionâ€™s value and the underlying assets implied volatility.

Represents the rate of change between the optionâ€™s delta and the underlying assets implied volatility.

Represents the rate of change between the optionâ€™s time value theta and the underlying assets implied volatility.

Answer : B

Notes:

Known as the optionâ€™s sensitivity to volatility

Vega indicates the amount the options price will change given a 1% change in implied volatility

What does the greek, Rho, represent?

Represents the rate of change between an optionâ€™s value and a 2% change in market price.

Represents the rate of change between an optionâ€™s value and a 3% change in delta.

Represents the rate of change between an optionâ€™s value and a 4% change in volatility.

Represents the rate of change between an optionâ€™s value and a 1% change in interest rates.

Answer : D

Notes:

This measures the sensitivity to interest rates.

When are Weekly options contracts issued?

Issued Wednesday and expire the following Thursday

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