## What Is an Option?

Options are financial instruments that are derivatives based on the value of underlying securities such as stocks. An options contract offers the buyer the opportunity to buy or sell—depending on the type of contract they hold—the underlying asset. Unlike futures, the holder is not required to buy or sell the asset if they choose not to.

- Call options allow the holder to buy the asset at a stated price within a specific timeframe.
- Put options allow the holder to sell the asset at a stated price within a specific timeframe.

Each option contract will have a specific expiration date by which the holder must exercise their option. The stated price on an option is known as the strike price. Options are typically bought and sold through online or retail brokers.

### Key Takeaways

- Options are financial derivatives that give buyers the right, but not the obligation, to buy or sell an underlying asset at an agreed-upon price and date.
- Call options and put options form the basis for a wide range of option strategies designed for hedging, income, or speculation.
- Although there are many opportunities to profit with options, investors should carefully weigh the risks.

#### Option

## How Options Work

Options are a versatile financial product. These contracts involve a buyer and a seller, where the buyer pays an options premium for the rights granted by the contract. Each call option has a bullish buyer and a bearish seller, while put options have a bearish buyer and a bullish seller.

Options contracts usually represent 100 shares of the underlying security, and the buyer will pay a premium fee for each contract. For example, if an option has a premium of 35 cents per contract, buying one option would cost $35 ($0.35 x 100 = $35). The premium is partially based on the strike price—the price for buying or selling the security until the expiration date. Another factor in the premium price is the expiration date. Just like with that carton of milk in the refrigerator, the expiration date indicates the day the option contract must be used. The underlying asset will determine the use-by date. For stocks, it is usually the third Friday of the contract's month.

Traders and investors will buy and sell options for several reasons. Options speculation allows a trader to hold a leveraged position in an asset at a lower cost than buying shares of the asset. Investors will use options to hedge or reduce the risk exposure of their portfolio. In some cases, the option holder can generate income when they buy call options or become an options writer.

American options can be exercised any time before the expiration date of the option, while European options can only be exercised on the expiration date or the exercise date. Exercising means utilizing the right to buy or sell the underlying security.

## Options Risk Metrics: The Greeks

The "Greeks" is a term used in the options market to describe the different dimensions of risk involved in taking an options position, either in a particular option or a portfolio of options. These variables are called Greeks because they are typically associated with Greek symbols. Each risk variable is a result of an imperfect assumption or relationship of the option with another underlying variable. Traders use different Greek values, such as delta, theta, and others, to assess options risk and manage option portfolios.

### Delta

Delta (Δ) represents the rate of change between the option's price and a $1 change in the underlying asset's price. In other words, the price sensitivity of the option relative to the underlying. Delta of a call option has a range between zero and one, while the delta of a put option has a range between zero and negative one. For example, assume an investor is long a call option with a delta of 0.50. Therefore, if the underlying stock increases by $1, the option's price would theoretically increase by 50 cents.

For options traders, delta also represents the hedge ratio for creating a delta-neutral position. For example if you purchase a standard American call option with a 0.40 delta, you will need to sell 40 shares of stock to be fully hedged. Net delta for a portfolio of options can also be used to obtain the portfolio's hedge ration.

A less common usage of an option's delta is it's current probability that it will expire in-the-money. For instance, a 0.40 delta call option today has an implied 40% probability of finishing in-the-money. (For more on the delta, see our article: Going Beyond Simple Delta: Understanding Position Delta.)

### Theta

Theta (Θ) represents the rate of change between the option price and time, or time sensitivity - sometimes known as an option's time decay. Theta indicates the amount an option's price would decrease as the time to expiration decreases, all else equal. For example, assume an investor is long an option with a theta of -0.50. The option's price would decrease by 50 cents every day that passes, all else being equal. If three trading days pass, the option's value would theoretically decrease by $1.50.

Theta increases when options are at-the-money, and decreases when options are in- and out-of-the money. Options closer to expiration also have accelerating time decay. Long calls and long puts will usually have negative Theta; short calls and short puts will have positive Theta. By comparison, an instrument whose value is not eroded by time, such as a stock, would have zero Theta.

### Gamma

Gamma (Γ) represents the rate of change between an option's delta and the underlying asset's price. This is called second-order (second-derivative) price sensitivity. Gamma indicates the amount the delta would change given a $1 move in the underlying security. For example, assume an investor is long one call option on hypothetical stock XYZ. The call option has a delta of 0.50 and a gamma of 0.10. Therefore, if stock XYZ increases or decreases by $1, the call option's delta would increase or decrease by 0.10.

Gamma is used to determine how stable an option's delta is: higher gamma values indicate that delta could change dramatically in response to even small movements in the underlying's price.Gamma is higher for options that are at-the-money and lower for options that are in- and out-of-the-money, and accelerates in magnitude as expiration approaches. Gamma values are generally smaller the further away from the date of expiration; options with longer expirations are less sensitive to delta changes. As expiration approaches, gamma values are typically larger, as price changes have more impact on gamma.

Options traders may opt to not only hedge delta but also gamma in order to be delta-gamma neutral, meaning that as the underlying price moves, the delta will remain close to zero.

### Vega

Vega (V) represents the rate of change between an option's value and the underlying asset's implied volatility. This is the option's sensitivity to volatility. Vega indicates the amount an option's price changes given a 1% change in implied volatility. For example, an option with a Vega of 0.10 indicates the option's value is expected to change by 10 cents if the implied volatility changes by 1%.

Because increased volatility implies that the underlying instrument is more likely to experience extreme values, a rise in volatility will correspondingly increase the value of an option. Conversely, a decrease in volatility will negatively affect the value of the option. Vega is at its maximum for at-the-money options that have longer times until expiration.

Those familiar with the Greek language will point out that there is no actual Greek letter named vega. There are various theories about how this symbol, which resembles the Greek letter nu, found its way into stock-trading lingo.

### Rho

Rho (p) represents the rate of change between an option's value and a 1% change in the interest rate. This measures sensitivity to the interest rate. For example, assume a call option has a rho of 0.05 and a price of $1.25. If interest rates rise by 1%, the value of the call option would increase to $1.30, all else being equal. The opposite is true for put options. Rho is greatest for at-the-money options with long times until expiration.

### Minor Greeks

Some other Greeks, with aren't discussed as often, are lambda, epsilon, vomma, vera, speed, zomma, color, ultima.

These Greeks are second- or third-derivatives of the pricing model and affect things such as the change in delta with a change in volatility and so on. They are increasingly used in options trading strategies as computer software can quickly compute and account for these complex and sometimes esoteric risk factors.

## Risk and Profits From Buying Call Options

As mentioned earlier, the call options let the holder buy an underlying security at the stated strike price by the expiration date called the expiry. The holder has no obligation to buy the asset if they do not want to purchase the asset. The risk to the call option buyer is limited to the premium paid. Fluctuations of the underlying stock have no impact.

Call options buyers are bullish on a stock and believe the share price will rise above the strike price before the option's expiry. If the investor's bullish outlook is realized and the stock price increases above the strike price, the investor can exercise the option, buy the stock at the strike price, and immediately sell the stock at the current market price for a profit.

Their profit on this trade is the market share price less the strike share price plus the expense of the option—the premium and any brokerage commission to place the orders. The result would be multiplied by the number of option contracts purchased, then multiplied by 100—assuming each contract represents 100 shares.

However, if the underlying stock price does not move above the strike price by the expiration date, the option expires worthlessly. The holder is not required to buy the shares but will lose the premium paid for the call.

## Risk and Profits From Selling Call Options

Selling call options is known as writing a contract. The writer receives the premium fee. In other words, an option buyer will pay the premium to the writer—or seller—of an option. The maximum profit is the premium received when selling the option. An investor who sells a call option is bearish and believes the underlying stock's price will fall or remain relatively close to the option's strike price during the life of the option.

If the prevailing market share price is at or below the strike price by expiry, the option expires worthlessly for the call buyer. The option seller pockets the premium as their profit. The option is not exercised because the option buyer would not buy the stock at the strike price higher than or equal to the prevailing market price.

However, if the market share price is more than the strike price at expiry, the seller of the option must sell the shares to an option buyer at that lower strike price. In other words, the seller must either sell shares from their portfolio holdings or buy the stock at the prevailing market price to sell to the call option buyer. The contract writer incurs a loss. How large of a loss depends on the cost basis of the shares they must use to cover the option order, plus any brokerage order expenses, but less any premium they received.

As you can see, the risk to the call writers is far greater than the risk exposure of call buyers. The call buyer only loses the premium. The writer faces infinite risk because the stock price could continue to rise increasing losses significantly.

## Risk and Profits From Buying Put Options

Put options are investments where the buyer believes the underlying stock's market price will fall below the strike price on or before the expiration date of the option. Once again, the holder can sell shares without the obligation to sell at the stated strike per share price by the stated date.

Since buyers of put options want the stock price to decrease, the put option is profitable when the underlying stock's price is below the strike price. If the prevailing market price is less than the strike price at expiry, the investor can exercise the put. They will sell shares at the option's higher strike price. Should they wish to replace their holding of these shares they may buy them on the open market.

Their profit on this trade is the strike price less the current market price, plus expenses—the premium and any brokerage commission to place the orders. The result would be multiplied by the number of option contracts purchased, then multiplied by 100—assuming each contract represents 100 shares.

The value of holding a put option will increase as the underlying stock price decreases. Conversely, the value of the put option declines as the stock price increases. The risk of buying put options is limited to the loss of the premium if the option expires worthlessly.

## Risk and Profits From Selling Put Options

Selling put options is also known as writing a contract. A put option writer believes the underlying stock's price will stay the same or increase over the life of the option—making them bullish on the shares. Here, the option buyer has the right to make the seller, buy shares of the underlying asset at the strike price on expiry.

If the underlying stock's price closes above the strike price by the expiration date, the put option expires worthlessly. The writer's maximum profit is the premium. The option isn't exercised because the option buyer would not sell the stock at the lower strike share price when the market price is more.

However, if the stock's market value falls below the option strike price, the put option writer is obligated to buy shares of the underlying stock at the strike price. In other words, the put option will be exercised by the option buyer. The buyer will sell their shares at the strike price since it is higher than the stock's market value.

The risk for the put option writer happens when the market's price falls below the strike price. Now, at expiration, the seller is forced to purchase shares at the strike price. Depending on how much the shares have appreciated, the put writer's loss can be significant.

The put writer—the seller—can either hold on to the shares and hope the stock price rises back above the purchase price or sell the shares and take the loss. However, any loss is offset somewhat by the premium received.

Sometimes an investor will write put options at a strike price that is where they see the shares being a good value and would be willing to buy at that price. When the price falls, and the option buyer exercises their option, they get the stock at the price they want, with the added benefit of receiving the option premium.

#### Pros

A call option buyer has the right to buy assets at a price that is lower than the market when the stock's price is rising.

The put option buyer can profit by selling stock at the strike price when the market price is below the strike price.

Option sellers receive a premium fee from the buyer for writing an option.

#### Cons

In a falling market, the put option seller may be forced to buy the asset at the higher strike price than they would normally pay in the market

The call option writer faces infinite risk if the stock's price rises significantly and they are forced to buy shares at a high price.

Option buyers must pay an upfront premium to the writers of the option.

## Real World Example of an Option

Suppose that Microsoft (MFST) shares are trading at $108 per share and you believe that they are going to increase in value. You decide to buy a call option to benefit from an increase in the stock's price.

You purchase one call option with a strike price of $115 for one month in the future for 37 cents per contact. Your total cash outlay is $37 for the position, plus fees and commissions (0.37 x 100 = $37).

If the stock rises to $116, your option will be worth $1, since you could exercise the option to acquire the stock for $115 per share and immediately resell it for $116 per share. The profit on the option position would be 170.3% since you paid 37 cents and earned $1—that's much higher than the 7.4% increase in the underlying stock price from $108 to $116 at the time of expiry.

In other words, the profit in dollar terms would be a net of 63 cents or $63 since one option contract represents 100 shares ($1 - 0.37 x 100 = $63).

If the stock fell to $100, your option would expire worthlessly, and you would be out $37 premium. The upside is that you didn't buy 100 shares at $108, which would have resulted in an $8 per share, or $800, total loss. As you can see, options can help limit your downside risk.

## Options Spreads

Options spreads are strategies that use various combinations of buying and selling different options for a desired risk-return profile. Spreads are constructed using vanilla options, and can take advantage of various scenarios such as high- or low-volatility environments, up- or down-moves, or anything in-between.

Spread strategies, can be characterized by their payoff or visualizations of their profit-loss profile, such as bull call spreads or iron condors, are theoretically possible. See our piece on 10 common options spread strategies to learn more about things like covered calls, straddles, and calendar spreads.