# Call and Put Options

This is an introductory page in Options. If you are unfamiliar with any of the terms, you can refer to the Options Glossary.

An option is a financial derivative on an underlying asset and represents the right to buy or sell the asset at a fixed price at a fixed time. As options offer you the right to do something beneficial, they will cost money. This is explored further in Option Value, which explains the intrinsic and extrinsic value of an option.

A call option gives the buyer the right to buy the asset at a certain price, and hence he would benefit as the price of the underlying goes up.

A put option gives the buyer the right to sell the asset at a certain price, hence he would benefit as the price of the underlying goes down.

Options can also be used to **hedge** against an existing position in the underlying. This reduces the risk of holding the asset as it offers protection/insurance against adverse price movements.

Options allow you to **speculate** on the direction and extent of price movements. Furthermore, since options can be purchased at a fraction of the cost/required outlay of the underlying, this allows for a position to be greatly **leveraged**. This would magnify any losses or gains (and losses are not limited to the value of the portfolio), which is why options are said to be risky.

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## Call Option

A **call option** is the right (but not obligation) to buy the underlying for a specified price (strike price K), on a specified date (expiry). If the underlying fails to rise above the strike price before expiration, then the call expires worthless as it would be cheaper to buy the underlying directly from the market. As there is no upper bound on the price of the underlying, the potential profit of a call is theoretically unlimited.

Let's consider how a call option works. Say that the stock A is currently priced at $10. You believe that it will rise over the next month, so you buy the call option on the $11 strike expiring in a month for $1.

**Scenario 1.** If the stock is worth $15 on expiration, then you can exercise the call option and buy the stock at the strike price of $11. You close out your position by selling the stock in the market for $15, which is a gain of $\$ 15 - \$11 = \$4$. Accounting for the initial cost of the option, your net profit is $\$4 - \$1 = \$3$.

**Scenario 2.** If, however, the stock were to drop in value to $8, then it is pointless to exercise the call option. As such, all that you have lost is the initial cost (premium) of the option, so your net profit is $- \$ 1$.

The payoffs (net profit) of this trade when the stock expires at different values is summarized in the following graph:

You are long the Jan Call on the $90 strike.

On expiration, the stock closed at $100. When the trade settles, what do you need to do so that you will no longer have a position?

**Trading Call Options**

Even though the option value will increase as the stock price increases, it is not necessarily profitable to buy calls even though you believe that the stock price will increase, unless the extent of increase is large enough to compensate for the theta that you are paying. For example, consider the case where the underlying is trading at $100, and (all that you do is) you buy the $110 strike for $2. Then you will need the underlying to be above $112 on expiration, in order for you to have profited on this trade.

Furthermore, in the stock market, option volatility often decreases as the stock price increases, as it reflects investor confidence in the company. Hence, buying upside calls when the stock goes up could still lose you money on vega and theta.

Consider buying calls in the following situations:

- You believe that the underlying will move up more than the implied volatility.
- You believe that the underlying will move up and that volatility will increase.
- You believe that the underlying will move up more than the cost of theta.

Consider selling calls in the following situations:

- You believe that the underlying will move down.
- You strongly believe that the underlying will not move up significantly.

**Greeks of Call Options**

The greeks of a call option are as follows:

There are explained in detail in the corresponding pages about the Greeks.

## Put Option

A **put option** is the right (but not obligation) to sell the underlying for a specified price (strike price K), on a specified date (expiry). If the underlying fails to fall below the strike price before expiration, then the put expires worthless as it would be more profitable to sell the underlying directly in the market. Since the price of a stock does not fall below 0, the potential profit of a put is capped at the strike price.

What is a put?

Let's consider how a put option works. Say that the stock B is currently priced at $10. You believe that it will drop over the next month, so you buy the put option on the $8 strike expiring in a month for $1.

**Scenario 1** If the stock is worth $5 on expiration, then you can exercise the put option, which allows you to sell the stock for $8. You close out your position by buying it in the market for $5, which is a gain of $\$8 - \$5 = \$3$. Accounting for the initial cost of the option, your net profit is $\$3 - \$1 = \$2$.

**Scenario 2** If, however, the stock were to rise in value to $12, then it is pointless to exercise the put option. As such, all that you have lost is the premium (initial cost) of the option, so your net profit is $- \$ 1$.

The payoffs (net profit) of this trade when the stock expires at different values is summarized in the following graph:

On expiration, the stock closed at $100. When the trade settles, what do you need to do if you are short the put on the $90 strike to close out your position?

**Trading Put Options**

Even though the option value will increase as the stock price decreases, it is not necessarily profitable to buy puts even though you believe that the stock price will decrease, unless the extent of decrease is large enough to compensate for the theta that you are paying. For example, consider the case where the underlying is trading at $100, and (all that you do is) you buy the put on the $90 strike for $2. Then you will need the underlying to be below $88 on expiration, in order for you to have profited on this trade.

Consider buying puts in the following situations:

- You believe that the underlying will move down significantly.
- You believe that the underlying will move down more than the cost of theta.

Consider selling puts in the following situations:

- You believe that the underlying will move up.
- You strongly believe that the underlying will not move down significantly.

**Greeks of Put Options**

The Greeks of a put option are as follows:

There are explained in detail in the corresponding pages about the Greeks.

**Cite as:**Call and Put Options.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/call-and-put-options/