# Home: What is a call option?

Options give their holders the right but not the obligation to do something in the future. The holder of an option is called the option buyer. The option seller is the party who grants the right to the option buyer.

There are two types of options: a call and a put. A call gives the option buyer the right to buy the underlying at an agreed fixed price, while a put gives the right to sell. Options have expiration dates, meaning that a buyer can exercise his right by a specific time in the future.

## Why would an investor decide to buy a call option?

Usually, because he believes the price of the underlying will go up before the expiration date.

## Basic characteristics of call options

Here is a simple example to introduce the basic characteristics of call options. The stock price of Microsoft (MSFT) is about $47.00 as of December, 2014. Investor Y believes that MSFT share price will rise in the next 6 months. In other words, investor Y is bullish on MSFT stock. He decides to buy one of the call options available for MSFT (MSFT is called the 'underlying security', or just the 'underlying'). Investor Y selects a call option that expires in approximately 6 months on June 15, 2015 (expiration date) and that gives him the right to purchase one share of MSFT at any time before the option expires for a price of $48.00 (exercise price). Investor Y pays $3.00 (option premium) to acquire this call option.

Here are the terms explained:

**Underlying**

The underlying is what you can buy if you hold a call option. The underlying of a call option is usually but not necessarily an asset. There are call options on stocks as in our example above (stock options), on indices like the S&P 500 Index (index options), on bonds (bond options), on interest rates (interest rate options), on currencies (currency options), on futures (options on futures), on commodities like gold and oil (commodity options), even on things like electricity and weather.

**Expiration date**

The expiration date is the date at which the call option expires. What happens with the price of the underlying after the expiration date is irrelevant for the buyer and seller of the call option. In the example above, the expiration date is June 15, 2015. The time to expiration is currently about six months. As time passes however, the time to expiration diminishes. It is stated that the investor has the right to exercise the option at any time before or on the expiration date. Such an option is called American. If the option were European, the investor could exercise it only on its expiration date June 15, 2015.

**Exercise price**

The exercise price is also called the strike price, striking price, or simply the strike. It is the price at which the call buyer can buy the underlying if he decides to exercise the option. Let us imagine it is February 2, 2015, and the stock price of MSFT is $51.00. Investor Y decides to exercise his American call option. He pays the option seller the strike price of $47.00 and receives one MSFT share in return. Even though one share of MSFT is trading at $51.00 on the stock market, the option seller (also called the option writer) is obliged to sell it for only $47.00 to the option holder. The call option seller does not always own the underlying when the option contract is entered. This situation is called "naked option" and is very risky for the option seller because if the price of the underlying rises significantly above the strike, the option seller will have to buy it on the market at this high price and sell it to the call option buyer at the much lower strike price, thus realizing a significant loss.

**Option premium**

While the option buyer has the right to buy the underlying, the option seller has the obligation to sell it if the option is exercised. Then why would the option seller agree to write the call in the first place? It is because he is compensated for it. To acquire the call option, the option buyer pays the option seller a price called an option premium.

**Moneyness**

Another important characteristic of options is called "moneyness". The terms in-the-money, at-the-money, and out-of-the-money are used. A call option is in-the-money when the market price of the underlying is above the strike price; in other words, when the holder of the option will make money if he exercises. Similarly, a call is out-of-the-money when the market price of the underlying is below the strike. An at-the-money call means that the strike equals the market price of the underlying.

## Call option pricing

Call options just like other financial instruments have a value. In this section, we discuss the pricing and valuation of call options.

**Value at expiration**

It is easiest to determine call options' value at expiration because at that time, there is no uncertainty about the price of the underlying. If the price of the underlying at expiration is below the exercise price, the call option is worthless. If, however, the price of the underlying is above the exercise price, the call option's value is equal to the positive difference between the market price and the strike. At expiration, a call option's value is called its payoff and is found by the following equation:

Call value at expiration = Maximum (0, market price at expiration - strike price)

Note that a call's value at expiration is either zero or a number greater than zero (without an upper limit). The value found by the equation above is called a call option's intrinsic value (or exercise value). At expiration, an option's value is equal to its intrinsic value.

Let us go back to the MSFT example. In order to draw the call option payoff at expiration, we need the option's strike price which is $48.00. In the table below, we calculate the call option's value for different stock prices at expiration:

MSFT share price on June 15, 2015 |
Call option value at expiration |

$40.00 | $0.00 |

$48.00 | $0.00 |

$56.00 | $8.00 (= $56.00 - $48.00) |

$64.00 | $16.00 (= $64.00 - $48.00) |

From the payoff of the call option at expiration, we can form the profit and loss for the call option buyer. The call option buyer receives the call value but has paid the call premium of $3.00 at the beginning of the option. The table below summarizes the profit and loss for the option buyer for different stock prices at expiration:

MSFT share price on June 15, 2015 |
Call buyer P&L |

$40.00 | -$3.00 (= $0.00 - $3.00) |

$48.00 | -$3.00 (= $0.00 - $3.00) |

$56.00 | $5.00 (= $8.00 - $3.00) |

$64.00 | $13.00 (= $16.00 - $3.00) |

We use the information in the tables above to graph the call option payoff and P&L:

**Value before expiration**

Prior to expiration, an option costs more than its intrinsic value. The formal expression is:

Option price/premium = Intrinsic value + Time value

At any time before expiration, even if the underlying price is below the strike price (even if the intrinsic value is zero), a call option costs something. The time value reflects the potential for the call option's intrinsic value to become positive as time progresses. All else equal, more time to expiration means higher time value. At expiration, the time value is zero.

**Maximum and minimum values**

From our discussion above it follows that a call value cannot be negative. In other words, the minimum value of a call option is zero. No matter whether the call option is European or American, its maximum value is the current value of the underlying. The call gives the right to buy the underlying. It does not make sense to pay more for this right than the value of the underlying itself.

## Factors affecting a call option's value

The math behind the option-pricing models is beyond the scope of this article but we summarize the effect of different factors on the call value in the table below:

Factor | Direction | Call option value |

Price of the underlying | Increases | Increases |

Volatility of the underlying | Increases | Increases |

Time to expiration | Decreases | Decreases |

Interest rate | Increases | Increases |

Dividends | Increases | Decreases |

Early exercise | Increases |

All else equal, the call option value increases when the price of the underlying, its volatility, and the interest rates in the economy increase. The early-exercise option associated with the American call options also theoretically increases the value of a call. Higher dividends or cash income on the underlying means lower call value. As time to expiration decreases, the value of a call falls.

## Additional Examples

For more call option examples and info, please see Born To Sell's Call Option Tutorial or the Put Option Tutorial.