### All Right, Time for the Basics

Options are derivatives. This means that the value of an option depends on and is derived from one or more underlying values. Possible underlying values include stocks, foreign currencies, and interest rates. If not specified otherwise this article will take stocks or index futures as the underlying in our examples. Here are the four basic positions one can have as far as calls and puts are concerned:

*Long Call:*The right to buy 100 shares at the strike price.*Short Call:*The obligation to sell 100 shares at the strike price.*Long Put:*The right to sell 100 shares at the strike price.*Short Put:*The obligation to buy 100 shares at the strike price.

When we are long the call, it means we bought it (and thus the other party is short). Note that the underlying amount can vary for various reasons. For simplicity, we will only discuss options with an underlying amount of 100 (the UK, for instance has underlying 1000, meaning the right to sell/buy 1000 shares). If I thus buy an Apple 105 put, I have the right to sell 100 Apple shares at a price of 105 (dollars).

Besides this distinction between calls and puts, one also has to specify what type of option he/she is trading. The two most commonly traded types are:
**European options. **These options can only be exercised on the expiration date, generally by cash settlement; you will get cash on your account instead of stock. Most index options are European options.
**American options. **These options can be exercised at any moment up to and including the expiration date; for example most stock options. They are exercised by physical delivery of the underlying item instead of by cash settlement.
The last day of an option contract's maturity is called the expiration day. In the USA and Europe this is usually third Friday of the month. If the third Friday falls on an exchange holiday, the expiration date will move to the Thursday preceding the third Friday. At that point in time the option contract will either be worth its intrinsic value ("in the money," or ITM) or will expire worthless ("'out of the money" or OTM). The price specified in the contract is called the strike price (strike). If the holder uses his right to buy or sell the underlying item, we say the holder is exercising the option whereas we say that the counterparty is being assigned.
The price of an option depends on the following factors:

- The price of the underlying
- The strike price of the option
- Maturity of the option (time to expiration)
- The volatility of the underlying value (the most important factor in daily trading!)
- (Risk-free) interest rate (and short stock interest rate)
- Possible dividend payouts during the maturity of an option

A call (put) option gives the holder the right to buy (sell) the underlying at a predetermined price (the strike price), on—or before—a predetermined date. The seller of the call (put) option has the obligation to sell (buy) the underlying when the buyer exercises his right. This is called being assigned.

### Payoff

The influence of the first two factors on the price of an option should be obvious: *ceteris paribus*, if the price of the underlying increases, the value of a call option will increase.
This is because the option gives the holder the right to buy stock that has become more valuable for a predetermined price. Consequently, the call option with the lowest strike (the deepest ITM) has the highest possible value relative to the other calls, since it gives its holder the right to buy the stock at the lowest possible price.

### Example 1: Long Call

**Transaction:** Buy call with strike price A
**Characteristics:** Long call offers limited downside risk (“premium” paid) and unlimited upside potential. Value increases in a “bull” market (uptrend).
**Profit on expiration:** Unlimited to the upside (i.e. when the share price moves up)
**Loss:** Limited to the paid premium (when the share price drops)
**Break-even:** Point where the share price is equal to the strike price of the option plus the paid premium. For example, if the premium paid for a call is €1 and the strike price is €10, the breakeven point will be reached when the stock is trading at €11.

### Example 2: Long Put

**Transaction:** Buy a put with strike price A.
**Characteristics:** Long put with limited upward risk (premium) and a downward potential (limited to the strike price). Value increases in a “bear” market (downtrend).
**Profit on expiration:** Limited to the strike price (share price cannot drop below 0)
**Loss on expiration:** Limited to the paid premium
**Break-even:** Point where the share price is equal to the strike price of the option minus the paid premium. For example, if the premium paid is €1 and the strike price is €10, the breakeven point will be reached when the stock is trading at €9.

### Example 3: Short Call

**Transaction:** Sell a call with strike price A.
**Characteristics:** Short call offers an unlimited upward risk and a maximum profit of the received premium on or below the strike. When the option expires, the seller is left with the premium received.
**Profit on expiration:** Limited when the share price decreases (up to the received premium).
**Loss on expiration:** Unlimited when the share price rises.
**Break-even:** Point where the share price (underlying price) is equal to the strike price of the option plus the received premium.

### Example 4: Short Put

**Transaction:** Sell a put with strike price A.
**Characteristics:** Short put offers a downward risk limited to the strike price. The maximum profit is achieved when the underlying expires on or above the strike price. The seller is then left with the received premium.
**Profit on expiration:** Limited when the share price rises (to a maximum of the received premium).
**Loss on expiration:** Limited to the difference between the strike price and the received premium, when the underlying value drops (a share cannot trade below 0).
**Break-even:** Point where the share price is equal to the strike price of the option price plus the received premium.

### In/Out/At the Money

An option is either in-the-money, out-of-the-money or at-the-money. An option is called

*in-the-money*if it has intrinsic value,*out-of-the-money*when exercising it leads to negative cash flow, and*at-the-money*if the strike price is at the price of the underlying.

The table below shows that if a call option is in-the-money, then the put option with the same maturity and strike price (X) is out-of-the-money, and vice versa. If an in-the-money option is exercised and there is a positive cash flow, this positive cash flow is called the intrinsic value of the option. However, in most calculations we calculate the intrinsic value based on the future price (F) instead of the stock price (S), thereby taking the interest costs for buying the share and the dividends into account. These costs are also referred to as the "costs of carry." Hence, the intrinsic value will be max(F-X, 0) for a call option and max(X-F, 0) for a put option. By definition, it is impossible for both the call and the put (with the same strike and maturity) to have an intrinsic value.

Moneyness |
Call Option |
Put option |
---|---|---|

In the money |
S>X |
S |

At the money |
S=X |
S=X |

Out of the money |
S |
S>X |

### Maturity

For American options it holds that the longer the maturity, the more expensive the option. Consider two similar American options which only differ in maturity. The holder of the option with the longer maturity has exactly the same rights as the holder of the option with shorter maturity. Moreover, the holder of the long-term option can exercise this option after the short-term option has expired. Hence the long-term option has to be at least as valuable as the short-term option.This does not have to hold for European options, because there is no possibility of early exercise and therefore factors like dividend could play a role.

### Volatility

This is the most complicated and important variable when it comes to pricing options and will therefore be covered extensively later on. For now, it is sufficient to know that the volatility is a measure for the degree of uncertainty in future movements of the underlying stock. It is, therefore, a measure of the expected movement of the underlying over a certain period of time.

### Interest rate

Regarding the influence of the interest rate on options, we may look at its influence on the value of the future. If we were to sell the underlying stock at present, place the money in a savings account and take it out in one year's time, we would receive our deposit plus accumulated interest over that amount. It follows that the value of the future (on any underlying) will increase by the amount of interest that could be accumulated until the time to expiration. Therefore, if the interest rate increases, the future increases. An increase in the future will result in an increase in the value of the call and a decrease in the value of the put. A rate that is commonly used by market participants to fit the market is the LIBOR rate. Option theory often refers to the risk-free rate, which doesn’t really exist. One could price his options on EONIA, Euribor, LIBOR or any other rate that one assumes to be the correct rate in order to fit the market.

### Dividend

Dividends are payments made by a company to its shareholders. They can be paid in cash or in stock. A dividend leads to a drop in the value of the stock/future, thus influencing the price of an option.

### To Summarize

The following table shows how the value of different options changes when there is an increase in one of the variables. For European-style options, "maturity" should be blank because it is not clear if there is a dividend within the maturity. For American style, this does not matter because of early exercise.

### How Variables Affect a Price of an Option

Variable |
Call |
Put |
---|---|---|

Stock Price |
+ |
- |

Strike Price |
- |
+ |

Maturity |
+ |
+ |

Volatility |
+ |
+ |

Interest Rate |
+ |
- |

Dividend |
- |
+ |

### Books for Beginning Options Traders

The go-to title for all starting option traders. Combined with Hull (which is more theoretical) this book covers all you need to know about options. Often used in the industry.

The other essential guide for all starting option traders. Combined with Natenberg (which is more practical) this book covers all you need to know about options. Often used in the industry.

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