# Level 1 CFA® Exam:

Options - Introduction

An option is a contract entered into by two parties. One party to the contract enjoys a right to buy or sell an underlying asset in the future, whereas the other party is obligated to sell or buy the underlying in the future if the counterparty requests this.

Depending on whether an option involves a right to buy or a right to sell the underlying, we distinguish two types of options:

- a call option and
- a put option.

### Call Option

A call option on a stock gives the option buyer (the option holder; the long), a right to buy a stock in the future at a specified price from the option seller (the option writer; the short). In other words, the option seller is obliged to sell the stock on the holder's request.

Assume that three months ago you bought a call option on a stock of Company A. At that time, the price of the stock was USD 60 and the exercise price (aka. strike price) of the option, i.e. the price at which you will be able to buy the stock in the future is USD 65. At present, the stock is trading at USD 70. Should you exercise the option?

Since the call option gives you a right to buy the stock at USD 65, which is less than the current market price, you will want to exercise the option. It pays more to buy the stock for USD 65 from the option writer than for USD 70 on the stock exchange.

### Put Option

A put option on a stock gives its holder a right to sell a stock in the future at a specified price to the seller of the option. The seller of a put option is obliged to buy the underlying stock on the option holder's request.

Assume that three months ago you bought a put option on a stock of Company X. At that time, the share price was USD 60. The exercise price of the option, i.e. the amount at which you will be able to sell the stock in the future, is USD 65. At present, the stock is trading at USD 70. Should you exercise the option?

(...)

Now, what have we learnt about options from these two examples?

- The option holder enjoys a right that he may or may not exercise. In Example 1 we exercised our option, in Example 2, we didn’t.
- The seller of an option has a commitment to buy or sell the underlying depending on the type of the option. When we decided to exercise the call option in Example 1, the seller was bound to sell us the stock. Note that if we had a put option on a stock and if we decided to exercise it, the seller of the option would have to buy the stock from us.
- You will want to exercise a call option if the exercise price is lower than the current market price of the stock.
- You will want to exercise a put option if the exercise price is higher than the current market price. In Example 2 the opposite was the case, so we decided not to exercise the option.

### Option Premium

Options are derivative instruments that are counted among contingent claims. The long party will require that the short complete the transaction only if this transaction is profitable for the long party.

Since the party who buys an option is in a better position than the party who sells it, unlike in the case of futures and forward contracts, a payment is made when the parties enter into the option contract. The long (the buyer) pays to the short (the seller) a certain amount called the option price, option premium, or simply premium.

### Option Payoff

The stock option payoff depends on the difference between exercise price and stock price.

The payoff to the long party, regardless of whether she holds a call or a put, is always equal to or greater than zero.

\(c_{T} = Max(0,S_{T} - X)\)

- \(c_{T}\) - value of the option at expiration
- \(S_{T}\) - price of the underlying at the expiration date
- \(X\) - exercise price of the option

\(-c_{T} = -Max(0,S_{T} - X)\)

- \(c_{T}\) - value of the option at expiration
- \(S_{T}\) - price of the underlying at the expiration date
- \(X\) - exercise price of the option

\(p_{T} = Max(0,X - S_{T})\)

- \(p_{T}\) - payoff to the put buyer
- \(X\) - exercise price of the option
- \(S_{T}\) - price of the underlying at the expiration date

\(-p_{T} = -Max(0,X - S_{T})\)

- \(p_{T}\) - payoff to the put seller
- \(X\) - exercise price of the option
- \(S_{T}\) - price of the underlying at the expiration date

### Option Profit

When calculation option profit we have to take into account both option payoff and option premium.

\(\Pi = Max(0,S_{T} - X) - c_{0}\)

- \(\Pi\) - profit to the call buyer
- \(S_{T}\) - price of the underlying at the expiration date
- \(X\) - exercise price of the option
- \(c_{0}\) - money paid for the option at time zero

\(\Pi = -Max(0,S_{T} - X) + c_{0}\)

- \(\Pi\) - profit to the call seller
- \(S_{T}\) - price of the underlying at the expiration date
- \(X\) - exercise price of the option
- \(c_{0}\) - money paid for the option at time "zero"

\(\Pi = Max(0,X - S_{T}) - p_{0}\)

- \(\Pi\) - profit to the put buyer
- \(X\) - exercise price of the option
- \(S_{T}\) - price of the underlying at the expiration date
- \(p_{0}\) - money paid for the option at time "zero"

\(\Pi = -Max(0,X - S_{T}) + p_{0}\)

- \(\Pi\) - profit to the put seller
- \(X\) - exercise price of the option
- \(S_{T}\) - price of the underlying at the expiration date
- \(p_{0}\) - money paid for the option at time "zero"

(...)

The basic characteristics of an option contract include:

- the underlying asset,
- the size of the contract,
- the expiration date,
- the type of option,
- the exercise style.

### Exercise Style

Depending on the exercise style, two types of options are distinguished:

- American options and
- European options.

The holder of an American option can exercise the option at any moment from taking the long position until expiration.

European option can be only exercised at expiration.

Example 3

For example, if you buy a 2-month European option, you will only be able to exercise it exactly in two months. If you take the long position in a 2-month American option, you will be able decide when to exercise it – today, tomorrow, or on any day two months from now.

Since American options give their holders greater choice as far as the exercise date is concerned than their European equivalents (that is to say options with the same parameters, except of course for the exercise style), the value of American options is always equal to or greater than the value of European options. Only American call options on non-dividend paying stocks have the same value as their European equivalents.

- An option involves the holder's right, but not an obligation, to buy or sell a specified quantity of an underlying asset at a specified price in the future. While the holder of an option may decide whether or not to exercise it, the option writer is legally bound either to sell or to buy the underlying, depending on the type of the option, when the holder wishes to exercise the option.
- According to the right given to the option holder, we distinguish two types of options: call options and put options.
- The long pays to the short a certain amount called the option premium.
- The stock option payoff depends on the difference between exercise price and stock price.
- When calculation option profit we have to take into account both option payoff and option premium.
- If the exercise of an option produces a positive payoff, the option is in-the-money. If the exercise of an option produces a negative payoff, the option is out-of-the-money. If the exercise of an option produces a payoff equal to 0, the option is at-the-money.
- The holder of an American option can exercise the option at any moment from taking the long position until expiration. European option can be only exercised at expiration.
- The value of an American option is always equal to or greater than the value of an equivalent European option.