Stock Options

A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock. Is a ‘contingent claim’ – cash flows only if certain event happens. There are two basic option types.  Call options are options to buy the underlying asset.  Put options are options to sell an underlying asset. Listed Option contracts are standardized to facilitate trading and price reporting.  Listed stock options give the option holder the right to buy or sell 100 shares of stock.

Option contracts are legal agreements between two parties—the buyer of the option, and the seller of the option. The minimum terms stipulated by stock option contracts are:  The identity of the underlying stock.  The strike price, or exercise price.  The option contract size.  The option expiration date, or option maturity.  The option exercise style (American or European).  The delivery, or settlement, procedure. Stock options trade at organized options exchanges, such as the CBOE, as well as over-the-counter (OTC) options markets.

A list of available option contracts and their prices for a particular security is known as an option chain. Option chains are available online through many sources, including the CBOE ( and Yahoo! ( Stock option ticker symbols include:  Letters to identify the underlying stock.  A Letter to identify the expiration month as well as whether the option is a call or a put. (A through L for calls; M through X for puts).  A Letter to identify the strike price (a bit more complicated—see Yahoo or Stock-Trak for tables to explain this letter.)

The Options Clearing Corporation (OCC) is a private agency that guarantees that the terms of an option contract will be fulfilled if the option is exercised. The OCC issues and clears all option contracts trading on U.S. exchanges. Note that the exchanges and the OCC are all subject to regulation by the Securities and Exchange Commission (SEC). Visit the OCC at:

A basic question asked by investors is: “Why buy stock options instead of shares in the underlying stock?” To answer this question, we compare the possible outcomes from these two investment strategies:  Buy the underlying stock  Buy options on the underlying stock

Suppose IBM is selling for $90 per share and call options with a strike price of $90 are $5 per share. Investment for 100 shares:  IBM Shares: $9,000  One listed call option contract: $500 Suppose further that the option expires in three months. Finally, let’s say that in three months, the price of IBM shares will either be: $100, $80, or $90.

Let’s calculate the dollar and percentage return given each of the prices for IBM stock: Buy 100 IBM Shares ($9000 Investment): Buy One Call Option ($500 Investment): Dollar Profit: Percentage Return: Dollar Profit: Percentage Return: Case 1: $100$1, %$500100% Case 2: $80-$1, %-$ % Case 3: $90$00%-$ %

Whether one strategy is preferred over another is a matter for each individual investor to decide.  That is, in some instances investing in the underlying stock will be better. In other instances, investing in the option will be better.  Each investor must weight the risk and return trade-off offered by the strategies. It is important to see that call options offer an alternative means of formulating investment strategies.  For 100 shares, the dollar loss potential with call options is lower.  For 100 shares, the dollar gain potential with call options is lower.  The positive percentage return with call options is higher.  The negative percentage return with call options is lower.

“In-the-money” option: An option that would yield a positive payoff if exercised “Out-of-the-money” option: An option that would NOT yield a positive payoff if exercised Use the relationship between S (the stock price) and K (the strike price): Note for a given strike price, only the call or the put can be “in-the-money.” In-the-MoneyOut-of-the-Money Call OptionS > KS ≤ K Put OptionS < KS ≥ K 15-13

The act of selling an option is referred to as option writing. The seller of an option contract is called the writer.  The Writer of a call option contract is obligated to sell the underlying asset to the call option holder.  The call option holder has the right to exercise the call option (i.e., buy the underlying asset at the strike price).  The Writer of a put option contract is obligated to buy the underlying asset from the put option holder.  The put option holder has the right to exercise the put option (i.e., sell the underlying asset at the strike price). Because option writing obligates the option writer, the option writer receives the price of the option today from the option buyer.

Option holders have the right to exercise their option.  If this right is only available at the option expiration date, the option is said to have European-style exercise.  If this right is available at any time up to and including the option expiration date, the option is said to have American-Style exercise. Exercise style is not linked to where the option trades. European-style and American-Style options trade in the U.S., as well as on other option exchanges throughout the world. Very Important: Option holders also have the right to sell their option at any time (terminate, reverse trade, close-out). That is, they do not have to exercise the option if they no longer want it.

Option investment strategies involve initial and terminal cash flows.  Initial cash flow: option price (often called the option premium).  Terminal cash flow: the value of an option at expiration (often called the option payoff. The terminal cash flow can be realized by the option holder by exercising the option. Option Profits = Terminal cash flow − Initial cash flow

Protective put - Strategy of buying a put option on a stock already owned. This protects against a decline in value (i.e., it is "insurance") Covered call - Strategy of selling a call option on stock already owned. This exchanges “upside” potential for current income. Straddle - Buying or selling a call and a put with the same exercise price. Buying is a long straddle; selling is a short straddle.

There are many option trading strategies available to option traders. For ideas on option trading strategies, see:  

Arbitrage:  No possibility of a loss  A potential for a gain  No cash outlay In finance, arbitrage is not allowed to persist.  “Absence of Arbitrage” = “No Free Lunch”  The “Absence of Arbitrage” rule is often used in finance to calculate option prices. Think about what would happen if arbitrage were allowed to persist. (Easy money for everybody)

Call option price must be less than the stock price. Otherwise, arbitrage will be possible. How?  Suppose you see a call option selling for $65, and the underlying stock is selling for $60.  The Arbitrage: sell the call, and buy the stock.  Worst case? The option is exercised and you pocket $5.  Best case? The stock sells for less than $65 at option expiration, and you keep all of the $65.  Zero cash outlay today, no possibility of loss, and potential for gain.

Put option price must be less than the strike price. Otherwise, arbitrage will be possible. How? Suppose there is a put option with a strike price of $50 and this put is selling for $60. The Arbitrage: Sell the put, and invest the $60 in the bank. (Note you have zero cash outlay).  Worse case? Stock price goes to zero.  You must pay $50 for the stock (because you were the put writer).  But, you have $60 from the sale of the put (plus interest).  Best case? Stock price is at least $50 at expiration.  The put expires with zero value (and you are off the hook).  You keep the entire $60, plus interest.

Option prices must be at least zero.  By definition, an option can simply be discarded. To derive a meaningful lower bound, we need to introduce a new term: intrinsic value. The intrinsic value of an option is the payoff that an option holder receives if the underlying stock price does not change from its current value.

That is, if S is the current stock price, and K is the strike price of the option: Call option intrinsic value = max [0, S – K ]  In words: The call option intrinsic value is the maximum of zero or the stock price minus the strike price. Put option intrinsic value = max [0, K – S ]  In words: The put option intrinsic value is the maximum of zero or the strike price minus the stock price.

“In the Money” options have a positive intrinsic value.  For calls, the strike price is less than the stock price.  For puts, the strike price is greater than the stock price. “Out of the Money” options have a zero intrinsic value.  For calls, the strike price is greater than the stock price.  For puts, the strike price is less than the stock price. “At the Money” options is a term used for options when the stock price and the strike price are about the same.

Call options with American-style exercise must sell for at least their intrinsic value. (Otherwise, there is arbitrage) Suppose: S = $60; C = $5; K = $50. Instant Arbitrage. How?  Borrow and buy the call for $5.  Immediately exercise the call, and buy the stock for $50.  In the next instant, sell the stock at the market price of $60. You made a profit with zero cash outlay.

Put options with American-style exercise must sell for at least their intrinsic value. (Otherwise, there is arbitrage) Suppose: S = $40; P = $5; K = $50. Instant Arbitrage. How?  Buy the put for $5.  Buy the stock for $40.  Immediately exercise the put, and sell the stock for $50. You made a profit with zero cash outlay.

To prevent arbitrage, option prices cannot be less than intrinsic value.  Otherwise, arbitrage will be possible.  Note that immediate exercise was needed.  Therefore, options needed to have American-style exercise. Using equations: Call option price  max [0, S – K ] Put option price  max [0, K – S ]

Essentially, an employee stock option is a call option that a firm grants (i.e., gives) to employees.  ESOs allow employees to buy shares of stock in the company.  Giving stock options to employees is a widespread practice. Because you might soon be an ESO holder, an understanding of ESOs is important.

ESOs have features that ordinary call options do not. The Details vary by firm, but:  The life of the ESO is generally 10 years.  ESOs cannot be sold.  ESOs have a “vesting” period of about 3 years.  Employees cannot exercise their ESOs until they have worked for the company for this vesting period.  If an employee leaves the company before the ESOs are “vested," the employees lose the ESOs.  If an employee stays for the vesting period, the ESOs can be exercised any time over the remaining life of the ESO.

Owners of a corporation (i.e., the stockholders) have a basic problem. How do they get their employees to make decisions that help the stock price increase? ESOs are a powerful motivator, because payoffs to options can be large.  High stock prices: ESO holders gain and shareholders gain.  All good??? GM, AIG, Wachovia ESO’s? ESOs have no upfront costs to the company.  ESOs can be viewed as a substitute for ordinary wages.  Therefore, ESOs are helpful in recruiting employees.

ESOs are generally issued exactly “at the money.”  Intrinsic value is zero.  There is no value from immediate exercise.  But, the ESO is still valuable. If the stock price falls after the ESO is granted, the ESO is said to be “underwater.” Occasionally, companies will lower the strike prices of ESOs that are “underwater.”  This practice is called “restriking” or “repricing.”  This practice is controversial.

PRO: Once an ESO is “underwater,” it loses its ability to motivate employees.  Employees realize that there is only a small chance for a payoff from their ESOs.  Employees may leave for other companies where they get “fresh” options. CON: Lowering a strike price is a reward for failing.  After all, decisions by employees made the stock price fall.  If employees know that ESOs will be repriced, the ESOs loose their ability to motivate employees.

Most companies award ESO on a regular basis.  Quarterly  Annually Therefore, employees will always have some “at the money” options. Regular grants of ESOs means that employees always have some “unvested” ESOs—giving them the added incentive to remain with the company.

Put-Call Parity is perhaps the most fundamental relationship in option pricing. Put-Call Parity is generally used for options with European- style exercise. Put-Call Parity states: the difference between the call price and the put price equals the difference between the stock price and the discounted strike price

In the formula:  C is the call option price today  S is the stock price today  r is the risk-free interest rate  P is the put option price today  K is the strike price of the put and the call  T is the time remaining until option expiration Note: this formula can be rearranged:

If two securities have the same risk-less pay-off in the future, they must sell for the same price today. Today, suppose an investor forms the following portfolio:  Buys 100 shares of Microsoft stock  Writes one Microsoft call option contract  Buys one Microsoft put option contract. At option expiration, this portfolio will be worth:

Notice that the portfolio is always worth $K at expiration. That is, it is riskless. Therefore, the value of this portfolio today is $K/(1+r) T. That is, to prevent arbitrage: today’s cost of buying 100 shares and buying one put (net of the proceeds of writing one call), should equal the price of a risk-less security with a face value of $K, and a maturity of T. Fun fact: If S = K (and if r > 0), then C > P.

A stock index option is an option on a stock market index. The most popular stock index options are options on the S&P 100, S&P 500, and Dow Jones Industrial Average. Because the actual delivery of all stocks comprising a stock index is impractical, stock index options have a cash settlement procedure.

For information on options ticker symbols, see:   For more information on options education:  To learn more about options, see:    Exchanges that trade index options include:   

Options on Common Stocks  Option Basics  Option Price Quotes The Options Clearing Corporation Why Options? Option “Moneyness” Option Payoffs and Profits  Option Writing  Option Payoffs  Payoff Diagrams  Option Profits Option Strategies  The Protective Put Strategy  The Covered Call Strategy  Straddles

Option Prices, Intrinsic Values, and Arbitrage  The Upper Bound for a Call Option Price  The Upper Bound for a Put Option Price  The Lower Bounds on Option Prices Employee Stock Options (ESOs)  Features  Repricing Put-Call Parity Stock Index Options  Features and Settlement  Index Option Price Quotes Homework: 3, 4, 5, 8, 9, 10, 21