Basics of Stock Options Timothy R. Mayes, Ph.D. FIN 3600: Chapter 15

Introduction Options are very old instruments, going back, perhaps, to the time of Thales the Milesian (c. 624 BC to c. 547 BC). Thales, according to Aristotle, purchased call options on the entire autumn olive harvest (or the use of the olive presses) and made a fortune. Joseph de la Vega (in “Confusión de Confusiones,” 1688, 104 years before the NYSE was founded under the buttonwood tree) also wrote about how options were dominating trading on the Amsterdam stock exchange. Dubofsky reports that options existed in ancient Greece and Rome, and that options were used during the tulipmania in Holland from In the U.S., options were traded as early as the 1800’s and were available only as customized OTC products until the CBOE opened on April 26, 1973.

What is an Option? A call option is a financial instrument that gives the buyer the right, but not the obligation, to purchase the underlying asset at a pre- specified price on or before a specified date A put option is a financial instrument that gives the buyer the right, but not the obligation, to sell the underlying asset at a pre-specified price on or before a specified date A call option is like a rain check. Suppose you spot an ad in the newspaper for an item you really want. By the time you get to the store, the item is sold out. However, the manager offers you a rain check to buy the product at the sale price when it is back in stock. You now hold a call option on the product with the strike price equal to the sale price and an intrinsic value equal to the difference between the regular and sale prices. Note that you do not have to use the rain check. You do so only at your own option. In fact, if the price of the product is lowered further before you return, you would let the rain check expire and buy the item at the lower price.

Options are Contracts The option contract specifies:  The underlying instrument  The quantity to be delivered  The price at which delivery occurs  The date that the contract expires Three parties to each contract  The Buyer  The Writer (seller)  The Clearinghouse

The Option Buyer The purchaser of an option contract is buying the right to exercise the option against the seller. The timing of the exercise privilege depends on the type of option:  American-style options can be exercised any time before expiration  European-style options may only be exercised during a short window before expiration Purchasing this right conveys no obligations, the buyer can let the option expire if they so desire. The price paid for this right is the option premium. Note that the worst that can happen to an option buyer is that she loses 100% of the premium.

The Option Writer The writer of an option contract is accepting the obligation to have the option exercised against her, and receiving the premium in return. If the option is exercised, the writer must:  If it is a call, sell the stock to the option buyer at the exercise price (which will be lower than the market price of the stock).  If it is a put, buy the stock from the put buyer at the exercise price (which will be higher than the market price of the stock). Note that the option writer can potentially lose far more than the option premium received. In some cases the potential loss is (theoretically) unlimited. Writing and option contract is not the same thing as selling an option. Selling implies the liquidation of a long position, whereas the writer is a party to the contract.

The Role of the Clearinghouse The clearinghouse (the Options Clearing Corporation) exists to minimize counter-party risk. The clearinghouse is a buyer to each seller, and a seller to each buyer. Because the clearinghouse is well diversified and capitalized, the other parties to the contract do not have to worry about default. Additionally, since it takes the opposite side of every transaction, it has no net risk (other than the small risk of default on a trade). Also handles assignment of exercise notices.

Examples of Options Direct options are traded on:  Stocks, bonds, futures, currencies, etc. There are options embedded in:  Convertible bonds  Mortgages  Insurance contracts  Most corporate capital budgeting projects  etc. Even stocks are options!

Option Terminology Strike (Exercise) Price - this is the price at which the underlying security can be bought or sold. Premium - the price which is paid for the option. For equity options this is the price per share. The total cost is the premium times the number of shares (usually 100). Expiration Date – This is the date by which the option must be exercised. For stock options, this is usually the Saturday following the third Friday of the month. In practice, this means the third Friday. Moneyness – This describes whether the option currently has an intrinsic value above 0 or not:  In-the-Money – for a call this is when the stock price exceeds the strike price, for a put this is when the stock price is below the strike price.  Out-of-the-Money – for a call this is when the stock price is below the strike price, for a put this is when the stock price exceeds the strike price. American-style - options which can be exercised before expiration. European-style - options which cannot be exercised before expiration.

The Intrinsic Value of Options The intrinsic value of an option is the profit (not net profit!) that would be received if the option were exercised immediately:  For call options: IV = max(0, S - X)  For put options: IV = max(0, X - S) At expiration, the value of an option is its intrinsic value. Before expiration, the market value of an option is the sum of the intrinsic value and the time value. Since options can always be sold (not necessarily exercised) before expiration, it is almost never optimal to exercise them early. If you did so, you would lose the time value. You’d be better off to sell the option, collect the premium, and then take your position in the underlying security.

Profits from Buying a Call

Selling a Call

Profits from Buying a Put

Selling a Put

Combination Strategies We can construct strategies consisting of multiple options to achieve results that aren’t otherwise possible, and to create cash flows that mimic other securities Some examples:  Buy Write  Straddle  Synthetic Securities

The Buy-Write Strategy This strategy is more conservative than simply owning the stock It can be used to generate extra income from stock investments In this strategy we buy the stock and write a call

The Straddle If we buy a straddle, we profit if the stock moves a lot in either direction If we sell a straddle, we profit if the stock doesn’t move much in either direction This straddle consists of buying (or selling) both a put and call at the money

Synthetic Securities With appropriate combinations of the stock and options, we can create a set of cash flows that are identical to puts, calls, or the stock We can create synthetic:  Long Stock — Buy Call, Sell Put  Long Call — Buy Put, Buy Stock  Long Put — Buy Call, Sell Stock  Short Stock — Sell Call, Buy Put  Short Call — Sell Put, Sell Stock  Short Put — Sell Call, Buy Stock The reasons that this works requires knowledge of Put- Call Parity

Put-Call Parity Put-Call parity defines the relationship between put prices and call prices that must exist to avoid possible arbitrage profits: In other words, a put must sell for the same price as a long call, short stock and lending the present value of the strike price (why?). By manipulating this equation, we can see how to create synthetic securities (in the above form it shows how to create a synthetic put option).

Put-Call Parity Example Assume that we find the following conditions:  S = 100X = 100  r = 10%t = 1 year  C = 16.73P = ?

Synthetic Long Stock Position We can create a synthetic long position in the stock by buying a call, selling a put, and lending the strike price at the risk-free rate until expiration

Synthetic Long Call Position We can create a synthetic long position in a call by buying a put, buying the stock, and borrowing the strike price at the risk-free rate until expiration

Synthetic Long Put Position We can create a synthetic long position in a put by buying a call, selling the stock, and lending the strike price at the risk-free rate until expiration

Synthetic Short Stock Position We can create a synthetic short position in the stock by selling a call, buying a put, and borrowing the strike price at the risk-free rate until expiration

Synthetic Short Call Position We can create a synthetic short position in a call by selling a put, selling the stock, and lending the strike price at the risk-free rate until expiration

Synthetic Short Put Position We can create a synthetic short position in a put by selling a call, buying the stock, and borrowing the strike price at the risk-free rate until expiration

Option Valuation The value of an option is the present value of its intrinsic value at expiration. Unfortunately, there is no way to know this intrinsic value in advance. The most famous (and first successful) option pricing model, the Black-Scholes OPM, was derived by eliminating all possibilities of arbitrage. Note that the Black-Scholes models work only for European-style options.

Option Valuation Variables There are five variables in the Black-Scholes OPM (in order of importance):  Price of underlying security  Strike price  Annual volatility (standard deviation)  Time to expiration  Risk-free interest rate

Variables’ Affect on Option Prices Call Options  Direct  Inverse  Direct Put Options  Inverse  Direct  Inverse  Direct Variable –Stock Price –Strike Price –Volatility –Interest Rate –Time

Option Valuation Variables: Underlying Price The current price of the underlying security is the most important variable. For a call option, the higher the price of the underlying security, the higher the value of the call. For a put option, the lower the price of the underlying security, the higher the value of the put.

Option Valuation Variables: Strike Price The strike (exercise) price is fixed for the life of the option, but every underlying security has several strikes for each expiration month For a call, the higher the strike price, the lower the value of the call. For a put, the higher the strike price, the higher the value of the put.

Option Valuation Variables: Volatility Volatility is measured as the annualized standard deviation of the returns on the underlying security. All options increase in value as volatility increases. This is due to the fact that options with higher volatility have a greater chance of expiring in- the-money.

Option Valuation Variables: Time to Expiration The time to expiration is measured as the fraction of a year. As with volatility, longer times to expiration increase the value of all options. This is because there is a greater chance that the option will expire in-the-money with a longer time to expiration.

Option Valuation Variables: Risk-free Rate The risk-free rate of interest is the least important of the variables. It is used to discount the strike price, but because the time to expiration is usually less than 9 months (with the exception of LEAPs), and interest rates are usually fairly low, the discount is small and has only a tiny effect on the value of the option. The risk-free rate, when it increases, effectively decreases the strike price. Therefore, when interest rates rise, call options increase in value and put options decrease in value.

Note The following few slides on the Black-Scholes model will not be tested. I consider the use of these models to be beyond the scope of this course. I am including this information only for those interested.

The Black-Scholes Call Valuation Model At the top (right) is the Black-Scholes valuation model for calls. Below are the definitions of d 1 and d 2. Note that S is the stock price, X is the strike price,  is the standard deviation, t is the time to expiration, and r is the risk-free rate.

B-S Call Valuation Example Assume a call with the following variables:  S = 100X = 100  r = 0.05  = 0.10  t = 90 days = 0.25 years

The Black-Scholes Put Valuation Model At right is the Black- Scholes put valuation model. The variables are all the same as with the call valuation model. Note: N(-d 1 ) = 1 - N(d 1 )

B-S Put Valuation Example Assume a put with the following variables:  S = 100X = 100  r = 0.05  = 0.10  t = 90 days = 0.25 years