Basics of Stock Options

1
Basics of Stock Options

• Timothy R. Mayes, Ph.D.FIN 3600 Chapter 15

2
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 1624-1636.
• In the U.S., options were traded as early as the
  1800s and were available only as customized OTC
  products until the CBOE opened on April 26, 1973.

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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.

4
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

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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.

6
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.

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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.

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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!

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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.

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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. Youd be better
  off to sell the option, collect the premium, and
  then take your position in the underlying
  security.

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Profits from Buying a Call
12
Selling a Call
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Profits from Buying a Put
14
Selling a Put
15
Combination Strategies

• We can construct strategies consisting of
  multiple options to achieve results that arent
  otherwise possible, and to create cash flows that
  mimic other securities
• Some examples
• Buy Write
• Straddle
• Synthetic Securities

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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

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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
  doesnt move much in either direction
• This straddle consists of buying (or selling)
  both a put and call at the money

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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

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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).

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Put-Call Parity Example

• Assume that we find the following conditions
• S 100 X 100
• r 10 t 1 year
• C 16.73 P ?

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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

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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

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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

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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

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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

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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

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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.

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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

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Variables Affect on Option Prices

• Call Options
• Direct
• Inverse
• Direct
• Direct
• Direct

• Put Options
• Inverse
• Direct
• Direct
• Inverse
• Direct

• Variable
• Stock Price
• Strike Price
• Volatility
• Interest Rate
• Time

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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.

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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.

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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.

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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.

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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.

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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.

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The Black-Scholes Call Valuation Model

• At the top (right) is the Black-Scholes valuation
  model for calls. Below are the definitions of d1
  and d2.
• Note that S is the stock price, X is the strike
  price, s is the standard deviation, t is the time
  to expiration, and r is the risk-free rate.

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B-S Call Valuation Example

• Assume a call with the following variables
• S 100 X 100
• r 0.05 s 0.10
• t 90 days 0.25 years

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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(-d1) 1 - N(d1)

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B-S Put Valuation Example

• Assume a put with the following variables
• S 100 X 100
• r 0.05 s 0.10
• t 90 days 0.25 years