Chapter 9 Options

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Chapter 9 - Options

• What is an option contract?
• What are calls and puts?
• How are options traded?
• How can we determine the value of options?
• What is put-call parity?
• Why might we use options for investing?

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What is an option contract?

• Options give the right, not the obligation, to
  buy or sell an asset at a fixed price before
  maturity
• Call option is right to buy
• Put option is right to sell
• Key distinction between forward/future
  derivatives and options is performance
• Only option sellers (writers) are required to
  perform under the contract (if exercised)
• After paying the premium, option owners have no
  duties under the contract

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Some Terminology

• The exercise or strike price is the agreed on
  fixed price at which the option holder can buy or
  sell the underlying asset
• Exercising the option means to force the seller
  to perform at the exercise price
• Expiration date is the date at which the option
  ceases to exist
• American options allow holder to exercise at any
  point until expiration
• European option only allows holder to exercise on
  the expiration date

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Option quotes (p.314)

• The premium is the amount paid for an option (the
  price)
• The owner pays the premium to own the right to
  buy an asset (if a call) or sell an asset (if a
  put)
• The seller receives the premium but must perform
  if the option holder exercises

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Moneyness

• Intrinsic value is the maximum of zero and the
  value of the option if exercised immediately
  (from the owners point of view)
• If the greater than zero, the option is called
  in-the-money
• It is better to exercise than to let expire
• If the asset value is near the exercise price, it
  is called near-the-money or at-the-money
• If the exercise price is unfavorable to the
  option owner, it is out-of-the-money
• Also, deep-in-the-money and deep-out-of-the-money

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Options markets

• Contracts are standardized
• One stock option contract is for 100 shares of
  stock
• Other assets are defined by the contract
• Chicago Board Options Exchange (CBOE) is biggest
• As with futures, you must post a margin

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Option Value Buying Calls

• At maturity
• If XgtS, option expires worthless
• If SgtX, option value is S-X
• Owners of call options want the price of the
  underlying stock to increase
• See p. 317 for an example

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Option Value Selling Calls

• If XgtS, option expires worthless
• Seller earns premium paid
• If SgtX, option value is S-X
• seller must provide stock at price X

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Option Values Buying Puts

• At maturity
• If SgtX, option expires worthless
• If XgtS, option value is X-S
• Owners of put options want the price of the
  underlying stock to decrease
• See p.325

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Option Value Selling Puts

• If SgtX, option expires worthless
• Seller earns premium paid
• If SltX, option value is X-S
• Seller must buy stock at price X

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Option portfolio strategies Combining options

• Various strategies use combinations of options
  and the underlying stock
• Some of the strategies
• Protective puts
• Spreads
• Straddles
• Collars

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Protective Put Hedging Stock Values

• Owning the underlying stock and owning a put
  option
• When the stock price drops below the exercise
  price, the put hedges further losses
• The portfolio is protected
• Has a minimum value equal to the strike price

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Spreads

• A spread is buying and selling options of the
  same type (calls or puts) with different exercise
  prices or different expiration dates
• A time spread uses the same exercise price but
  buys and sells options with different expirations
• A price spread uses the same expiration date but
  buys/sells options with different strike prices

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Straddles

• A long straddle is buying a call and a put on the
  same stock at the same exercise price and the
  same expiration
• Why would you do this?
• What is a short straddle?

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Collars

• Collars protect the value of the portfolio by
  providing upper and lower bounds on its value
• We saw protective puts provide a lower bound for
  portfolio value
• The strike price is below the current value of
  the stock
• To fund the purchase of the put, we sell a
  covered call
• The exercise price is above the current stock
  price
• See p. 329

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Index options

• One specific type of option that is popular is an
  option on a stock index such as the SP 500
• Instead of requiring the seller to deliver the
  entire index, the option is cash settled so that
  one contract on the SP 500 is defined as 100
  times the value of the index
• There are options written on many markets
• Major market index (MMI), Utilities index,
  semi-conductor, etc.

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Interest rate options

• Options on Treasury notes and/or bonds
• Note that a call on long-term interest rates
  provides similar protection as a put on bonds

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Pricing Options

• Suppose we form two portfolios
• Stock plus put
• Call plus 45.45
• Interest rate is 10, options are European and
  expire in one year
• Consider two cases

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Put-Call Parity

• Note that at maturity, these portfolios are
  equivalent regardless of value of S
• Since the options are European, these portfolios
  must always have the same value
• If not, there is an arbitrage opportunity

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Example

• Suppose that a one-year European call option has
  an exercise price of 50 and has a value of 5
• The underlying stock price is 45 and the
  one-year risk free rate is 10
• If the value of a put option with an exercise
  price of 50 sells for 4, is there an arbitrage
  opportunity?

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Black-Scholes Option Pricing Model

• PcPrice of a call option
• Xexercise price
• texpiration in years
• sigmavolatility of stock (standard deviation of
  return)

• rrisk free rate over same period
• N()cumulative density of the standard normal
  distribution
• p.372-3

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Review Chapter 9

• Definitions calls and puts
• Obligations of buyer / seller
• Payoff diagrams
• Portfolios of calls and puts
• Put-call parity and Black-Scholes