Option Valuation and Strategies

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Chapter 20

• Option Valuation and Strategies

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Option Valuation and Strategies

• Option valuation
• determines what an option is worth.
• Option strategy
• means to use options as speculative or
  risk-management tools.

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Option Value

• What determines line DEs position?

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Black / Scholes Option Valuation Model

• Value of an option depends on
• price of the stock,
• strike price,
• time to the option's expiration,
• variability of the stocks return, and
• rate of interest.

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Black / Scholes Model in Equation Form

• V0 Ps x F(d1) - Pe/erT x F(d2)

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Black / Scholes Option Valuation Model

• Except for the variability of a stock's return,
  all the variables are observable.
• The historical standard deviation of a stock's
  return is often used to measure the current
  variability of a stock's return.

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The Anticipated Relationships (for calls)

• Higher stock price - higher valuation
• Lower strike price - higher valuation
• Longer term - higher valuation
• Increased variability - higher valuation
• Higher interest rate - higher valuation

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Variability

• Generally increased variability (increased risk)
  is associated with lower security valuations,BUT
• More variability increases the likelihood the
  stock's price may rise, and
• a higher stock price increases a call option's
  valuation.

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Interest Rates

• Generally higher interest rates are associated
  with lower security valuations,BUT
• Higher interest rates reduce the present value of
  the call option's strike price. This reduction
  increases the option's valuation.

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Black / Scholes

• Black/Scholes uses a normal probability
  distribution.
• As the probability of an option being exercised
  rises, so does the valuation.

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Black / Scholes
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Black / Scholes
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Expensing Options

• Employee options as a cost
• Expensing options reduces earnings.
• Usage of Black-Scholes to expense options

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Expensing Options

• May be required by Financial Accounting Standards
  Board (FASB)
• Differences in impact on earnings

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Put-Call Parity

• The values of stocks, options, and debt
  instruments are interrelated.
• Put-call parity verifies the interrelationships.

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Price of Stock

• The price of a stock must equal
• price of the call, plus
• present value of the strike price, minus
• price of the put.

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Put-Call Parity Equation

• Ps Pp Pc Pe/(1i)
• If the two sides are not equal
• an opportunity for a risk-free arbitrage exists.
• If price of one of the four components changes,
  the price change is transferred to the remaining
  three.

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Hedge Ratio

• Determines the number of options necessary to
  offset a price movement in a stock
• Is derived from the Black/Scholes valuation model

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Covered Put Strategy

• Short the stock and sell the put.
• The opposite of the "covered call"
• buy the stock and sell the call
• Takes advantage of the declining time premium
  paid for the put.

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Covered Put Strategy

• Limited profit but unlimited potential loss

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Protective Call Strategy

• Short the stock and buy the call
• The opposite of the "protective put"
• buy the stock and the put
• Protects from the price of the stock rising.

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Profit / Loss Profile for the Protective Call
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Buying The Straddle

• Buy a call and a put with the same strike price.
• Takes advantage of
• major movements in the price of the stock, and
• uncertainty concerning the direction of change in
  a stocks price.

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Buying The Straddle

• Buying a straddle generates profits only if the
  price of the stock moves sufficiently to cover
  the cost of the two options purchased.

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Buying The Straddle
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Selling The Straddle

• Writing a straddle is selling a call and a put
  with the same strike price.
• Is profitable if the price of the stock is stable.

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Selling The Straddle
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The Bull Spread

• Requires two options with different strike prices
  and the same expiration date
• To construct a bull spread using calls
• buy the option with the lower strike price, and
• sell the option with the higher strike price.

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The Bear Spread

• Requires two options with different strike prices
  and the same expiration date
• To construct a bear spread using calls
• sell the option with the lower strike price, and
• buy the option with the higher strike price.

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Bull and Bear Spreads

• Bull and bear spreads have limited potential
  profits.
• Bull and bear spreads have limited potential for
  loss.

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Bull and Bear Spreads

• Profits and losses on bull and bear spreads are
  mirror images

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Bull and Bear Spreads
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The Butterfly Spread

• Requires three options with
• different strike prices, and
• the same expiration date.
• Buy one each of the options with the extreme
  strike prices and sell two of the options with
  the middle strike price.

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The Butterfly Spread

• The process may be reversed Sell one each of the
  options with the extreme strike prices and buy
  two of the options with the middle strike price.

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The Butterfly Spread
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The Butterfly Spread

• Profits and losses from the two butterfly spreads
  are mirror images.
• The butterfly spread has limited potential
  profits, but limited potential for loss.

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Collars

• Used when an investor owns a stock and desires to
  lock in a large gain.
• Sell a call at one strike price and
• Buy a put with a lower strike price

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Collars

• The cash inflow from the sale offsets the cost of
  the put.
• The put protects the investor from a decline in
  the stock price.

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Buying Call and Treasury Bill

• Alternative to the protective put
• Limits loss
• Retains potential for gain if stock price rises