Options: Chapter 11

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Options Chapter 11

• Options give the buyer the right but not the
  obligation to buy or sell something in the
  future. The seller of an option has the
  obligation to either sell or buy, as requested.
• Call Option right to buy
• Put Option right to sell

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• European Style exercisable at maturity.
• American Style exercisable anytime up to
  maturity.
• History of Options
• 1600s, sold during the Dutch tulip bulb mania
• Traded in London during the 1700s
• Prior to 1973 traded over the counter
• Exchange traded options

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Kinds of Options

• Options on Individual Stocks
• Options on Foreign Currency
• Options on Stock Indexes
• Options of T-bonds T-bills
• Options on futures contracts

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• Maturity Options expire on the Saturday,
  following the 3rd Friday in their stated month.
• Option Terms
• Mkt. Price of Stock PM
• Strike Price PS is the price that the option
  can be exercised at. Example an option to buy
  at 40.
• Option Price PO is the price paid for the
  option itself.

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• Intrinsic (Formula) Value of an Option
• Call Option FV Mkt. Price Strike Price
• Put Option FV Strike Price Mkt. Price
• This the value if the option were exercised
  today.
• If FV gt 0, then option is in the money
• If FV lt 0, then option is out of the money
• Note from the quotes that
• PO gt FV up to expiration
• Most options will not be exercised early because
  to do so would result in a loss of value.

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What Determines the Value of a Call Option?

• Price of the Stock The higher the stock price
  the more valuable the option.
• The Strike Price The higher the strike price
  the less valuable the option.
• Time to Expiration The greater the time to
  expiration the more valuable the option.
• Volatility Higher volatility means a more
  valuable option.
• Interest Rate The higher are interest rates the
  more valuable the option.
• Cash Dividend The higher the dividend the lower
  the value of the call option.

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Profit Diagrams
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Uses of Options

• I. Who Should Consider Using Protective Puts?
• An investor who currently holds a stock, but does
  not want to sell because he believes the stock
  may rise in value. This investor would like to be
  able to participate in the rise without risking
  all of his profit (if any).
• An investor who is considering purchasing a stock
  but is concerned with downside risk.
• A protective put is buying a put on an existing
  stock holding.

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• II. Who Should Consider Covered Calls?1. An
  investor who is neutral to moderately bullish on
  some equities in his portfolio.2. An investor
  who is willing to limit his upside potential in
  exchange for some downside protection.3. An
  investor who would like to be paid for assuming
  the obligation of selling a particular stock at a
  specified price. Covered call writing is either
  the simultaneous purchase of stock and the sale
  of a call option or the sale of a call option
  against a stock currently held by an investor.
  Generally, one call option is sold for every 100
  shares of stock.

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• III. Who Should Consider Selling Cash-Secured
  Puts?
• An investor who would like to acquire a position
  in a particular security, but is willing to wait
  for it to trade at his desired price.
• This strategy is used by large portfolio managers
  as well as individual investors because it "pays"
  them for assuming the obligation to buy a
  particular stock. In other words, certain
  investors who are considering buying a stock (or
  more of a stock they already own) may want to
  sell cash-secured puts.

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• IV. Buy Index Straddles in Anticipation of a
  Major Market Move
• A variation combining the buy call and buy put
  strategies (discussed in the previous two
  examples) is called a "straddle" - it involves
  holding both a long call and a long put position
  with the same strike price and time to
  expiration. You might use this strategy if you
  believe that the market is poised for a major
  move but are unsure of the direction.

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• V. Who Should Consider Buying Calls?1. An
  investor who is very bullish on a particular
  stock.2. An investor who would like to take
  advantage of what purchasing options offers
  leverage with a limited dollar risk.3. An
  investor who anticipates a rise in the value of a
  particular stock but does not want to commit all
  of the capital needed to purchase the stock.

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• Examples of Using Financial Options
• Mr. Lloyd, a commercial loan officer, wants to
  make a commitment to provide a fixed-rate loan
  for 1 million in 3 months for a fixed rate
  today.
• Lloyd could by puts on t-bond futures contracts
  due in three months.
• If rates move up, option values rise.
• If rates move down, options expire worthless. He
  loses what he paid for the option.

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• Examples of Using Financial Options
• Ms. Smith, manages a 70 million stock portfolio
  and fears the market may drop.
• Smith could by puts on SP Stock Index future
  contracts due in three months.
• If stocks fall, option values rise.
• If stock rise, options expire worthless. She
  loses what he paid for the option.

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Problem 1

• Suppose Mr. Lloyd hedges his 1 million loan
  commitment with options on T-bond futures.
• T-Bond futures are for 100,000 each. The
  current price is 97 12/32.
• An at-the-money, 3-month put option costs 1,000.
• Show what happens in each case
• Rates fall, t-bond futures rise to 98
• Rates rise, t-bond futures rise to 96 25/32
• Rates rise, t-bond futures fall to 95

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• T-bond futures rise to 98
• Sell 10 100,000 97.375 973,750
• Buy 10 100,000 98.000 980,000
• Profit (6,250)
• Option (10,000)
• Gain/Loss (10,000)
• T-bond futures fall to 96 25/32
• Sell 10 100,000 97.375 973,750
• Buy 10 100,000 96.781 967,813
• Profit 5,938
• Option
  (10,000)
• Gain/Loss (4,063)

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• T-bond futures fall to 95
• Sell 10 100,000 97.375 973,750
• Buy 10 100,000 95.000 950,000
• Profit 23,750
• Option (10,000)
• Gain/Loss 13,750
• Compare these results to hedging with futures

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Problem 2

• Suppose Ms. Smith hedges her 70 million stock
  portfolio (Beta 1.2) with 240 options on SP
  500 futures contracts.
• Suppose the SP Index is at 1,400. An SP 500
  Index futures contract costs 2501,400
• An at-the-money, 3-month option on an SP futures
  contract costs 10,000 each.
• Suppose the market stays at 1,400
• Suppose the market falls to 1,200
• Suppose the market rises to 1,470

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• Market Stays at 1,400
• Sell 240 250 1,400 84,000,000
• Buy 240 250 1,400 84,000,000
• Profit -
• Option (2,400,000)
• Gain/Loss (2,400,000)
• Market Falls to 1,200
• Sell 240 250 1,400 84,000,000
• Buy 240 250 1,200 72,000,000
• Profit 12,000,000
• Option (2,400,000)
• Gain/Loss 9,600,000

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• Market Rises to 1,470
• Sell 240 250 1,400 84,000,000
• Buy 240 250 1,470 88,200,000
• Profit (4,200,000)
• Option (2,400,000)
• Gain/Loss (2,400,000)
• Compare Hedging with Options to Futures Hedging
• With Options you know the cost of the hedge up
  front.
• With Futures you get a better hedge, but you
  dont know the cost up front. It can eliminate
  all your potential gain as well as all your loss.
• With Options you dont have to worry about margin
  calls when the hedge runs against you.

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Homework

• Problem 13, page 361