Lecture 22: Other Derivatives

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Lecture 22 Other Derivatives
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Option Parameters

• Delta Partial derivative of option price with
  respect to underlying price ?C/?S
• Gamma Second partial derivative of option price
  with respect to underlying ?2C/?S2
• Theta Partial derivative of option price with
  respect to time ?C/?T. (Equals minus the partial
  derivative with respect to time remaining until
  exercise)
• Vega Partial derivative of option price with
  respect to volatility ?C/?s

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Option Delta

• Option delta is derivative of option price with
  respect to stock price
• For calls, if stock price is way below exercise
  price, delta is nearly zero
• For calls, if option is at the money, delta is
  roughly a half, but price of option may be way
  below half the price of the stock.
• For calls, if stock price is way above the
  exercise price, delta is nearly one and one pays
  approximately stock price minus pdv of exercise
  price, like buying stock with credit pdv(E)

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Call Delta ?C/?S
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?log(C)/?log(S)
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Call Gamma ?2C/?S2
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Call Theta ?C/?T
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Behavioral Aspects of Options Demand

• Thalers mental categories theory
• Writing an out-of-the-money call on a stock one
  holds, appears to be a win-win situation
  (Shefrin)
• Buying an option is a way of attaining a more
  leveraged, risky position
• Lottery principle in psychology, people
  inordinately attracted to small probabilities of
  winning big
• Margin requirements are circumvented by options

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Swaps and Risk Management

• Swaps are simple exchanges between parties of one
  risk for another
• Started in 1981, now in trillions of dollars
  worldwide

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Precursor to SwapsParallel Loan Agreements

• Breakdown of Bretton Woods fixed exchange rates
  in 1973 led to new ways to manage exchange rate
  risks
• US firm with UK subsidiary lends dollars to a UK
  firm with US subsidiary. They lend pounds to US
  firm.
• Hedges exchange rate risk
• Long-term, to terms of parties, hence better than
  futures market hedging

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Problems with Parallel Loan Agreements

• Default Risk loans are independent instruments,
  so default by one party does not release other
  from obligated payments
• Balance sheet impact parallel loans will inflate
  the balance sheet, which leads to possible
  problems with financial covenants, with public
  perception of safety of their stock

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Efforts to Stabilize Earnings

• Currency swings caused major changes in income
  statements of firms.
• Zeckhauser and Patel show that firms rarely lose
  earnings, truncated distribution of earnings
  change
• GE showed steadily growing earnings for last 20
  years

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Swaps as Parallel Loan Agreements Stapled
Together

• First privately arranged swaps occurred in mid
  1970s
• First public introduction of a currency swap
  between IBM and World Bank 1981.

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Interest Rate Swaps

• Swap fixed for floating
• A bank with a lot of long-term investments and
  short-term deposits may swap the short-term
  deposits for long-term

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Swaps on Telerate ScreenTreasury-LIBOR Swap

• 2 Yr. T70 T74
• 3 Yr. T74 T77
• 4 Yr. T74 T78
• 5 Yr. T74 T79
• 7 Yr. T73 T79
• 10 Yr. T73 T78

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Spiders
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MITTs Market Index Target Term Securities

• Traded on AMEX, often issued by Merrill Lynch
• What if I told you theres an investment that
  will give you no downside but an unlimited
  upside?
• Example Five-year MITTs issued in 1992 for 10
  pay promise to pay the 10(1x1.15) back in five
  years, where x is percentage increase in the SP
  if positive, otherwise zero.
• Downsides You get no dividends, your floor of
  10 is pretty low given that interest rates were
  around 5 a year in 1992

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Futures Options
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Why Options on Futures?

• Futures market more liquid, up-to-date, than spot
  market
• Easier to hedge an options position in futures
  market than in spot market

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Futures on REITs

• August 1998 Chicago Mercantile Exchange announced
  plan for futures on the SP Real Estate Trust
  Composite Index
• Screen-traded rather than open-outcry