1Introductory Comments on Options and SWAPs

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1Introductory Comments on Options and SWAPs

• Options are nonlinear derivative contracts, and
  may come in an infinity of forms. The most
  common are puts and calls. Variations on the
  maturity conditions give rise to American and
  European options among other types.
• Defn The purchaser of a European (American) call
  has the right, but not the obligation, to buy a
  certain specified asset at (by) a certain
  specified future time for a certain specified
  price.
• The date in question is said to be the expiration
  or maturity date, while the specified price is
  the exercise or strike price.

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2Option Definitions

• Defn The purchaser of a European (American) put
  has the right, but not the obligation, to sell a
  certain specified asset at (by) a certain
  specified future time for a certain specified
  price.
• Note, there are net zero puts and calls. Someone
  out there has generated these rights. These
  people are said to write, or short, the options.
• In contrast to futures, options are generally not
  marked to market daily. Thus, the natural
  comparison is with forwards rather than with
  futures.

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3Comparison

• A forward contract gives the long (short) holder
  the obligation to buy (sell) at a specified price
  at a specified date. Both parties are treated
  symmetrically. There is no element of choice,
  except that one party may seek to negotiate out
  of the contract.
• A long option contract gives the holder the right
  to buy (for a call) or sell (for a put) at a
  specified price. There is a discretionary
  choice, and the option writer faces an obligation
  to make the transaction if the option owner
  chooses to exercise the option.

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4Position Diagrams for Options

• Long Call in Hull2. Look up the premium in the
  WSJ. It will be explained later that this
  position diagram gives the intrinsic value of the
  option.
• What is the price paid (premium) for the call?
  What determines where the corner (kink) is? Note
  that the diagram shows that payout increases with
  the price of the underlying asset.
• Long Put in Hull2. Note that here payout
  decreases with the price of the underlying. The
  bet is that price will fall.

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5Approximate Analysis of Option Pricing

• Consider an IBM call with July 1999 maturity and
  100 strike price. Let ST be the as yet unknown
  July price, and let it have the distribution
  G(ST). The July payout for the call is MaxST -
  100, 0. Ignoring the time value of money, the
  risk-neutral trader would value the option at
• EMaxST - 100, 0 ?A MaxST - 100, 0 dG(ST)
  ?A (ST - 100) dG(ST) where A
  100, ?.
• Interest rate considerations make the problem
  more difficult.

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6Source of Option Value

• The premium is paid to the option writer, and the
  position diagram must be modified accordingly.
• The premium arises because the long position on
  an option has limited liability. In contrast to
  a futures position, the long option can only lose
  so much.

Put option Payouts Gross and Net of Premium
Payout
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7Written Options. Also, SWAPs Defined

• Short call and short put in Hull2. Note, these
  position diagrams are the reflections of the long
  option positions in the horizontal axis. This is
  because, from an accounting perspective, options
  are zero sum games.
• Defn A SWAP is an agreement to exchange cash
  flows at specified future times according to
  specified conditions.
• Example An agreement by GM to receive 3 month
  LIBOR (London interbank offer rate) and pay a
  fixed rate of 5 per annum every six months for
  two years on a notional principal of 200 million.