Options and their Applications

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Options and their Applications
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Some Details about Option Contracts

• Options Grants its owner the right, but not the
  obligation, to buy (if purchasing a call
  option) or sell (if purchasing a put option) a
  given asset on a specified date at a specified
  price (the strike price) at the origination of
  the contract.
• Key Features
• Calls allow you to bet on increases in the
  assets value.
• Puts allow you to bet on decreases in the assets
  value.
• The option buyer pays a premium to acquire the
  option.
• The seller of the option does have an obligation
  to buy/sell the asset. Much riskier than buying
  the option.
• Options can be in-the-money, at-the-money,
  and out-of-the-money.
• An option is a portfolio of forward contract and
  a riskless bond. Also, can create forwards from
  options!

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Option Details (cont.)

• Call owner has the right to buy an asset at a
  strike price specified today at some time in the
  future.
• Put owner has the right to sell an asset at a
  strike price specified today at some time in the
  future.
• Call seller/writer has the obligation to sell an
  asset at a strike price specified today.
• Put seller/writer has the obligation to buy an
  asset at a strike price specified today.
• Two main types of options European and American.
• American option value always greater than/equal
  to a European options value.

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Why Use Options?

• Allows you to protect against adverse price
  movements but still allows for upside potential.
• Easy to buy protection you need and sell off the
  coverage you dont need (e.g., buy a put at X
  50 and sell a put at X 20).
• Options can be purchased on exchanges or in the
  OTC market (thus giving users a wider choice of
  markets).
• You can sell options and earn the premium to
  boost income or cushion losses.

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Option Payoffs

• Option payoffs are non-linear.
• Owners Net Payoffs are similar to that of a
  portfolio of a forward contract and a riskless
  bond.
• Call owner C max0, (S X) - Premium
• Put owner P max0, (X S) - Premium
• Main incentive of call/put seller is to earn the
  premium.
• Call seller Premium min0, (X S)
• Put seller Premium min0, (S X)

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Put-Call Parity Relation

• Portfolio 1 own a Call (C) and a riskless bond
  (XD, where D a TVM discount factor).
• Portfolio 2 own a Put (P) and a share of stock
  at the current spot price (S).
• Note Both portfolios have identical payoffs,
  thus they must have the same value (assuming no
  arbitrage).
• Can use the above relation to price a put option
  based on the calls price
• P C (S XD)

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Inter-relationships between Options and Forwards

• Recall that there are six building blocks (two
  linear and four non-linear).
• We can use the non-linear payoffs of options to
  construct linear payoffs that are identical to a
  forward contracts payoffs
• (1) Long Call and Short Put Long Forward
• C P F
• (2) Short Call and Long Put Short Forward
• -C P -F

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Factors affecting an Options Value
Factor Call Owner Put Owner
Current Price (S) -
Exercise Price (X) -
Time to Expir. (T) /-
Volatility (s)
Risk-free rate (rf) -
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The Black-Scholes Option Pricing Model
In the limit, the binomial method becomes the
Black-Scholes OPM

• C SN(d1) - Xe rfTN(d2)
• d1
• d2 d1 - s t
• See Spreadsheet File.

ln(S/X) rf (s2/2)T s t
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Assumptions underlying the Black-Scholes OPM

• Option is European-style.
• Stock pays no dividend during the options term.
• Interest rates are constant.
• No restrictions on short sales of stock.
• Trading is done continuously and share prices
  follow a continuous Ito process.
• The distribution of terminal stock prices is
  lognormal

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American Options

• Differ from European options because American
  options can be exercised at any time (not just at
  expiration).
• If the stock pays no dividend, it is never
  optimal to exercise the option early (i.e., can
  sell it for S XD which is always greater than
  S X).
• For a dividend-paying stock, early exercise will
  be optimal only if the dividend is sufficiently
  large
• Exercise early when Dividend gt C (S X).

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Using Options to Hedge Interest Rate Risk

• Interest Rate Cap this contract represents a
  call option on an interest rate (rather than a
  bond price).
• Interest Rate Floor this contract represents a
  put option on an interest rate (betting that
  rates will fall).
• Interest Rate Collar created by buying a cap and
  selling a floor (at different strike prices).
  You can use this when you want to lock in a range
  of interest rates.

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Uses of FX Rate Options

• Used to protect against adverse movements in
  currencies that can affect the value of a firms
  international receivables, fixed assets,
  liabilities, etc.
• Typically used to hedge firm commitments and,
  increasingly, anticipated cash flows.
• Protection (and its cost) will vary depending on
  whether the option is at- or out-of-the money.
• Puts and calls can be bought/sold to create
  combined payoffs that lock in a range of
  acceptable prices.

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Uses of FX Rate Options (cont.)

• Hedge Overseas Revenues/Assets against a
  weakening foreign currency (buy puts on the
  foreign currency and/or sell calls).
• Hedge Overseas Costs/Liabilities against a
  strengthening foreign currency (buy calls on the
  foreign currency and/or sell puts).
• Use the above strategies to protect cash flows
  and, more broadly, protect operating margins,
  gain a competitive advantage, and provide greater
  customer satisfaction.

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Uses of Commodity Options

• Options on commodities such as metals can protect
  against adverse price movements that can affect
  basic inputs and outputs of the production
  process.
• Hedging with commodity options can
• protect operating margins,
• ensure cash flow is available for new
  investments,
• facilitate long-term planning and budgeting, and
• give the firm a pricing / service advantage.
• Option Spreads can be used to target the RANGE
  and/or COST of the commodity price protection.
  (See Spreadsheet File).

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Uses of Equity Options

• Traditionally used by institutional equity
  investors and investment banks/dealers.
• Growing use of equity options by non-financial
  firms related to
• Stock repurchase programs,
• Mergers, acquisitions, and divestitures,
• Managing employee stock option programs,
• Protecting an investment portfolio or enhancing
  yields.