Options : Definition, Valuation and Portfolio Management

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Options Definition, Valuation and Portfolio
Management

• Patrick Roger
• DEA-Management

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Introduction Consumption transfers

• Pure consumption transfers
• Saving and borrowing (risky or not)
• Suitable financial assets
• Bonds
• Stocks

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Contingent transfer at date 1

• Exchange of date-1 consumption across states of
  nature
• Suitable assets
• Forward and future contracts

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Intertemporal contingent transfer

• Suitable assets
• Options (almost all kinds)

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Summary

• Chapter I Definition of option contracts and
  simple strategies
• Chapter II The determinants of the premium
• Chapter III Discrete-time evaluation
• Chapter IV Continuous-time evaluation
• Chapter V Applications options portfolio
  management

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Basic references

• Cox-Rubinstein (1985) Options markets, Prentice
  Hall.
• Hull (2000) Futures, Options and other
  Derivatives, 4th edition, Prentice hall.
• Roger (1996) Evaluation des actifs financiers,
  De Boeck Université.
• Encyclopédie des marchés financiers (Economica,
  1997).

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Chapter I Option contracts and simple strategies

• Definition A european call gives its owner the
  right to buy a given quantity of an underlying
  asset at a given future date and for a
  pre-specified price.
• Définition A european put gives its owner the
  right to sell a given quantity of an underlying
  asset at a given future date and for a
  pre-specified price

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Web sites

• French Market
• www.monep.fr
• US Market (Chicago)
• www.cboe.com

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Examples (french notations for dates)

• Call / CAC40 / 06-03 / 3500
• Exercise if CAC40gt3500 on 30-06-2003
• Put US / 03-03 / 1.10
• Exercise if USlt1.10 on 31-03-2003

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The premium

• Remark The option buyer always gets positive
  cash-flows at the maturity date.
• The amount paid by the buyer at date 0 is called
  the premium.

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Simple strategies

• Buying a call
• Buying a put

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Combined Strategies

• Vertical Spreads (bullish and bearish)
• Straddle
• Butterfly spread
• Synthetic risk-free asset
• Covered calls and puts

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Vertical spread

• Buy and sell the same type of option (call or
  put) but at different strike prices.
• Examples
• Call vertical spread
• Buy call / XYZ / 0603 / 90
• Sell call / XYZ / 0603/ 100
• Put vertical spread
• Buy put / XYZ / 0303 / 110
• Sell put / XYZ / 0303 / 100
• There are also horizontal and diagonal spreads

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K2
K1
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Straddle

• Long straddle Buy a call and a put with the
  same characteristics (strike price, maturity)
• Buy call / XYZ / 0603 / 100
• Buy put / XYZ / 0603 / 100

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Butterfly spread

• Typical case Buy one call ITM, one call OTM and
  sell two calls ATM

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Maturity date

• End of the life of the contract Generally ends
  of months or quarters, depending on specific
  market rules.
• For details on the french option market (MONEP),
  see www.monep.fr
• For the US market (Chicago), see www.cboe.com

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Exercise price

• It is the price paid (received) by the buyer of
  the call (put) when she exercises the option
  contract at the maturity date (the seller
  delivers (receives) the underlying asset at the
  same time).
• Note In case of cash settlement, the buyer of
  the call (put) receives the difference between
  the price of the underlying (exercise price) and
  the exercise price (underlying price).

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Underlying assets of an option contract

• Stocks
• Stock Market Index
• Currencies
• Interest rates, Bonds
• Temperatures, etc

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European and American Options

• European option can be exercised at the
  maturity date only.
• Américan option can be exercised at any moment
  before the maturity date.
• EXAMPLE
• American Call on France Telecom June 2003
  Buying France Telecom stocks by exercizing the
  call may be realized up to the end of june 2003.

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Horizontal and diagonal spreads

• Horizontal Buy and sell the same type of option
  (call or put) with the same strike price and
  different maturities
• Diagonal combines vertical and horizontal
  spreads features.

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Glossary

• Call In The Money (ITM) S gtgt K
• Call Out of The Money (OTM) S ltlt K
• Call At The Money (ATM) S K
• For puts, inequalities are reversed