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Copyright 2004 McGraw-Hill AustraliaPty Ltd21-221.1 Options: The Basics21.2 Fundamentals of Options Valuation21.3 Valuing a Call Option21.4 Black–Scholes Option Pricing Model21.5 Equity as a Call Option on the Firm’s Assets21.6 Types of Equity Option Contracts21.7 Futures Contracts21.8 Term Structure of Interest Rates21.9 Summary and ConclusionsChapter Organisation
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-3Chapter Objectives• Understand the key terminology associated withoptions.• Outline the five factors that determine optionvalues.• Price call options using the Black–Scholes optionpricing model.• Discuss the types of equity option contracts offered.• Outline the types of warrants available to investors.• Discuss the characteristics of future contracts.• Understand the term structure of interest rates.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-4Option Terminology• Call option– Right to buy a specified asset at a specified price on orbefore a specified date.• Put option– Right to sell a specified asset at a specified price on orbefore a specified date.• European option– An option that can only be exercised on a particular date(on expiry).• American option– An option that can be exercised at any time up to itsexpiry date.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-5Option Terminology• Striking price– The contracted price at which the underlying asset can bebought (call) or sold (put).• Expiration date– The date at which an option expires.• Option premium– The price paid by the buyer for the right to buy or sell anasset.• Exercising the option– The act of buying or selling the underlying asset via theoption contract.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-7Option Valuation• S1 = share price at expiration• S0 = share price today• C1 = value of call option on expiration• C0 = value of call option today• E = exercise price on the option
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-8Share priceat expiration (S1)Call option valueat expiration (C1)S1 ≤ E S1 > EExercise price (E)45 °Value of Call Option at Expiration
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-9Value of Call Option at Expiration( ) 0if01 ESC 1 ≤−=Option is out of the money.( ) 0if 111 ESESC >−−=Option is in the money.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-11Call Option Boundaries• Upper bound—a call option will never be worth more than theshare itself:C0 ≤ S0• Lower bound—share price cannot fall below 0 and to preventarbitrage, the call value must be (S0 – E):The larger of 0 or (S0 – E)• Intrinsic value—option’s value if it was about to expire = lowerbound.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-12Factors Determining Option Values( )tfRE/SC +−=−=100priceexerciseofPVpriceSharevalueoptionCallThe value of a call option depends on four factors:• share price• exercise price• time to expiration• risk-free rate.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-13Another Factor to Consider?• The above four factors are relevant if the option is to finish inthe money.• If the option can finish out of the money, another factor toconsider is volatility.• The greater the volatility in the underlying share price, thegreater the chance the option has of expiring in the money.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-14The Factors that Determine OptionValueCurrent value of the underlying asset (+) (−)Exercise price on the option (−) (+)Time to expiration on the option (+) (+)Risk-free rate (+) (−)Variance of return on underlying asset (+) (+)Factor Calls Puts
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-16Black–Scholes Option Pricing Model( )( )tddttR/ESdf×σ−=×σ×σ×++=1220121n1Note: The risk-free rate, the standard deviation and thetime to maturity must all be quoted using the same timeunits.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-17Example—Black–Scholes OptionPricing Model• S0 = $25• E = $20• Rf = 8%∀ σ = 30%• t = 0.5 years
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-19Example—Black–Scholes OptionPricing Model (continued)• From the cumulative normal distribution table:N(d1) = N(1.34) = 0.9099N(d2) = N(1.13) = 0.8708• Therefore, the value of the call option is:( ) ( )( ) ( )016$73311674752287080209099025 500800....e.C ..=−=−=
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-20Equity: A Call Option• Equity can be viewed as a call option on thecompany’s assets when the firm is leveraged.• The exercise price is the value of the debt.• If the assets are worth more than the debt when itbecomes due, the option will be exercised and theshareholders retain ownership.• If the assets are worth less than the debt, theshareholders will let the option expire and theassets will belong to the bondholders.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-21Equity Option Contracts• Types of equity option contracts offered inAustralia:– Exchange traded put and call options on company shares– Exchange traded long dated contracts issued by afinancial institution that can then trade them (warrants)– Over-the-counter options on company shares– Convertible notes issued by companies, comprising botha debt and an equity component.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-22Warrants• A long-lived option that gives the holder the right tobuy shares in a company at a specified price.• Types of warrants available:equity warrants low exercise price warrantsfractional warrants endowment warrantsbasket warrants currency warrantsfully covered warrantsindex warrantsinstalment warrants
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-23Company Options• A holder is given the right to purchase shares in acompany at a specified price over a given period oftime.• Usually offered as a ‘sweetener’ to a debt issue.• These options are often detached and soldseparately.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-24Company Options versus Exchange-traded Options• Company options have longer maturity periods andare often European-type options.• Company options are issued as part of a capital-raising program and are therefore limited innumber.• The clearing house has no role in the trading ofcompany options.• Company options are issued by firms.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-25Earnings Dilution• Put and call options have no effect on the value ofthe firm.• Company options do affect the value of the firm.• Company options cause the number of shares onissue to increase when:– the options are exercised– the debts are converted.• This increase does not lower the price per sharebut EPS will fall.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-26Forward Contracts• A contract where two parties agree on the price of an assettoday to be delivered and paid for at some future date.• Forward contracts are legally binding on both parties.• They can be tailored to meet the needs of both parties andcan be quite large in size.• Positions– Long—agrees to buy the asset at the future date– Short—agrees to sell the asset at the future date• Because they are negotiated contracts and there is noexchange of cash initially, they are usually limited to large,creditworthy corporations.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-28Futures Contracts• An agreement between two parties to exchange aspecified asset at a specified price at a specifiedtime in the future.• Do not need to own an asset to sell a futurecontract.• Either buy before delivery or close out position withan opposite market position.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-29Futures Markets• Enable buyers and sellers to avoid risk incommodities (and other) markets with high pricevariability → hedging.• Involves standardised contracts.• Deposit required by all traders to guaranteeperformance.• Adverse price movements must be covered dailyby further deposits called margins (‘marked tomarket’).• Futures also available for short-term interest rates,to protect against interest rate movements.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-30Futures Quotes• Commodity, exchange, size, quote units– The contract size is important when determining the dailygains and losses for marking-to-market.• Delivery month– Open price, daily high, daily low, settlement price, changefrom previous settlement price, contract lifetime high andlow prices, open interest– The change in settlement price multiplied by the contractsize determines the gain or loss for the day:Long—an increase in the settlement price leads to a gainShort—an increase in the settlement price leads to a loss• Open interest is how many contracts are currentlyoutstanding.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-32Term Structure of Interest Rates• Yield curve shows the different interest ratesavailable for investments of different maturities, ata point in time.• The relationship between interest rates of differentmaturities is called the term structure.
Copyright 2004 McGraw-Hill AustraliaPty Ltd21-33Factors Determining the TermStructure• Risk preferences—borrowers prefer long-termcredit whereas lenders prefer short-term loans(explains upward-sloping yield curve only).• Supply−demand conditions—segmented capitalmarkets can cause supply−demand imbalances(explains all yield curve shapes).• Expectations about future interest rates (mostfavoured explanation)