11

Chapter 11Chapter 11 Options – Derivative Options – Derivative

SecuritiesSecurities

22Copyright © 1998 by Harcourt Brace & Company

Student Learning Student Learning ObjectivesObjectives

Basic Option Terminology Characteristics of option contracts Option values Common option trading strategies Option valuation Other securities that resemble

options

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Characteristics of Option Characteristics of Option ContractsContracts

Option contracts give the holder the right but not the obligation to: – buy or sell a stated number of shares (100) – at a specified price (exercise or strike price) – until a specified point in time (expiration

date) An option to buyoption to buy stock is a callcall option An option to selloption to sell stock is a putput option Options are called derivatives securitiesderivatives securities

because their value is derived from the value of the underlying security.

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Writing an OptionWriting an Option

The person who sells an option (writeswrites an option) receives a “premium”– the premium is the current market value of

the option and includes: time value intrinsic value (if in-the-money)

– Option Writer is said to be “short” Covered Call Writer – owns stock Naked Call Writer – does not own stock If Exercised – writer must deliver stock

to option call buyer

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Call OptionsCall Options

“In-the-moneyIn-the-money”: stock price exceeds the exercise price

“at-the-moneyat-the-money”: stock price equals the exercise price it is

“Out-of-the-moneyOut-of-the-money”: stock price is less than the exercise price

The option buyer has a “long position”

The option seller (writer) has a “short position”

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Put OptionsPut Options

“In-the-moneyIn-the-money”: stock price less than the exercise price

“at-the-moneyat-the-money”: stock price equals the exercise price

“Out-of-the-moneyOut-of-the-money”: stock price is greater than the exercise price

Naked PutsNaked Puts – not protecting a long stock position

Married PutsMarried Puts – protecting a long stock position

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Option ExpectationsOption Expectations

Call options bought by investors that expect prices to rise [relatively soon].

Put options bought by investors that expect price to decline. [ditto]

Call options sold by investors that expect prices to decline [soon].

Put options sold by investors that expect prices to rise [soon].

For every option traded there is both a long and a short position

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Option ValueOption Value

Option values:– Intrinsic valueIntrinsic value is the difference

between the stock price and the exercise price

zero if the option is not “in-the-money.” can never be negative.

– Time valueTime value is the difference between the intrinsic value and the price of the option.

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Call Option Value at ExpirationCall Option Value at Expiration

Value at expiration depends on price of underlying stock– If stock price is less than or equal to

the exercise price, then call option is worthless.

– If stock price is more than exercise price, a call option is “in-the-money”.

May be sold for the profit or exercised to obtain the stock by paying

the exercise or strike price.

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Expiration Date & ExerciseExpiration Date & Exercise

Saturday following third Friday of stated month in standard stock option contracts (last trade day is Friday!)

American: exercisable up till expiration

European: exercisable only on expiration

Bermuda: exercisable on multiple dates

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Profit and Loss From an Profit and Loss From an OptionOption

The profit and loss for an option writer and buyer are complements.– The expense of buying an option is

income to the writer/seller.– The profit/loss of the buyer is

opposite of the profit/loss of the seller and the net sum of the buyer and seller profit/loss is zero.

In a zero sum gamezero sum game, in order for one to make money, another must lose

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Option TradingOption Trading

Options are traded using market or limit orders.

Organized trading on exchanges has certain advantages over OTC trading:– Standardized contracts– Increased liquidity– More comprehensive disclosure and

surveillance– Guaranteed clearing of contracts– Lower transaction costs

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Options on Other SecuritiesOptions on Other Securities

Index optionsIndex options are calls or puts based on a stock market index, settled by settled by cashcash rather than delivery of underlying securities

Foreign currency optionsForeign currency options allow the holder to buy or sell a quantity of foreign currency for a specified amount of U. S. Dollars

Long-term optionsLong-term options, called LEAPS® have expiration dates up to two years from the date of issue

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Option Risks and Option Risks and OpportunitiesOpportunities

Options can be used to hedgeto hedge [reduce risk of long or short] stock positions or to speculateor to speculate.

Options trading provides leverage opportunities, similar to margin

Leverage is a double-edged sword, and can result in total loss of the cost of an option

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Call Option StrategiesCall Option Strategies

CALLCALL Strategy based on expectationsexpectations:– Call buyers expect market to go up:

Sellers expect market to go down or sideways.

– BuyerBuyer: deep out-of-the-money or short time period to expiration options have a greater potential return and increased risk of losing premiums paid.

– SellerSeller: at the money or long duration options have greater potential returns and greater risk of loss. Especially Naked writers.

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Put Option StrategiesPut Option Strategies

PUTPUT Strategy based on expectationsexpectations::– Put buyers expect market to go down:

Sellers expect market to go up or sideways.

– BuyerBuyer: deep out-of-the-money or short time period to expiration options have a greater potential return and greater risk.

– SellerSeller: near at-the money or long time period to expiration have more profit potential and greater risk of loss.

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Combining Option Combining Option and Stock Positionsand Stock Positions

Options can be used to provide income and reduce loss on a long stock position.– Writing a covered call: increase income on

owned stock, & reduces some downside loss.

– A protective put: Buying put options on owned stock reduce downside loss.

– A covered short sale: Buying call options on stock sold short to reduce position risk.

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Writing Naked CallsWriting Naked Calls

High risk Call Option [Speculation]:– Writing a naked call: Writing calls on

stock not owned - very risky play if writer is wrong about future direction.

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Determinants of Option Determinants of Option ValuesValues

Option’s value function of Option’s value function of – stock pricestock price– strike pricestrike price– stock return volatilitystock return volatility– riskless interest rate (t-bill rate)riskless interest rate (t-bill rate)– length of time to expirationlength of time to expiration

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Determinants of Option Determinants of Option ValuesValues

Stock Price:Stock Price: higher the stock price, more higher the stock price, more valuable the call.valuable the call.

Strike price:Strike price: higher the strike price, less higher the strike price, less valuable the call.valuable the call.

Volatility:Volatility: more volatile price of more volatile price of underlying stock, more valuable the underlying stock, more valuable the call.call.

Interest rate:Interest rate: higher the interest rate, higher the interest rate, more valuable the call.more valuable the call.

Time to maturity:Time to maturity: longer time to longer time to maturity, more valuable callmaturity, more valuable call

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Models for Valuing OptionsModels for Valuing Options

Black-Scholes option pricing modelBlack-Scholes option pricing model Binomial option pricing modelBinomial option pricing model Put-call parityPut-call parity

2222Copyright © 1998 by Harcourt Brace & Company

Black-Scholes Option Pricing Black-Scholes Option Pricing ModelModel

Assumes that a riskless hedge Assumes that a riskless hedge between an option and its between an option and its underlying stock should yield the underlying stock should yield the riskless return. riskless return.

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Hedge RatioHedge Ratio

In Black-Scholes model, number of In Black-Scholes model, number of calls written that would exactly calls written that would exactly offset stock price movement of offset stock price movement of number of shares of underlying number of shares of underlying stock held.stock held.– Small move in stock’s price would be Small move in stock’s price would be

precisely offset by change in value of precisely offset by change in value of option position with ratio of number option position with ratio of number of calls to number of shares of stockof calls to number of shares of stock

– Investor theoretically holding Investor theoretically holding equivalent of risk-free asset.equivalent of risk-free asset.

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Binomial OPMBinomial OPM

Simple model assumesSimple model assumes– price at end of period will be one of price at end of period will be one of

two values (basis for “Bi” in Binomial)two values (basis for “Bi” in Binomial)– alternative to call option is to borrow alternative to call option is to borrow

enough so to buy one share of stock enough so to buy one share of stock and just breakeven if stock closes at and just breakeven if stock closes at lower pricelower price

– Price of call option will be based on Price of call option will be based on how many calls are necessary to how many calls are necessary to duplicate loan strategy, and equity to duplicate loan strategy, and equity to set up loanset up loan

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Put-Call ParityPut-Call Parity

CC0 0 = P = P00 + S + S00 – X – X e errff t t

  CC00 = call value= call value

PP00 = put value= put valuerrff = risk-free rate= risk-free rateee = 2.718 (the natural logarithmic constant)= 2.718 (the natural logarithmic constant)SS00 = initial stock price= initial stock priceXX = strike price= strike pricett = time to expiration as a fraction of a year= time to expiration as a fraction of a year

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Simple Positions and Simple Positions and SyntheticSynthetic EquivalentsEquivalents

Simple PositionSimple Position Synthetic EquivalentSynthetic Equivalent Long StockLong Stock Long a Call & Short a PutLong a Call & Short a Put Short StockShort Stock Short a Call & Long a PutShort a Call & Long a Put Long a CallLong a Call Long Stock & Long a PutLong Stock & Long a Put Short a CallShort a Call Short Stock & Short a PutShort Stock & Short a Put Long a PutLong a Put Short Stock & Long a Short Stock & Long a

CallCall Short a PutShort a Put Long Stock & Short a CallLong Stock & Short a Call

Synthetic Call: Long stock, sell a bond, Synthetic Call: Long stock, sell a bond, and buy a put. Exercise price = FV of and buy a put. Exercise price = FV of bond.bond.

Synthetic Put: Short stock, long call.Synthetic Put: Short stock, long call.

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Convertible SecuritiesConvertible Securities

Convertible BondsConvertible Bonds Convertible Preferred StocksConvertible Preferred Stocks Concepts the sameConcepts the same

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Conversion RatioConversion Ratio

Conversion Ratio = Par / Conversion Ratio = Par / Conversion PriceConversion Price

Conversion Price defined in Conversion Price defined in indentureindenture

Conversion ratio (or exchange Conversion ratio (or exchange ratio) = # of shares of common ratio) = # of shares of common stock received upon conversionstock received upon conversion

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Conversion Value & PremiumConversion Value & Premium

Conversion Value = Conversion Value = Conversion Ratio x Price of Conversion Ratio x Price of Common StockCommon Stock

Conversion Premium = Conversion Premium = Market Price of Bond – Conversion Market Price of Bond – Conversion ValueValue

% Conversion Premium = % Conversion Premium = Conversion Premium / Conversion Conversion Premium / Conversion ValueValue

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Value of Bond asDebt and as Stock

Value of ComparableNonconvertible Bond(Straight-Debt Value)

Price of Stock

Conversion Value

Bond Market Value

ConversionPremium

Conversion ValuesConversion Values

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Convertibles Always CallableConvertibles Always Callable

Allows company to force Allows company to force conversionconversion

Investor must convert or saleInvestor must convert or sale After call date, no longer accrues After call date, no longer accrues

interest or is convertibleinterest or is convertible

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Rates of Return on Rates of Return on ConvertiblesConvertibles

Historically:Historically:– Better than non-convertiblesBetter than non-convertibles– Worse direct ownership of equityWorse direct ownership of equity

Less risky than equity, riskier than Less risky than equity, riskier than straight debtstraight debt