1 Chapter 11 Options – Derivative Securities

2 Copyright © 1998 by Harcourt Brace & Company Student Learning Objectives Basic Option Terminology Characteristics of option contracts Option values Common option trading strategies Option valuation Other securities that resemble options

3 Characteristics of Option Contracts 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) option to buycall An option to buy stock is a call option option to sellput An option to sell stock is a put option derivatives securities Options are called derivatives securities because their value is derived from the value of the underlying security.

4 Writing an Option writes The person who sells an option (writes 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

5 Call Options In-the-money “In-the-money”: stock price exceeds the exercise price at-the-money “at-the-money”: stock price equals the exercise price it is Out-of-the-money “Out-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”

6 Put Options In-the-money “In-the-money”: stock price less than the exercise price at-the-money “at-the-money”: stock price equals the exercise price Out-of-the-money “Out-of-the-money”: stock price is greater than the exercise price Naked Puts Naked Puts – not protecting a long stock position Married Puts Married Puts – protecting a long stock position

7 Option 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

8 Option Value Option values: – Intrinsic value – Intrinsic 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 value – Time value is the difference between the intrinsic value and the price of the option.

9 Call 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.

10 Expiration 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

11 Profit and Loss From an Option 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. zero sum game In a zero sum game, in order for one to make money, another must lose

12 Option 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

13 Options on Other Securities Index options settled by cash Index options are calls or puts based on a stock market index, settled by cash rather than delivery of underlying securities Foreign currency options Foreign currency options allow the holder to buy or sell a quantity of foreign currency for a specified amount of U. S. Dollars Long-term options Long-term options, called LEAPS® have expiration dates up to two years from the date of issue

14 Option Risks and Opportunities to hedge or to speculate Options can be used to hedge [reduce risk of long or short] stock positions or 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

15 Call Option Strategies CALLexpectations CALL Strategy based on expectations: – – Call buyers expect market to go up: Sellers expect market to go down or sideways. – Buyer – Buyer: deep out-of-the-money or short time period to expiration options have a greater potential return and increased risk of losing premiums paid. – Seller – Seller: at the money or long duration options have greater potential returns and greater risk of loss. Especially Naked writers.

16 Put Option Strategies PUTexpectations: PUT Strategy based on expectations: – – Put buyers expect market to go down: Sellers expect market to go up or sideways. – Buyer – Buyer: deep out-of-the-money or short time period to expiration options have a greater potential return and greater risk. – Seller – Seller: near at-the money or long time period to expiration have more profit potential and greater risk of loss.

17 Combining Option and 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.

18 Writing 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.

19 Determinants of Option Values Option’s value function of Option’s value function of – stock price – strike price – stock return volatility – riskless interest rate (t-bill rate) – length of time to expiration

20 Determinants of Option Values Stock Price: higher the stock price, more valuable the call. Stock Price: higher the stock price, more valuable the call. Strike price: higher the strike price, less valuable the call. Strike price: higher the strike price, less valuable the call. Volatility: more volatile price of underlying stock, more valuable the call. Volatility: more volatile price of underlying stock, more valuable the call. Interest rate: higher the interest rate, more valuable the call. Interest rate: higher the interest rate, more valuable the call. Time to maturity: longer time to maturity, more valuable call Time to maturity: longer time to maturity, more valuable call

21 Models for Valuing Options Black-Scholes option pricing model Black-Scholes option pricing model Binomial option pricing model Binomial option pricing model Put-call parity Put-call parity

22 Copyright © 1998 by Harcourt Brace & Company Black-Scholes Option Pricing Model Assumes that a riskless hedge between an option and its underlying stock should yield the riskless return. Assumes that a riskless hedge between an option and its underlying stock should yield the riskless return.

23 Hedge Ratio In Black-Scholes model, number of calls written that would exactly offset stock price movement of number of shares of underlying stock held. In Black-Scholes model, number of calls written that would exactly offset stock price movement of number of shares of underlying stock held. – Small move in stock’s price would be precisely offset by change in value of option position with ratio of number of calls to number of shares of stock – Investor theoretically holding equivalent of risk-free asset.

24 Binomial OPM Simple model assumes Simple model assumes – price at end of period will be one of two values (basis for “Bi” in Binomial) – alternative to call option is to borrow enough so to buy one share of stock and just breakeven if stock closes at lower price – Price of call option will be based on how many calls are necessary to duplicate loan strategy, and equity to set up loan

25 Put-Call Parity C 0 = P 0 + S 0 – X  e r f t C 0 = call value P 0 = put value P 0 = put value r f = risk-free rate e= (the natural logarithmic constant) S 0 = initial stock price X= strike price t= time to expiration as a fraction of a year

26 Simple Positions and Synthetic Equivalents Simple PositionSynthetic Equivalent Long StockLong a Call & Short a Put Long StockLong a Call & Short a Put Short StockShort a Call & Long a Put Short StockShort a Call & Long a Put Long a CallLong Stock & Long a Put Long a CallLong Stock & Long a Put Short a CallShort Stock & Short a Put Short a CallShort Stock & Short a Put Long a PutShort Stock & Long a Call Long a PutShort Stock & Long a Call Short a PutLong Stock & Short a Call Short a PutLong Stock & Short a Call Synthetic Call: Long stock, sell a bond, and buy a put. Exercise price = FV of bond. Synthetic Put: Short stock, long call.

27 Convertible Securities Convertible Bonds Convertible Bonds Convertible Preferred Stocks Convertible Preferred Stocks Concepts the same Concepts the same

28 Conversion Ratio Conversion Ratio = Par / Conversion Price Conversion Ratio = Par / Conversion Price Conversion Price defined in indenture Conversion Price defined in indenture Conversion ratio (or exchange ratio) = # of shares of common stock received upon conversion Conversion ratio (or exchange ratio) = # of shares of common stock received upon conversion

29 Conversion Value & Premium Conversion Value = Conversion Value = Conversion Ratio x Price of Common Stock Conversion Premium = Conversion Premium = Market Price of Bond – Conversion Value % Conversion Premium = % Conversion Premium = Conversion Premium / Conversion Value

30 Conversion Values

31 Convertibles Always Callable Allows company to force conversion Allows company to force conversion Investor must convert or sale Investor must convert or sale After call date, no longer accrues interest or is convertible After call date, no longer accrues interest or is convertible

32 Rates of Return on Convertibles Historically: Historically: – Better than non-convertibles – Worse direct ownership of equity Less risky than equity, riskier than straight debt Less risky than equity, riskier than straight debt