Chapter 15 Options Markets Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

15-2 Option Terminology 1.What is a listed stock call option? –A contract giving the holder the right to buy 100 shares of stock at a preset price called the exercise or strike price. –Expirations of 1,2,3,6,& 9 months and sometimes 1 year are normal contract periods. Contracts expire on the third Saturday of the expiration month. –Contracts may be resold prior to maturity. 2. What is a listed stock Put option? - A contract giving the holder the right to sell 100 shares of stock at a preset price

15-3 Option Characteristics If a call option holder wishes to purchase the stock, he or she will exercise the option. The option holder must pay the exercise price to the option writer. Exercise prices are adjusted for stock splits and stock dividends, but not cash dividends. The cost of an option is called the premium and it is a small percentage of the cost of the underlying asset. The option buyer pays the cost; the option writer receives the cost at the time of sale of the option. The underlying company is not involved in the option market. Options are a zero sum game.

15-4 American vs. European Options American: European: the option can be exercised any time, but no Later than the expiration date the option can only be exercised at the expiration date

15-5 Figure 15.1 Options on IBM

Uses of options: a.To hedge changes in stock price. b.Change your risk and return profile For example, buying a call is analogous to buying stock on margin. c.Short sale constraints can be avoided with puts.

15-7 Option Clearing Corporation (OCC) OCC is jointly owned by option exchanges OCC backs performance of both counterparties –To limit OCC’s risk, option seller (or writer) must post margin. Margin varies with option price and whether the option position is covered or exposed. When an option is exercised an option seller is randomly selected. –If a call is exercised the selected call writer must deliver 100 shares of stock in exchange for receiving the strike price. –If a put is exercised the selected put writer must purchase 100 shares of stock at the strike price.

Types of options o Listed Options vs OTC Options Index Options Options on Futures Foreign Currency Options Interest Rate Options Exotic Options

Values of Options at Expiration

Symbols & Valuation C t =Price paid for a call option at time t. t = 0 is today, T =option's expiration date. P t =Price paid for a put option at time t. S t =Stock price at time t. Xc, Xp= Exercise or Strike Price A call is “in the money” if S t ____ Xc. A call is “out of the money” if S t ____ Xc. A put is “in the money” if S t ____ Xp. A put is “out of the money” if S t ____ Xp. > > > >

The basics of option pricing a) Price boundaries o – o oJust before expiration at time T: If S T X then C T = 0 C T = S T – X oP t  0 oP t  X - S t oP t  Max (0, X – S t ) If C t < S t – X How could you take advantage of this? $5 $60 $50 Thus C t  Max (0, S t – X) C t ≥ 0,Why? C t ≥ S t – X,Why?

15-12 IBM Option Quotes

Option strategies and profits at expiration S T = X + C 0 Breakeven – C 0 + S T – X– C 0 = Profit S T – X0+C T – C 0 S T > XS T < XProfit Table BUYING A CALL

15-14 Call profit at expiration IBM Jul 100 call option Stock Price = $96.14 Exercise = $100 Call premium = $735 Contract Size 100 shares Ex = $100 Stock Price T Profit $0 -$735  Bullish or bearish?  High or low volatility strategy? -C 0 -C 0 + S T – X S T = X + C 0 $100 $ $92.65

15-15 Writing a naked call S T = X + C 0 Breakeven +C 0 – S T + X+C 0 = Profit –(S T – X)0– C T +C 0 S T > XS T < XProfit Table WRITING A NAKED CALL

15-16 Writing a naked call Stock Price T Profit $0 +C 0 +C 0 – S T + X X  Bullish or bearish?  High or low volatility strategy? S T = X + C 0

15-17 Buying a put option S T = X – P 0 Breakeven – P 0 X – S T – P 0 = Profit 0X – S T +P T – P 0 S T > XS T < XProfit Table BUYING A PUT

15-18 IBM Option Quotes

15-19 X – S T – P 0 Buying a put option IBM Dec 100 put option Stock price = $96.14 Exercise = $100 Put premium = $1,166 Contract Size 100 shares Ex = $100 Stock Price t Profit $0 -$1,166 Put $100 $88.34 $8,834  Bullish or bearish? Alternative Stock Strategy?  High or low volatility strategy? – P 0 Short position in IBM B.E.: S T = X – P 0 $111.66

15-20 Writing a put option S T = X – P 0 Breakeven +P 0 S T – X + P 0 = Profit 0–(X – S T )– P T +P 0 S T > XS T < XProfit Table Writing A Put

15-21 Writing a put option IBM Jul 100 put option Stock price = $96.14 Exercise = $100 Put premium = $1,166 Contract Size 100 shares Xx = $100 Stock Price t Profit $0 $1,166$100$111.66$ $8,834  Bullish or bearish? Alternative Stock Strategy?  High or low volatility strategy? S T – X + P 0 S T – X + P 0 +P 0 Long Position in IBM

15-22 Buy stocks and at the money puts: Protective Put Stock Price t Profit $0 Hedged profit equals sum of profits of put and stock at each stock price. Long position in IBM Hedged Position Put X

15-23 Writing Covered Calls Stock Price t Profit $0 Long position in IBM Written call Covered Call Bullish or bearish? High or low volatility strategy? S T = S 0 - C 0 S0S0

15-24 Bullish Price Spread  Bull perpendicular or price spread with calls; write (sell) the high exercise price call and buy the low exercise price call. All other option terms identical. L=low exercise price, H=high exercise price

15-25 Bullish Price Spread + S T = X L + C 0L – C 0H– Breakeven X H – X L – C 0L + C 0H S T – X L – C 0L +C 0H C 0H – C 0L = Profit –(S T – X H )00– C TH S T – X L 0+C TL +C 0H – C 0L S T > X H X L < S T < X H S T < X L Profit Table BULLISH PRICE SPREAD Stock Price t Profit XLXLXLXL XHXHXHXH Bullish or bearish?Bullish or bearish? High or low volatility strategy?High or low volatility strategy?

15-26 Long or Bull Straddle Long or bull straddle: buy a put and a call with the same T and X. (For bear or short straddle, sell both put and call and just flip the graph upside down.)

15-27 Long or Bull Straddle S T = X + C 0 + P 0 S T = X – C 0 – P 0 Breakeven S T – X – C 0 – P 0 X – S T – C 0 – P 0 = Profit 0X – S T +P T S T – X0+C T – P 0 – C 0 S T > XS T < XProfit Table BULL STRADDLE Stock Price t t Profit $0 Stock Price t t Profit $0 X – C 0 – P 0 X + C 0 + P 0 Bullish or bearish? _____________Bullish or bearish? _____________ High or low volatility strategy?High or low volatility strategy? X Neutral Max Loss: C 0 + P 0

15-28 Strips and Straps Long or bull strap; buy two calls and one put, more bullish than straddle. Long or bull strip; buy two puts and one call, more bearish than straddle. Think about bear versions of each.

15-29 Short Strangle: Sell out of the money put and call S T = X H + P 0L + C 0H+S T = X L – P 0L – C 0H Breakeven X H – S T + P 0L + C 0H P 0L + C 0H S T – X L + P 0L + C 0H = Profit –(S T – X H )00– C TH 00– (X L – S T )– P TL +C 0H + P 0L S T > X H X L < S T < X H S T < X L Profit Table Short Strangle Stock Price t Profit XLXL XHXH S T = X L –P 0L –C 0H S T = X H + P 0L + C 0H

Warnings about options positions oOptions may have to move 10-15% or more in a short time period before an investor recovers the price & commission. oOptions are by definition short term instruments; an investor can ride out bad times in spot markets but not in options. –The limited loss feature makes options appear safer than they are. –You have to compare equal $ investments in stocks and options to really see the higher risk of the option position. oOptions are traded in a highly competitive market.

Warnings about options positions What’s wrong with selling options? oCovered calls (writing calls against stock you own) –The investor never gets the occasional large stock price run up and suffers most of the loss of a big price drop. Eliminates any positive skewness of stock returns –Wind up with portfolio of poorer performers oNaked calls (writing calls when you do not own the stock) –Maximum gain is limited to call premium but unlimited loss, poor strategy in volatile markets

15-32 Optionlike Securities 1.Callable bonds –Issuing firm has the right to call in the bond and pay call price. –When will the firm want to exercise its call option?

15-33 Figure Values of Callable Bonds Compared with Straight Bonds

Convertible Securities Security holder has the option to convert the bond to a fixed number of shares of common stock. Bond’s Conversion Value = Conversion Ratio x Common Stock Price If a bond is convertible to 20 shares of stock, stock is priced at $60 per share. The bond’s conversion value = $1,200

15-35 Figure Value of a Convertible Bond as a Function of Stock Price The option is issued deep out the money, the ‘option cost’ is a lower coupon.

15-36 Convertibles (cont.) Theoretical value of a convertible bond = Value straight debt + Value of conversion option In reality there are three complicating factors: 1.The conversion price may increase over time effectively increasing the option’s exercise price. 2.Stocks may pay dividends, this makes it harder to value the option to convert 3.Virtually all convertible bonds are callable by the firm. The firm may call to force conversion, this makes the maturity of the bond and the option indeterminate.

Warrants –Firm sometimes issue warrants with its bonds. The warrants are call options to purchase new stock at a fixed price. –Detachable “sweetener” to help sell the bond –Exercise of warrants (and convertibles) can result in dilution of earnings per share

Collateralized loans –Suppose a borrower is obligated to pay back L dollars at loan maturity (Time T) and has posted collateral worth S t dollars. –The borrower has an option to repay the loan at maturity if L > S T, otherwise the borrower can default and give up the value of L. 5.A similar logic applies to corporate equity if a firm has debt. –Equity holders effectively have a call option on firm value as they can choose to pay off the debt if firm value > value of the debt or default otherwise.

15-39 Collateralized Loan Payoffs

15-40 Exotic Options  Asian Options  Barrier Options  Lookback Options Payoff depends on the average (rather than the final) price of the underlying asset during a portion of the life of the option. Example “down-and-out” expires worthless if the stock price drops below a specified barrier. Payoff depends on minimum or max price during life of option.

15-41 Exotic Options  Currency Translated Options or Quantos  Binary or Digital Options Allows a variable amount of foreign currency based on the performance of an investment to be translated to dollars at a fixed exchange rate. Pays a fixed amount if the option is in the money at expiration.

15-42 Problem 1 a. b. Purchase a straddle, i.e., buy both a put and a call on the stock. The total cost of the straddle would be: $10 + $7 = $17 $17

15-43 Problem 2 – S T = X L + C 0L – C 0H+ Breakeven X L – X H + C 0L – C 0H X L – S T – C 0H +C 0L C 0L – C 0H = Profit S T – X H 00+ C TH –(S T – X L ) 0– C TL – C 0H + C 0L S T > X H X L < S T < X H S T < X L Profit Table BEARISH PRICE SPREAD Stock Price t Profit XLXL XHXH

15-44 Problem 3 S T = $1,260 Breakeven S T – $1,260 – $60= Profit 0$1,200 – S T +P T – $60 – P 0 S T – $1,200 S T > $1,200S T < $1,200Profit Table Joe’s Protective Put Strategy S T = $1,245Breakeven S T – $1,245 – $75= Profit 0$1,170 – S T +P T – $45 – P 0 S T – $1,200 S T > $1,170S T < $1,170Profit Table Sally’s Protective Put Strategy Joe’s -$60 $1260 Sally’s -$75 $1245