McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 20 Options Markets: Introduction

20-2 Options A call [put] option give the buyer the right to purchase [sell] an asset for a predetermined price (the strike or eXercise price) through the maturity date. Options are only traded on volatile stocks These are side bets made on the price of a stock and issuer of the stock has nothing to do with the options markets on its stocks

20-3 Buy - Long Sell - Short Call Put Key Elements Exercise or Strike Price Premium or Price Maturity or Expiration Option Terminology

20-4 In the Money – immediate exercise of the option would yield a positive cash flow. Call: market price > exercise price Put: exercise price>market price Out of the Money - exercise of the option would yield a negative cash flow (so don’t exercise). Call: market price < exercise price Put: exercise price < market price At the Money - exercise price and asset price are equal. Market and Exercise Price Relationships

20-5 American - the option can be exercised at any time before expiration or maturity. European - the option can only be exercised on the expiration or maturity date. American vs. European Options

20-6 Adjustments to Contract If a stock splits there is a corresponding adjustment to the strike price. In other words, there is no difference in the payoffs to an option due to a stock split There is no adjustment for the cash dividends that a stock pays

20-7 Stock Options – may have to deliver the stock Index Options – are settled in cash Futures Options – options to buy future contracts at the exercise price Foreign Currency Options – right to buy foreign currency at a specified price Interest Rate Options – various interest rate related on fixed income securities or interest rate futures Different Types of Options

20-8 Notation T= expiration date Stock Price = S T eXercise Price = X Payoff to Call Holder ( S T - X) if S T >X 0if S T < X (the “optional” part) Profit to Call Holder Payoff - Purchase Price (or premium) Payoffs and Profits at Expiration - Calls

20-9 Payoff to Call Writer (put a minus sign in front of the payoff to call holder). The call writer does not have an option – must respond to the buyer of the option. - ( S T - X) if S T >X 0if S T < X Profit to Call Writer Payoff + Premium Payoffs and Profits at Expiration - Calls

20-10 Profit Profiles for Calls Profit Stock Price 0 Call Writer Call Holder X

20-11 Payoffs to Put Holder 0if S T > X (X - S T ) if S T < X Profit to Put Holder Payoff - Premium Payoffs and Profits at Expiration - Puts

20-12 Payoffs to Put Writer 0if S T > X -(X - S T )if S T < X Profits to Put Writer Payoff + Premium Payoffs and Profits at Expiration - Puts

20-13 Profit Profiles for Puts 0 Profits Stock Price Put Writer Put Holder X

20-14 InvestmentStrategyInvestment Equity onlyBuy shares$10,000 Options onlyBuy options*$10,000 LeveragedBuy options $1,000 equityBuy 3% $9,000 Yield Equity, Options & Leveraged Equity S 0 = 100, X=100 *10 contracts of 100 options

20-15 Ending Stock Price $95$105$115 All Stock$9,500$10,500$11,500 All Options$0 $5,000$15,000 Lev Equity $9,270* $9,770$10,770 Equity, Options Leveraged Equity - Payoffs

20-16 IBM Stock Price $95$105$115 All Stock-5.0%5.0% 15% All Options-100% -50% 50% Lev Equity -7.3%-2.3% 7.7% HPR - Rates of Return See Figure 20.6 for plot of hpr’s

20-17 Option Strategies - Protective Put Use – Portfolio insurance (limit loss) Position - long the stock and long the put PayoffS T X Stock S T S T Put X - S T 0 Portfolio X S T

20-18 Protective Put Profit (for X=S 0 ) STST Profit X-(S 0 +P) Stock Protective Put Portfolio -P

20-19 Covered Call Use – To increase the yield of your stock (by selling the call) when you think the stock won’t go up in the short run. Position - Own the stock and write a call. PayoffS T X Stock S T S T Call 0 - ( S T - X) Portfolio S T X

20-20 Covered Call Profit (S 0 = X) STST Profit Stock Covered Call Portfolio

20-21 Long Straddle (Same Exercise Price) Long Call and Long Put Useful if you believe the stock price will move a lot, but you don’t know in which direction See Figure for payoffs and profits Other Option Strategies

20-22 Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration. Vertical or money spread: Same maturity Different exercise price Horizontal or time spread: Different maturity dates Other Option Strategies

20-23 Put Call Parity – Consider a Ptf with 0 payoff ActionCF todayS T < XS T > X Buy Stock-S 0 STST STST Buy Put-PX - S T 0 Sell BondX/(1+r)-X Sell CallC0-(S T – X) Total CF*00 * = -S 0 – P + X/(1+r) + C = 0

20-24 Put – Call Parity -S 0 – P + X/(1+r) + C = 0 Rewrite as: P = X/(1+r) + C – S 0 Where: P=price of put C=price of call S = stock price today X = eXercise price r = risk free holding period return

20-25 Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal. C - P = S 0 - X / (1 + r f ) T If the prices are not equal arbitrage will be possible. Arbitrage & Put Call Parity

20-26 Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 10.25% Maturity =.5 yr X = 105 C - P > S 0 - X / (1 + r f ) T > (105/1.05) 12 > 10 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative. Put Call Parity - Disequilibrium Example

20-27 Put-Call Parity Arbitrage ImmediateCashflow in Six Months PositionCashflowS T 105 Buy Stock-110 S T S T Borrow X/(1+r) T = Sell Call+17 0-(S T -105) Buy Put S T 0 Total 2 0 0

20-28 Optionlike Securities Callable Bonds Convertible Securities Warrants (like call options, but issued by firm, and lead to some stock dilutions, though the firm receives the strike price) Collateralized Loans (value of the collateral becomes the S T, and the loan amount is the strike price) Financially engineered products

20-29 Exotic Options Asian Options – payoff depends on average prices over a period Barrier Options – payoff depends on whether a price has crossed a barrier Lookback Options – depends on max or min price over a period Currency Translated Options – asset or exercise price denominated in a foreign currency Binary Options – a fixed payoff depending on whether a condition is met