ADAPTED FOR THE SECOND CANADIAN EDITION BY: THEORY & PRACTICE JIMMY WANG LAURENTIAN UNIVERSITY FINANCIAL MANAGEMENT

CHAPTER 19 FINANCIAL OPTIONS AND APPLICATIONS IN CORPORATE FINANCE

CHAPTER 19 OUTLINE Financial Options Introduction to Option Pricing Models: The Binomial Approach The Valuation of Put Options Applications of Option Pricing in Corporate Finance Copyright © 2014 by Nelson Education Ltd. 19-3

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Financial Options An option is a contract that gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time Copyright © 2014 by Nelson Education Ltd. 19-5

What is the Single Most Important Characteristic of an Option? It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset. Copyright © 2014 by Nelson Education Ltd. 19-6

Option Terminology Call option: An option to buy a specified number of shares of a security within some future period Put option: An option to sell a specified number of shares of a security within some future period Copyright © 2014 by Nelson Education Ltd. 19-7

Option Terminology (cont’d) Strike (or exercise) price: The price stated in the option contract at which the security can be bought or sold Option price: The market price of the option contract Copyright © 2014 by Nelson Education Ltd. 19-8

Option Terminology (cont’d) American option: An option can be exercised any time before it expires. European option: An option can only be exercised on its expiration date Writer: The seller of an option Copyright © 2014 by Nelson Education Ltd. 19-9

Option Terminology (cont’d) BuyerSeller Call OptionRight to buy assetObligation to sell asset Put OptionRight to sell assetObligation to buy asset Copyright © 2014 by Nelson Education Ltd

Option Terminology (cont’d) Expiration date: The last day that the option contract can be exercised Exercise value: The value of an option if it were exercised today (for a call = current stock price – strike price; for a put = strike price – current stock price) Note: The exercise value is zero if the stock price is less than the strike price for a call. Exercise value = max [current price of stock – strike price, 0] for a call. Copyright © 2014 by Nelson Education Ltd

Option Terminology (cont’d) In-the-money call: A call whose strike price is less than the current price of the underlying stock Out-of-the-money call: A call option whose strike price exceeds the current stock price At-the-money call: A call option whose strike price is equal to the current stock price Copyright © 2014 by Nelson Education Ltd

Option Terminology (cont’d) In-the-money put: A put whose strike price exceeds the current price of the underlying stock Out-of-the-money put: A put option whose strike price is less than the current stock price At-the-money put: A put option whose strike price is equal to the current stock price Copyright © 2014 by Nelson Education Ltd

Option Terminology (cont’d) Covered option: A call option written against a stock held in an investor’s portfolio Naked (uncovered) option: An option sold without the stock to back it up Copyright © 2014 by Nelson Education Ltd

Option Terminology (cont’d) LEAPS: Long-Term Equity AnticiPation Securities, which are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years Copyright © 2014 by Nelson Education Ltd

Consider the Following Data: Strike price = $25 Stock PriceCall Option Price $25$ Copyright © 2014 by Nelson Education Ltd

Exercise Value of Option Price of stock (a) Strike price (b) Exercise value of option (a)–(b) $25.00 $ Copyright © 2014 by Nelson Education Ltd

Market Price of Option Price of stock (a) Strike price (b) Exer. val. (c) Mkt. Price of opt. (d) $25.00 $0.00 $ Copyright © 2014 by Nelson Education Ltd

Time Value of Option Price of stock (a) Strike price (b) Exer. Val. (c) Mkt. P of opt. (d) Time value (d) – (c) $25.00 $0.00 $ Copyright © 2014 by Nelson Education Ltd

Call Time Value Diagram Stock price Option value Market price Exercise value Copyright © 2014 by Nelson Education Ltd

Option Time Value vs. Exercise Value The time value, which is the option price less its exercise value, declines as the stock price increases. This is due to the declining degree of leverage provided by options as the underlying stock price increases and the greater loss potential of options at higher option prices. Copyright © 2014 by Nelson Education Ltd

Determinants of the Price of an Option As this variable increasesThe price of CALL optionThe price of PUT option Market price versus strike priceIncreasesDecreases Level of strike priceDecreasesIncreases Length of optionIncreases Volatility of stock priceIncreases Level of interest ratesIncreasesDecreases Copyright © 2014 by Nelson Education Ltd

Introduction to Option Pricing Models: The Binomial Approach All option pricing models are based on the concept of a riskless hedge. Portfolio replication is the technique often used to evaluate the option price. Option contracts can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as these options. The binomial approach assumes that stock prices can move to only two values over any short time period. Copyright © 2014 by Nelson Education Ltd

Binomial Option Pricing Five steps involved in the process: 1.Define the possible ending prices of the stock. 2.Find the range of option values at expiration. 3.Buy exactly enough stock to equalize the range of payoffs for the stock and the option. N = (C u – C d ) / (P u – P d ) Copyright © 2014 by Nelson Education Ltd

Binomial Option Pricing (cont’d) 4.Create a riskless hedged investment. The value of the portfolio stays regardless of whether stock goes up or down, so the portfolio is riskless. 5.Find the call option’s price. – PV of portfolio = current value of stock in portfolio – current option price – Current option price = current value of stock in portfolio – PV of portfolio Copyright © 2014 by Nelson Education Ltd

The Black-Scholes Option Pricing Model (OPM) OPM assumptions: The stock underlying the call option provides no dividends during the call option’s life. There are no transactions costs for the sale/purchase of either the stock or the option. R RF is known and constant during the option’s life. Copyright © 2014 by Nelson Education Ltd

Assumptions (cont’d) Security buyers may borrow any fraction of the purchase price at the short-term risk-free rate. No penalty for short selling, and sellers receive immediately the full cash proceeds at today’s price. The call option can be exercised only on its expiration date. Security trading takes place in continuous time, and stock prices move randomly in continuous time. Copyright © 2014 by Nelson Education Ltd

OPM Equations V = P[N(d 1 )] – Xe -r RF t [N(d 2 )] d 1 =  t 0.5 d 2 = d 1 –  t 0.5 ln(P/X) + [r RF + (  2 /2)]t Copyright © 2014 by Nelson Education Ltd

OPM Illustration Assume: P = $20 X = $20 r RF = 6.4% t = 0.25 year or 3 months σ 2 = 0.16 (that is, σ = 0.4) What is the value of the following call option according to the OPM? Copyright © 2014 by Nelson Education Ltd

First: Find D 1 and D 2 d 1 = {ln($20/$20) + [( /2)](0.25)} ÷ {(0.4)(0.25) 0.5 } d 1 = ( )/0.2 = d 2 = d 1 – (0.4)(0.25) 0.5 d 2 = – 0.20 =–0.020 Copyright © 2014 by Nelson Education Ltd

Second: Find N(D1) and N(D2) N(d 1 ) = N(0.180) = = N(d 2 ) = N(–0.020) = – = Note: Values obtained from Excel using NORMSDIST function. For example: N(d 1 ) = NORMSDIST(0.180) = Copyright © 2014 by Nelson Education Ltd

Third: Find Value of Option V = $20 × N(d 1 ) – $20 × e –(0.064)(0.25) × N(d 2 ) = $20(0.5714) – $20e –(0.064)(0.25) (0.4920) = $11.43 – $20(0.9851)(0.4920) = $11.43 – $9.69 = $1.74 Copyright © 2014 by Nelson Education Ltd

Impacts of OPM Parameters How do the following factors affect a call option’s value? Current stock price: A call option value increases as the current stock price increases. Strike price: As the exercise price increases, a call option’s value decreases. Copyright © 2014 by Nelson Education Ltd

Impact on Call Value (cont’d) Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.) Risk-free rate: Call option’s value tends to increase as r RF increases (reduces the PV of the exercise price). Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money). Copyright © 2014 by Nelson Education Ltd

Effects of OPM Factors CasePXTr RF σ2σ2 V call Base case$ %0.16$1.74 ↑P by $ %0.16$5.57 ↑x by $ %0.16$0.34 ↑t to 6 months %0.16$2.54 ↑r RF to 9% %0.16$1.81 ↑σ 2 to %0.25$2.13 Copyright © 2014 by Nelson Education Ltd

The Valuation of Put Options A put option gives its holder the right to sell a share of stock at a specified stock on or before a particular date. Copyright © 2014 by Nelson Education Ltd

Put-Call Parity Portfolio 1: – Put option – Share of stock, P Portfolio 2: – Call option, V – PV of exercise price, X Copyright © 2014 by Nelson Education Ltd

Portfolio Payoffs at Expiry Date T for P T <X and P T ≥X P T <XP T ≥X Port. 1Port. 2Port. 1Port. 2 StockPTPT PTPT PutX – P T 0 Call0P T – X CashXX TotalXXPTPT PTPT Copyright © 2014 by Nelson Education Ltd

Put-Call Parity Relationship Portfolio payoffs are equal, so portfolio values also must be equal. Put + Stock = Call + PV of Exercise Price Put + P = V + Xe -r RF t Put = V – P + Xe -r RF t Copyright © 2014 by Nelson Education Ltd

Illustration: Put-Call Parity Given: V call = $1.74, P = $20, X = $20, r RF = 6.4%, t = 0.25 year Apply the put-call parity relationship – V put = V call – P + Xe –r RF t =$1.74 – $20 + $20e –(0.064)(0.25) = $1.74 – $20 + $19.68 = $1.42 Note: This put must have the same exercise price and expiration date as the call. Copyright © 2014 by Nelson Education Ltd

Applications of Option Pricing in Corporate Finance Option pricing is used in four major areas in corporate finance: 1.Real options analysis for project (real asset) evaluation and strategic decisions 2.Risk management (options serve as insurance) 3.Capital structure decisions (equity seen as a call and option-like securities) 4.Compensation plans (stock option) Copyright © 2014 by Nelson Education Ltd