Option Pricing with Applications to Real Options.ppt
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1、,Financial optionsBlack-Scholes Option Pricing ModelReal optionsDecision treesApplication of financial options to real options,CHAPTER 17Option Pricing with Applications to Real Options,What is a real option?,Real options exist when managers can influence the size and risk of a projects cash flows b
2、y taking different actions during the projects life in response to changing market conditions.Alert managers always look for real options in projects.Smarter managers try to create real options.,An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an ass
3、et at some predetermined price within a specified period of time.,What is a financial option?,It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset.,What is the single most importantcharacteristic of an option?,Call option: An option to buy a
4、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.Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold.,Option Terminology,Op
5、tion price: The market price of the option contract. Expiration date: The date the option matures.Exercise value: The value of a call option if it were exercised today = Current stock price - Strike price.Note: The exercise value is zero if the stock price is less than the strike price.,Covered opti
6、on: A call option written against stock held in an investors portfolio.Naked (uncovered) option: An option sold without the stock to back it up.In-the-money call: A call whose exercise price is less than the current price of the underlying stock.,Out-of-the-money call: A call option whose exercise p
7、rice exceeds the current stock price.LEAPs: Long-term Equity AnticiPation securities that are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years.,Exercise price = $25.Stock PriceCall Option Price$25$ 3.00 30 7.50 35 12.00 40 16.50 45 21.00 50
8、25.50,Consider the following data:,Create a table which shows (a) stockprice, (b) strike price, (c) exercisevalue, (d) option price, and (e) premiumof option price over the exercise value.,Price of Strike Exercise ValueStock (a) Price (b) of Option (a) - (b)$25.00$25.00$0.00 30.00 25.00 5.00 35.00 2
9、5.00 10.00 40.00 25.0015.00 45.00 25.0020.00 50.00 25.0025.00,Exercise Value Mkt. Price Premium of Option (c) of Option (d) (d) - (c) $ 0.00 $ 3.00 $ 3.00 5.00 7.50 2.50 10.00 12.00 2.00 15.00 16.50 1.50 20.00 21.00 1.00 25.00 25.50 0.50,Table (Continued),Call Premium Diagram,5 10 15 20 25 30 35 40
10、45 50,Stock Price,Option value,30252015105,Market price,Exercise value,What happens to the premium of the option price over the exercisevalue as the stock price rises?,The premium of the option price over the exercise value declines as the stock price increases.This is due to the declining degree of
11、 leverage provided by options as the underlying stock price increases, and the greater loss potential of options at higher option prices.,The stock underlying the call option provides no dividends during the call options life.There are no transactions costs for the sale/purchase of either the stock
12、or the option.RRF is known and constant during the options life.,What are the assumptions of theBlack-Scholes Option Pricing Model?,(More.),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 full
13、 cash proceeds at todays price.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.,V = PN(d1) - Xe -rRFtN(d2).d1 = . td2 = d1 - t.,What are the three equations thatmake up the OPM?,ln(P/X) + rRF
14、 + (2/2)t,What is the value of the following call option according to the OPM?Assume: P = $27; X = $25; rRF = 6%;t = 0.5 years: 2 = 0.11,V = $27N(d1) - $25e-(0.06)(0.5)N(d2). ln($27/$25) + (0.06 + 0.11/2)(0.5)(0.3317)(0.7071) = 0.5736.d2 = d1 - (0.3317)(0.7071) = d1 - 0.2345 = 0.5736 - 0.2345 = 0.33
15、91.,d1 =,N(d1) = N(0.5736) = 0.5000 + 0.2168 = 0.7168.N(d2) = N(0.3391) = 0.5000 + 0.1327 = 0.6327.Note: Values obtained from Excel using NORMSDIST function.V = $27(0.7168) - $25e-0.03(0.6327) = $19.3536 - $25(0.97045)(0.6327) = $4.0036.,Current stock price: Call option value increases as the curren
16、t stock price increases.Exercise price: As the exercise price increases, a call options value decreases.,What impact do the following para-meters have on a call options value?,Option period: As the expiration date is lengthened, a call options value increases (more chance of becoming in the money.)R
17、isk-free rate: Call options value tends to increase as rRF 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).,How are real options different from financial options?,Financial opt
18、ions have an underlying asset that is traded-usually a security like a stock.A real option has an underlying asset that is not a security-for example a project or a growth opportunity, and it isnt traded.,(More.),How are real options different from financial options?,The payoffs for financial option
19、s are specified in the contract.Real options are “found” or created inside of projects. Their payoffs can be varied.,What are some types of real options?,Investment timing optionsGrowth options Expansion of existing product lineNew productsNew geographic markets,Types of real options (Continued),Aba
20、ndonment optionsContractionTemporary suspensionFlexibility options,Five Procedures for ValuingReal Options,1.DCF analysis of expected cash flows, ignoring the option. 2.Qualitative assessment of the real options value.3.Decision tree analysis.4.Standard model for a corresponding financial option.5.F
21、inancial engineering techniques.,Analysis of a Real Option: Basic Project,Initial cost = $70 million, Cost of Capital = 10%, risk-free rate = 6%, cash flows occur for 3 years. AnnualDemand Probability Cash FlowHigh30%$45Average40%$30Low30%$15,Approach 1: DCF Analysis,E(CF)=.3($45)+.4($30)+.3($15) =
22、$30.PV of expected CFs = ($30/1.1) + ($30/1.12) + ($30/1/13) = $74.61 million.Expected NPV = $74.61 - $70 = $4.61 million,Investment Timing Option,If we immediately proceed with the project, its expected NPV is $4.61 million.However, the project is very risky:If demand is high, NPV = $41.91 million.
23、*If demand is low, NPV = -$32.70 million.*_* See Ch 17 Mini Case.xls for calculations.,Investment Timing (Continued),If we wait one year, we will gain additional information regarding demand.If demand is low, we wont implement project. If we wait, the up-front cost and cash flows will stay the same,
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