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Chapter 15

CFIN501- Chapter 15- Option Valuation.docx

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FIN 501
Edward Blinder

CFIN501 Chapter 15 Option ValuationA Simple Model To Value Options Before ExpirationOption is worth its intrinsic value at expirationCalculate intrinsic valuewe need strike price and stock price at option expirationoWe know the strike price today and at option expiration stock price today we dont know what the stock price will be in one yearoAssume that today we know the range of possible values for the underlying asset at option expirationMany other pairs of stock prices also result in a zero value for the put selecting particular stock prices is not what allows us to calculate the call option priceAllows us to calculate the call option price wereoChosen pair of stock prices guarantees that the call option will finish in the moneyoChosen pair of stock prices also guarantees that a put option with the same strike will finish out the moneyPricing a call option when we are contain that the call option will finish somewhere in the money is easyoUse put option value if zero and the put call parity equation to obtain the value of the call option before it expiresThe OnePeriod Binomial Option Pricing ModelThe AssumptionsThe stock price in one period is either SuSdou up factorbigger than 1 od down factorless than 1The Set UpSuppose an investoroBuys one share of stockoSells one call optionWrite down all the prices that we know today and all the prices we know at expirationoWorld of option pricing modelscollection of stock or options prices is known as treeThe FormulaForm portfolio of stock and options that is worth the same amount regardless of the price of the stock in one periodoInstead of buying one sharesuppose the investor buys a fractional share of stock Key solutionhinges on the fact that the investor can choose the size of the fractional shareCCSuSdudCall price todayriskless portfolio today should be worth SC1rSC1rSuCuS1ruCuC1rWhat Is DeltaDelta is a proportion of shares to calls that is needed to form a risk free portfoliooPortfolio of shares and calls that does not change in value when stock price changes23 we need 2 shares and 3 calls to form a risk free portfoliooPortfolio is risk free losses gains in the call options are offset by gains losses in the stickFractional share amount needed to offset or hedge changes in price of one callThe TwoPeriod Binomial Option Pricing ModelCalculating the price of a European call optionuse this method to calculate the price of a put as wellSlight modification to allow for early exercisealso be used to calculate prices for American calls and putsCan be used to price an exotic array of optionsStep 1 Build A Price Tree For Stock Prices Through TimeThree stock prices in 2 periodscorresponding to a sequence of 1
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