CHAPTER TWENTY-FOURTYPES OF OPTION CONTRACTSCALL OPTIONSSlide 4PUT OPTIONSOPTION TRADINGOPTION TRADINGSlide 8THE VALUATION OF OPTIONSSlide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19THE BINOMIAL OPTION PRICING MODEL (BOPM)Slide 21Slide 22Slide 23Slide 24THE BINOMIAL OPTION PRICING MODEL (Price Tree)Slide 26Slide 27BOPM: REPLICATING PORTFOLIOSSlide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35THE HEDGE RATIOSlide 37Slide 38Slide 39PUT-CALL PARITYSlide 41Slide 42THE BLACK-SCHOLES MODELTHE BLACK-SCHOLES MODELSlide 45Slide 46Slide 47Slide 48Slide 491CHAPTER TWENTY-FOUROPTIONS2TYPES OF OPTION CONTRACTS•WHAT IS AN OPTION?–Definition: a type of contract between two investors where one grants the other the right to buy or sell a specific asset in the future–the option buyer is buying the right to buy or sell the underlying asset at some future date–the option writer is selling the right to buy or sell the underlying asset at some future date3CALL OPTIONS•WHAT IS A CALL OPTION CONTRACT?–DEFINITION: a legal contract that specifies four conditions–FOUR CONDITIONS•the company whose shares can be bought•the number of shares that can be bought•the purchase price for the shares known as the exercise or strike price•the date when the right expires4CALL OPTIONS•Role of Exchange•exchanges created the Options Clearing Corporation (CCC) to facilitate trading a standardized contract (100 shares/contract)•OCC helps buyers and writers to “close out” a position5PUT OPTIONS•WHAT IS A PUT OPTION CONTRACT?–DEFINITION: a legal contract that specifies four conditions•the company whose shares can be sold•the number of shares that can be sold•the selling price for those shares known as the exercise or strike price•the date the right expires6OPTION TRADING •FEATURES OF OPTION TRADING–a new set of options is created every 3 months–new options expire in roughly 9 months–long term options (LEAPS) may expire in up to 2 years–some flexible options exist (FLEX)–once listed, the option remains until expiration date7OPTION TRADING•TRADING ACTIVITY–currently option trading takes place in the following locations:•the Chicago Board Options Exchange (CBOS)•the American Stock Exchange•the Pacific Stock Exchange•the Philadelphia Stock Exchange (especially currency options)8OPTION TRADING•THE MECHANICS OF EXCHANGE TRADING–Use of specialist–Use of market makers9THE VALUATION OF OPTIONS•VALUATION AT EXPIRATION (E)–FOR A CALL OPTION-100100200stock pricevalueof optionE010THE VALUATION OF OPTIONS•VALUATION AT EXPIRATION–ASSUME: the strike price = $100–For a call if the stock price is less than $100, the option is worthless at expiration–The upward sloping line represents the intrinsic value of the option11THE VALUATION OF OPTIONS•VALUATION AT EXPIRATION–In equation formIVc= max {0, Ps, -E}where Ps is the price of the stock E is the exercise price12THE VALUATION OF OPTIONS•VALUATION AT EXPIRATION–ASSUME: the strike price = $100–For a put if the stock price is greater than $100, the option is worthless at expiration–The downward sloping line represents the intrinsic value of the option13THE VALUATION OF OPTIONS•VALUATION AT EXPIRATION–FOR A PUT OPTION100valueofthe optionstock priceE=100014THE VALUATION OF OPTIONS•VALUATION AT EXPIRATION–FOR A CALL OPTION•if the strike price is greater than $100, the option is worthless at expiration15THE VALUATION OF OPTIONS–in equation formIVc= max {0, - Ps, E}where Ps is the price of the stock E is the exercise price16THE VALUATION OF OPTIONS•PROFITS AND LOSSES ON CALLS AND PUTS100100p PPROFITS PROFITS00CALLS PUTSLOSSES LOSSES17THE VALUATION OF OPTIONS•PROFITS AND LOSSES–Assume the underlying stock sells at $100 at time of initial transaction–Two kinked lines = the intrinsic value of the options18THE VALUATION OF OPTIONS•PROFIT EQUATIONS (CALLS)C= IVC - PC= max {0,PS - E} - PC= max {-PC , PS - E - PC }This means that the kinked profit line for the call is the intrinsic value equation less the call premium (- PC )19THE VALUATION OF OPTIONS•PROFIT EQUATIONS (CALLS)P= IVP - PP= max {0, E - PS} - PP= max {-PP , E - PS - PP }This means that the kinked profit line for the put is the intrinsic value equation less the put premium (- PP )20THE BINOMIAL OPTION PRICING MODEL (BOPM)•WHAT DOES BOPM DO?–it estimates the fair value of a call or a put option21THE BINOMIAL OPTION PRICING MODEL (BOPM)•TYPES OF OPTIONS–EUROPEAN is an option that can be exercised only on its expiration date–AMERICAN is an option that can be exercised any time up until and including its expiration date22THE BINOMIAL OPTION PRICING MODEL (BOPM)•EXAMPLE: CALL OPTIONS–ASSUMPTIONS:•price of Widget stock = $100•at current t: t=0•after one year: t=T•stock sells for either$125 (25% increase)$ 80 (20% decrease)23THE BINOMIAL OPTION PRICING MODEL (BOPM)•EXAMPLE: CALL OPTIONS–ASSUMPTIONS: •Annual riskfree rate = 8% compounded continuously•Investors cal lend or borrow through an 8% bond24THE BINOMIAL OPTION PRICING MODEL (BOPM)•Consider a call option on WidgetLet the exercise price = $100the exercise date = Tand the exercise value:If Widget is at $125 = $25or at $80 = 025THE BINOMIAL OPTION PRICING MODEL (Price Tree)t=0 t=.5T t=T$125 P0=25$80 P0=$0$100$100$111.80$89.44$125 P0=65$100 P0=0$80 P0=0Annual Analysis:Semiannual Analysis:26THE BINOMIAL OPTION PRICING MODEL (BOPM)•VALUATION–What is a fair value for the call at time =0?•Two Possible Future States–The “Up State” when p = $125–The “Down State” when p = $8027THE BINOMIAL OPTION PRICING MODEL (BOPM)•SummarySecurity Payoff: Payoff: CurrentUp state Down state PriceStock $125.00 $ 80.00 $100.00Bond 108.33 108.33 $100.00Call 25.00 0.00 ???28BOPM: REPLICATING PORTFOLIOS•REPLICATING PORTFOLIOS–The Widget call option can be replicated –Using an appropriate combination of •Widget Stock and •the 8% bond–The cost of replication equals the fair value of the option29BOPM: REPLICATING PORTFOLIOS•REPLICATING PORTFOLIOS–Why?•if otherwise, there would be an arbitrage opportunity–that is, the investor could buy the cheaper of the two alternatives and sell the more expensive one30BOPM: REPLICATING PORTFOLIOS–COMPOSITION OF THE REPLICATING PORTFOLIO:•Consider a portfolio with Ns shares of