Chapter 11 Options Road Map Part A Introduction to nance Part B Valuation of assets given discount rates Part C Determination of risk adjusted discount rate Part D Introduction to derivatives Forwards and futures Options Real options Main Issues Introduction to Options Use of Options Properties of Option Prices Valuation Models of Options Chapter 11 Options 11 1 1 Introduction to Options 1 1 De nitions Option types Call Gives owner the right to purchase an as set the underlying asset for a given price exercise price on or before a given date expiration date Put Gives owner the right to sell an asset for a given price on or before the expiration date Exercise styles European Gives owner the right to exercise the option only on the expiration date American Gives owner the right to exercise the option on or before the expiration date Key elements in de ning an option Underlying asset and its price S Exercise price strike price K Expiration date maturity date T today is 0 European or American Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 11 2 Options Chapter 11 1 2 Option Payo The payo of an option on the expiration date is determined by the price of the underlying asset Example Consider a European call option on IBM with exercise price 100 This gives the owner buyer of the option the right not the obligation to buy one share of IBM at 100 on the expiration date Depending on the share price of IBM on the expiration date the option owner s payo looks as follows IBM Price 80 90 100 110 120 130 Action Not Exercise Not Exercise Not Exercise Not Exercise Exercise Exercise Exercise Exercise Payo 0 0 0 0 10 20 30 ST 100 Note The payo of an option is never negative Sometimes it is positive Actual payo depends on the price of the underlying asset 15 401 Lecture Notes c cid 2 J Wang Fall 2006 Chapter 11 Options 11 3 cid 2 Payo s of calls and puts can be described by plotting their payo s at expiration as function of the price of the underlying asset Payo of buying a call cid 3 100 100 cid 4 Payo of selling a call cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 100 100 cid 3 cid 3 cid 3 cid 2 Asset price Asset price cid 2 cid 3 cid 3 cid 3 cid 3 Payo of buying a put cid 3 100 cid 3 cid 3 cid 2 cid 2 cid 2 100 cid 4 Payo of selling a put cid 3 cid 3 cid 3 cid 3 cid 3 100 100 cid 2 cid 2 cid 2 cid 2 cid 2 Asset price Asset price cid 2 Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 11 4 Options Chapter 11 The net payo from an option must includes its cost Example A European call on IBM shares with an exercise price of 100 and maturity of three months is trading at 5 The 3 month interest rate not annualized is 0 5 What is the price of IBM that makes the call break even At maturity the call s net payo is as follows IBM Price 80 90 100 110 120 130 Action Payo Net payo Not Exercise Not Exercise Not Exercise Not Exercise Exercise Exercise Exercise Exercise 0 0 0 0 10 20 30 5 025 5 025 5 025 5 025 4 975 14 975 24 975 ST 100 ST 100 5 25 Payo cid 3 100 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 0 cid 2 cid 2 5 025 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 Asset price cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 100 The break even point is given by Net payo ST 100 5 1 0 005 0 or ST 105 025 15 401 Lecture Notes c cid 2 J Wang Fall 2006 Chapter 11 Options 11 5 Using the payo diagrams we can also examine the payo of a portfolio consisting of options as well as other assets Example Consider the following portfolio a straddle buy one call and one put with the same exercise price Its payo is Payo of a straddle cid 3 100 cid 3 cid 3 cid 3 cid 3 cid 3 cid 2 cid 2 cid 2 cid 2 cid 2 cid 3 cid 3 cid 2 cid 2 cid 3 cid 2 100 cid 2 Asset price Example The underlying asset and the bond with face value 100 have the following payo diagram cid 2 cid 2 cid 2 cid 2 Payo of asset cid 3 100 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 cid 2 Payo of bond cid 3 100 100 cid 2 Asset price 100 cid 2 Asset price Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 11 6 Options Chapter 11 1 3 Corporate Securities as Options Example Consider two rms A and B with identical assets but di erent capital structures in market value terms Balance sheet of A Asset 30 0 Bond Balance sheet of B Asset 30 25 Bond 30 Equity 5 Equity 30 30 30 30 Firm B s bond has a face value of 50 Thus default is likely Consider the value of stock A stock B and a call on the underlying asset of rm B with an exercise price 50 Asset Value of Value of Value of Call Value Stock A Stock B 0 0 0 0 0 0 10 10 30 30 50 50 20 40 50 60 80 100 20 40 50 60 80 100 Stock B gives exactly the same payo as a call option written on its asset Thus B s common stocks really are call options 15 401 Lecture Notes c cid 2 J Wang Fall 2006 Chapter 11 Options 11 7 Indeed many corporate securities can be viewed as options Common Stock A call option on the assets of the rm with the exercise price being its bond s redemption value Bond A portfolio combining the rm s assets and a short position in the call with exer cise price equal bond redemption value Warrant Call options on the stock issued by the rm Convertible bond A portfolio combining straight bonds and a call option on the rm s stock with the exercise price related to the conversion ratio Callable bond A portfolio combining straight bonds and a call written on the bonds Fall 2006 c cid 2 J Wang 15 401 Lecture Notes 11 8 Options Chapter 11 2 Use of Options Hedging Downside while Keeping Upside The put …