2015金融小汇总笔记讲义

1、Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.1Properties of Stock OptionsChapter 9Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.2Notation c :European call option price p :European put option price S0 :Stock price today K :Strik

2、e price T :Life of option :Volatility of stock price C :American Call option price P :American Put option price ST :Stock price at option maturity D :Present value of dividends during options life r :Risk-free rate for maturity T with cont compOptions, Futures, and Other Derivatives 6th Edition, Cop

3、yright John C. Hull 20059.3Effect of Variables on Option Pricing (Table 9.1, page 206) cpCPVariableS0KTrD+?+Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.4American vs European OptionsAn American option is worth at least as much as the corresponding European option

4、C cP pOptions, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.5Calls: An Arbitrage Opportunity?Suppose that c = 3 S0 = 20 T = 1 r = 10% K = 18 D = 0Is there an arbitrage opportunity?Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.6Lower Bou

5、nd for European Call Option Prices; No Dividends (Equation 9.1, page 211) c S0 Ke -rTOptions, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.7Puts: An Arbitrage Opportunity?Suppose that p= 1 S0 = 37 T = 0.5 r =5% K = 40 D = 0Is there an arbitrage opportunity?Options, Future

6、s, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.8Lower Bound for European Put Prices; No Dividends (Equation 9.2, page 212) p Ke -rTS0Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.9Put-Call Parity; No Dividends (Equation 9.3, page 212)Consider t

7、he following 2 portfolios:Portfolio A: European call on a stock + PV of the strike price in cashPortfolio C: European put on the stock + the stockBoth are worth max(ST , K ) at the maturity of the optionsThey must therefore be worth the same today. This means thatc + Ke -rT = p + S0 Options, Futures

8、, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.10Arbitrage OpportunitiesSuppose that c= 3 S0= 31 T = 0.25 r = 10% K =30 D = 0What are the arbitrage possibilities when p = 2.25 ? p = 1 ?Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.11Early Exerci

9、seUsually there is some chance that an American option will be exercised earlyAn exception is an American call on a non-dividend paying stockThis should never be exercised earlyOptions, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.12For an American call option: S0 = 100;

10、T = 0.25; K = 60; D = 0Should you exercise immediately?What should you do if you want to hold the stock for the next 3 months? you do not feel that the stock is worth holding for the next 3 months?An Extreme SituationOptions, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.1

11、3Reasons For Not Exercising a Call Early (No Dividends)No e is sacrificedPayment of the strike price is delayedHolding the call provides insurance against stock price falling below strike price Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.14Should Puts Be Exercis

12、ed Early ?Are there any advantages to exercising an American put when S0= 60; T = 0.25; r=10% K = 100; D = 0Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.15The Impact of Dividends on Lower Bounds to Option Prices(Equations 9.5 and 9.6, pages 218-219)Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 20059.16Extensions of Put-Call ParityAmerican options; D = 0S0 - K C - P 0c + D + Ke -rT = p + S0 (Equation 9.7, p. 219)American options; D 0S0 - D - K C - P S0 - Ke -rT(Equation 9.8, p. 219)