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1、Properties ofStock Option PricesChapter 7Notation c:European call option price p:European put option price S0:Stock price today X:Strike price T:Life of option :Volatility of stock price C:American Call option price P:American Put option price ST:Stock price at time T D:Present value of dividends du
2、ring options life r:Risk-free rate for maturity T with cont compEffect of Variables on Option Pricing(Table 7.1,page 169)cpCPVariableS0XTrD+?+American vs European OptionsAn American option is worth at least as much as the corresponding European option C cP pCalls:An Arbitrage Opportunity?Suppose tha
3、t c =3 S0=20 T =1 r =10%X =18 D=0Is there an arbitrage opportunity?Lower Bound for European Call Option Prices;No Dividends(Equation 7.1,page 172)c S0-Xe-rTPuts:An Arbitrage Opportunity?Suppose that p=1 S0=37 T =0.5 r =5%X =40 D =0Is there an arbitrage opportunity?Lower Bound for European Put Prices
4、;No Dividends(Equation 7.2,page 173)p Xe-rT-S0Put-Call Parity;No Dividends(Equation 7.3,page 174)Consider the following 2 portfolios:Portfolio A:European call on a stock+PV of the strike price in cashPortfolio B:European put on the stock+the stockBoth are worth MAX(ST,X)at the maturity of the option
5、sThey must therefore be worth the same todayThis means thatc +Xe-rT =p +S0 Arbitrage OpportunitiesSuppose that c=3 S0=31 T =0.25 r =10%X =30 D =0What are the arbitrage possibilities when p =2.25?p =1?Early ExerciseUsually there is some chance that an American option will be exercised earlyAn excepti
6、on is an American call on a non-dividend paying stockThis should never be exercised earlyFor an American call option:S0 =100;T =0.25;X =60;D =0Should you exercise immediately?What should you do if 1You want to hold the stock for the next 3 months?2You do not feel that the stock is worth holding for
7、the next 3 months?An Extreme SituationReasons For Not Exercising a Call Early(No Dividends)No income is sacrificed We delay paying the strike price Holding the call provides insurance against stock price falling below strike price Should Puts Be Exercised Early?Are there any advantages to exercising
8、 an American put when S0=60;T=0.25;r=10%X =100;D=0The Impact of Dividends on Lower Bounds to Option Prices(Equations 7.5 and 7.6,page 179)Extensions of Put-Call ParityAmerican options;D =0S0 -X C -P 0c +D +Xe-rT=p +S0 Equation 7.7 p.180American options;D 0S0 -D -X C -P S0 -Xe-rTEquation 7.8 p.1801、有
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