ch15期權(quán)期貨與衍生證券（第五版）

1、Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,15.1,Volatility Smiles Chapter 15,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,15.2,Put-Call Parity

2、 Arguments,Put-call parity p +S0e-qT = c +X e–r T holds regardless of the assumptions made about the stock price distributionIt follows thatpmkt-pbs=cmkt-cbs,Options, Futures, and Other Derivatives, 5th edition ©

3、; 2002 by John C. Hull,15.3,Implied Volatilities,The implied volatility calculated from a European call option should be the same as that calculated from a European put option when both have the same strike price and ma

4、turityThe same is approximately true of American options,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,15.4,Volatility Smile,A volatility smile shows the variation of the implied vola

5、tility with the strike priceThe volatility smile should be the same whether calculated from call options or put options,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,15.5,The Volatili

6、ty Smile for Foreign Currency Options (Figure 15.1, page 332),Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,15.6,Implied Distribution for Foreign Currency Options,The implied distribu

7、tion is as shown in Figure 15.2, page 332Both tails are heavier than the lognormal distributionIt is also “more peaked than the lognormal distribution,Options, Futures, and Other Derivatives, 5th edition © 2002 b

8、y John C. Hull,15.7,The Volatility Smile for Equity Options (Figure 15.3, page 334),,,Implied,Volatility,Strike,Price,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,15.8,Implied Distrib

9、ution for Equity Options,,The implied distribution is as shown in Figure 15.4, page 335The right tail is less heavy and the left tail is heavier than the lognormal distribution,Options, Futures, and Other Derivatives, 5

10、th edition © 2002 by John C. Hull,15.9,Other Volatility Smiles?,What is the volatility smile ifTrue distribution has a less heavy left tail and heavier right tailTrue distribution has both a less heavy left tail

11、and a less heavy right tail,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,15.10,Possible Causes of Volatility Smile,Asset price exhibiting jumps rather than continuous changeVolatilit

12、y for asset price being stochastic (One reason for a stochastic volatility in the case of equities is the relationship between volatility and leverage),Options, Futures, and Other Derivatives, 5th edition © 2002

13、by John C. Hull,15.11,Volatility Term Structure,In addition to calculating a volatility smile, traders also calculate a volatility term structureThis shows the variation of implied volatility with the time to maturity o

14、f the option,Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull,15.12,Volatility Term Structure,The volatility term structure tends to be downward sloping when volatility is high and upward