期货期权及其衍生品配套课件全34章Ch18.ppt

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1、Volatility Smiles,Chapter 18,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,1,赠梢汕捏附旱盎忆习瑰侠肖弛溪纠筷萄褂渺悍胎个祈冲兢果址醋第粒惹鸟期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,What is a Volatility Smile?,It is the relationship between implied volatility and

2、strike price for options with a certain maturityThe volatility smile for European call options should be exactly the same as that for European put optionsThe same is at least approximately true for American options,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull

3、 2008,2,晕男本过札辨歹潞纽涂成刑窟框镜杉怕砖贾摔瞎昌概路当迷食瓮圣茨悦柔期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Why the Volatility Smile is the Same for Calls and Put,Put-call parity p+S0e-qT=c+K er T holds for market prices(pmkt and cmkt)and for Black-Scholes prices(pbs and cbs)It follows that pmkt-pbs=cmk

4、t-cbsWhen pbs=pmkt,it must be true that cbs=cmktIt follows that 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 maturity,Options,Futures,and Other Derivatives,7th International Edi

5、tion,Copyright John C.Hull 2008,3,惧歌用蛀俱棚款埂矾滩通衫且栏戮瓷擅晌枫疥赣符束仇歇疯缮只大睹浙摩期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,The Volatility Smile for Foreign Currency Options(Figure 18.1,page 383),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,4,仟涪疯邢轩

6、殖舆蔬林谅得铣懒拷劈研杯恐台圣会肘麻渴赶漳寒缘肌瑞垦诊期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Implied Distribution for Foreign Currency Options(Figure 18.2,page 383),Both tails are heavier than the lognormal distributionIt is also“more peaked”than the lognormal distribution,Options,Futures,and Other De

7、rivatives,7th International Edition,Copyright John C.Hull 2008,5,赐惰华章云彩扩蛙柱搐彼刽腐哄蚂疏同驱熔但谱买参写糊由丽线购骗训荧期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,The Volatility Smile for Equity Options(Figure 18.3,page 386),Options,Futures,and Other Derivatives,7th International Edition,Copyright Joh

8、n C.Hull 2008,6,Implied,Volatility,Strike,Price,途思溺袄晓盟琢绣溅峦苑斤槛屠并焕寺佃涎诵衷缮懒鼠骂祥吻肺烛重搬宏期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Implied Distribution for Equity Options(Figure 18.4,page 386),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,7,T

9、he left tail is heavier and the right tail is less heavy than the lognormal distribution,坍诬弗疹菌拿洒傈候腋剐腔掇削偏暮火袒牵嗜欲漓禹鹰慢江孝频仆轮梗焊期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Other Volatility Smiles?,What is the volatility smile ifTrue distribution has a less heavy left tail and heavier ri

10、ght tailTrue distribution has both a less heavy left tail and a less heavy right tail,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,8,路崇腑慷杆竟酬柯午轮厦潞幌太譬恶税竭铜丫全阅始甸倡舷沏漏响裸阑尸期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Ways of Characterizing th

11、e Volatility Smiles,Plot implied volatility against K/S0(The volatility smile is then more stable)Plot implied volatility against K/F0(Traders usually define an option as at-the-money when K equals the forward price,F0,not when it equals the spot price S0)Plot implied volatility against delta of the

12、 option(This approach allows the volatility smile to be applied to some non-standard options.At-the money is defined as a call with a delta of 0.5 or a put with a delta of 0.5.These are referred to as 50-delta options),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.

13、Hull 2008,9,恍砌龄溶辕诌哩叁菌笆秽积烁银尸钥岭朝偷侥陌乔挽摄吠教旱奄缸覆厌株期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Possible Causes of Volatility Smile,Asset price exhibits jumps rather than continuous changesVolatility for asset price is stochasticIn the case of an exchange rate volatility is not heavily c

14、orrelated with the exchange rate.The effect of a stochastic volatility is to create a symmetrical smileIn the case of equities volatility is negatively related to stock prices because of the impact of leverage.This is consistent with the skew that is observed in practice,Options,Futures,and Other De

15、rivatives,7th International Edition,Copyright John C.Hull 2008,10,馆皋资寒溶窄臭辊劝尾仙捕窒债篆蓬冯订渠蹄复衍汇木娇青针绊恰讼努低期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Volatility Term Structure,In addition to calculating a volatility smile,traders also calculate a volatility term structureThis shows the v

16、ariation of implied volatility with the time to maturity of the option,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,11,超占童价隶种乔展棕朽岂悠狭淖欢珐材暖蔚遣苞刽惺贡采孽纪苑乖哪舒嫉期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Volatility Term Structure,The volatilit

17、y term structure tends to be downward sloping when volatility is high and upward sloping when it is low,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,12,音拇译瞄臂授取橇纯尿袒呜陆源檀藕散傍寓脊真意薪鹊织嚎杆米带沃壹诧期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Exampl

18、e of a Volatility Surface(Table 18.2,page 389),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,13,称仲综联肮拯哩席蒜涸沾脖氖玄哄枯耍乔舰菇童贱难叮蒂影毖郁诫吃咽鸭期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,Greek Letters,If the Black-Scholes price,cBS is expressed as a

19、function of the stock price,S,and the implied volatility,simp,the delta of a call isIs the delta higher or lower than,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,14,一黄媚羞蛮须垣省浑堰讯缺点秤蔗录肌撤圭砰味拴拴状胆亥潜萝爽洪患烷期货期权及其衍生品配套课件（全34章）Ch18Options,Futures,and Other Derivatives,7e,