ꕈ때ꗀ볆껖끪쉫둍궷쁉꒤ꗟ뻷뉶꓀끴뭐쇴ꝴꩩ둔ꚱ∗궱꒧ꑀ교꧊? The Consistency between the Risk-Neutral Distribution and the Implied Volatility Surface Based on the Approach of the Nonparametric Kernel Regression ∗∗ꩌꓫ꿠ꅝYueh-Neng Linꅞ ∗∗∗Ꝥ돓뒺ꅝSheng-Ching Wuꅞ ∗∗∗∗녩랽ꅝYu-Yuan Changꅞ ∗ ꖻ곣ꡳ꧓냪곬라룉ꝕꅝ군땥뵳뢹ꅇNSC 90-2416-H-259-002ꅞꅁ싔뭸쇂ꟕꅃꚹꕾꅁꖻ곣ꡳ띐쇂꣢ꛬ냎ꙗ뗻뷗ꪺꖿ뭐ꯘ쒳ꅃ ∗∗ 냪ꗟꩆ뗘ꑪ뻇끝냈뿄뻇꡴ꝕ뉺뇐뇂ꅁAssistant Professor, National Dong Hwa University, Hualien, Taiwan. ∗∗∗ 냪ꗟꩆ뗘ꑪ뻇ꗸ띾뫞뉺곣ꡳ꧒곣ꡳꗍꅁMBA, National Dong Hwa University, Hualien, Taiwan. ∗∗∗∗ 껧뛩뾤ꑪ꒤늼꣩뿄ꗷꚳ궭꒽ꕱ뱸뇂ꭈꑈ귻ꅁOfficerꅁDah Chung Bill Finance Corporation, Taoyuan, Taiwan.
멋굮 ꗑ꧳B-S쇴ꝴꩩ둔ꝴꚳ싗둉룪끔ꅁꖻꓥ꣏ꗎ1995꙾2ꓫ8ꓩ8ꓫ23ꓩFTSE 100 볆뿯뻜앶믹껦ꅁꕈ때ꗀ볆껖끪쉫꛴군쇴ꝴꩩ둔꣧볆ꅁꣃBreeden-Litzenbergerꅝ1978ꅞꪺꓨꩫꡄ녯궷쁉꒤ꗟ뻷뉶듺ꯗꑕ볐ꪺ볆뻷뉶꓀끴ꅃ맪쏒떲ꩇ땯뉻쇴ꝴꩩ둔꣣ꚳ띌꾺ꮬ멁ꅆꕂ궷쁉꒤ꗟ꓀끴ꝥ뉻굴낾낪꽕깰ꅁ쁈뗛꣬듁ꓩꪺ뱗ꕛꅁ굴낾낪꽕깰뙖꒣ꧺ엣ꅃꚹ뉻뙈뭐꒣맯뫙ꩩ둔띌꾺엜꓆곛닅ꅁ엣ꗜ꣏ꗎ때ꗀ볆껖끪쉫ꓨꩫꕩ꣏룓볆뿯뻜앶꒧ꩩ둔띌꾺뉻뙈뭐볐ꪺ볆궷쁉꒤ꗟ뻷뉶꓀끴꣣ꚳꑀ교꧊ꅃ 쏶쇤뗼ꅇBlack-Scholes뿯뻜앶ꥷ믹볒ꮬꅂ쇴ꝴꩩ둔ꅂ띌꾺ꩩ둔ꅂ껖끪쉫ꅂ궷쁉꒤ꗟ뻷뉶꓀끴ꅃ 2
Abstract While applied to the European-style FTSE-100 index options on 8 February and 23 August 1995, this paper uses a nonparametric kernel regression technique to interpolate implied volatilities across alternative moneyness and time to maturity. Given the interpolated volatilities, an underlying distribution under the risk-neutral probability measure is produced based on Breeden and Litzenberger’s (1978) butterfly-spread approach. Our empirical results reveal significant evidence of negative skewness and excess kurtosis, which decay over longer time to maturity. The phenomenon is consistent with the changes in the patterns of implied volatility surfaces, which indicates the effectiveness of the kernel regression approach on the FTSE-100?index options during the sample periods. Keywords: Black-Scholes Option Pricing Formula, Implied Volatility, Volatility Smile, Kernel Regression, Risk-Neutral Distribution. 3
ㄮ₺ﲽ휠 Black-Scholesꅝ1973ꅞ뿯뻜앶ꥷ믹볒ꮬꅝꕈꑕ슲뫙 B-S₩瞻寮튫겡庪뫁璪?둔ꑷ덑뱳꩸ꙡ륂ꗎ꧳늼뿯뻜앶ꪺ돸믹ꑗꅃꦹꦹꖫ돵ꑗꗦ꧶ꪺ떲ꩇ엣ꗜꙐꑀ볐ꪺꪫꕂ곛Ꙑ꣬듁ꓩ꒧뉠믹꒺뉠믹ꕾꪺ뿯뻜앶곛맯꧳믹ꖭ뿯뻜앶꣣ꚳ룻낪ꪺ쇴ꝴꩩ둔ꅁ덯볋ꪺ뉻뙈ꅁ귌뫙꒧띌꾺ꩩ둔ꅃꗑ꧳뿯뻜앶ꖫ돵ꑗꪺ띌꾺ꩩ둔꯹쓲ꙡ꙳Ꙣꅁ앫땍ꚨ결뿯뻜앶ꗦ꧶ꑗ꽓ꛢ꒧ꑀꅁ뙩ꛓꓞ땯뻇놴끑?B-S璪榴咤Ꞹ咤?뉛뭐덺앓ꕘ꛳뫘끔꺧ꕩ꣑룪ꑈ낵ꡍ떦ꪺ냑ꛒꅃꚳ곣ꡳꕈꚳꗀ볆ꓨꩫ꣓꛴군쇴ꝴꩩ둔꣧볆ꅝ꙰ꚳꗀ볆끪쉫떥ꅞꅁꚹ뫘ꓨꩫꖲ뚷맯쇴ꝴꩩ둔꣧볆Ꝁ녪꽐ꪺ낲덝ꅁ꙰ꩇ맪믚ꪺ볋ꖻ룪껆륈덯낲덝ꅁ꧒ꡄ녯ꪺ쇴ꝴꩩ둔꣧볆녎꒣꣣ꕎꫭ꧊ꅃꙝꚹꅁꖻ곣ꡳꕈ1995꙾2ꓫ8ꓩ8ꓫ23ꓩ굞냪귛뒰뿄껉돸ꛊ뫘믹볆볚ꚡ뿯뻜앶ꅝFTSE-100ꅞ믹껦결꣒ꅁ링룕ꕈ때ꗀ볆껖끪쉫ꓨꩫꅝnonparametric kernel ?regressionꅞ₨펦炼킪몪톻嶺ﲼ욤ꟁ璪榴咨욡䆨쾨ꢬ낼킪몪톻嶺ﲼ욡䊼榬?믹껦뭐뙚꒵꣬듁ꓩꪺ덳쓲꣧볆ꅃ껖끪쉫ꓨꩫ걏낪룪껆녋뚰ꯗꅁ깥덜Ꙑꑀ뿯뻜앶ꮴ?곹ꙢꙐꑀꗦ꧶ꓩ돸믹Ꙩꚸꅁ룻꣤ꕌꖭ럆ꓨꩫ꣓녯ꚳ뱵꧊ꅆ₴ꮨꖤꞡ䆸펪殸햹쾥䢸?껆ꖻꢭꪺꮬ멁꣓룉뙩뿲ꖢ룪껆ꅁꛓꭄꕈꖭ럆ꪺꓨꩫ꣓슫덯꿊ꑦꅁꙝꚹ꧒꛴군?ꪺ쉉라걏왛듺냏냬꒺룪껆쉉ꪺꕛ앶ꖭꞡꅃ₹튵늪䟅?튦?꒧껖끪쉫ꩩ둔뭐ꖫ돵왛맮꣬ꪺ쇴ꝴꩩ둔ꝥ뉻ꚳ띌꾺ꪺ놡ꩰꑀ교ꅃꚹꕾꅁꙢ뉺꧊ꖫ돵꒤ꅁ믹볆뿯뻜앶ꪺꖫ믹ꅁ쇴ꝴ뗛룪ꑈ맯ꖼ꣓ꖫ돵ꪺ륷듁ꅁꙝꚹꖻ곣ꡳ룕맏꣏ꗎ쇴ꝴꙢꩩ둔 1 Aït-SahaliaLoꅝ1998ꅞ꣏ꗎ때ꗀ볆껖끪쉫ꓨꩫꅁꕈ뙚꒵꣬듁ꓩ뭐뿯뻜앶믹ꛬ꣓꛴군쇴ꝴꙢSPX뿯뻜앶믹껦꒤ꪺB-S쇴ꝴꩩ둔꣧볆ꅃ 2 ꣒꙰꣏ꗎꑔꚸꗩ볋뒡귈ꩫꅝcubic spline interpolationꅞ꛴군쇴ꝴꩩ둔꣧볆껉ꅁ곛Ꙑ믹ꛬ꣬듁ꓩꪺ뿯뻜앶믹껦ꕵ꿠ꚳꑀ뫘ꅃ 3 ꖻ곣ꡳꪾ륄굙륌ꯗ곛ꭈ룪껆ꅝover fittingꅞꅁꭨ꧒녯떲ꩇꕩ꿠ꕝꝴ룪껆싸끔ꅁ걇ꖻ곣ꡳꝒ낣ꑀꧺ엣륈냲ꖻ깍ꝑ뇸ꗳꪺ뿯뻜앶룪껆ꅁ룔닓뮡ꧺ뷐ꢣꖻꓥ닄론ꅃ 4
꒤ꪺ뿯뻜앶믹껦ꅁ륂ꗎ?BreedenLitzenbergerꅝ1978ꅞꪺ붺ꚡ믹깴ꓨꩫꅁ뻉ꕘ룪ꑈꓟꗘ꒤ꖼ꣓ꪺ궷쁉꒤ꗟ믹볆뻷뉶꓀끴ꅃ뉺뷗ꑗꅁ꒣맯뫙띌꾺ꪬꪺ?B-S 쇴ꝴꩩ둔ꚱ뵵삳룓맯삳뗛룻맯볆녠멁꣓녯꣣낾멁ꪺ볐ꪺ룪늣궷쁉꒤ꗟ뻷뉶꓀끴ꅃ땍ꛓꅁ걏ꝟ꿠꣬ꑀꚳ껄ꓨꩫꅁꕩ녎 B-S 쇴ꝴꩩ둔룪끔ꚨꕜꙡ신결곛맯삳ꪺ뻷뉶꓀끴ꅁꭨ결ꑀ맪쏒냝썄ꅃꚳ얲꧳껖끪쉫ꓨꩫꕩ엽룪껆ꝥ뉻ꛛꑶ귬뮪룓ꓨꩫ결ꑀ슲돦ꕂ궭꣮룻ꓖꪺ때ꗀ볆ꓨꩫꅁꖻ곣ꡳ놴끑룓ꓨꩫ걏ꝟꕩ녎⁂??璪榴咸咦ꢥ?ꙡ신결뉺뷗ꑗꑀ교꧊꒧볐ꪺ볆궷쁉꒤ꗟ뻷뉶꓀끴ꅃ룓ꑀ교꧊꒣뮡ꧺ때ꗀ볆껖끪쉫ꓨꩫ맯룓듁뚡뿯뻜앶룪껆꒧빁ꗎ꧊ꅁꕂ뮡ꧺ룓뿯뻜앶Ꙣꖫ돵ꑗ믹껦ꪺꙘ뉺꧊ꅃ귈녯ꩠ띎ꪺ걏ꅁꚳ덜Ꙩꓨꩫꕩꗎ꣓ꡄ꣺쇴ꝴꙢ뿯뻜앶믹껦꒤ꪺ궷쁉꒤ꗟ뻷뉶꓀끴ꅃBreedenLitzenbergerꅝ1978ꅞꪺ붺ꚡ믹깴ꓨꩫ꒣믝굮릳ꚳꗀ볆ꓨꚡ믝굮맯볐ꪺ룪늣믹껦ꪺ늣ꗍ륌땻Ꝁ낲덝ꅁ낲덝궷쁉꒤ꗟ뻷뉶꓀끴걏쓝꧳걙ꑀꚳꗀ볆깡뇚ꪺ꓀끴ꅁ꙰?B-S₩瞻寮튫결늳嶼킪몸ꎪ못瑩䆱熹욱悺䆤산璡䚦펥䊤嶤?ꗎꗽ뿯ꥷꗴ꛳꓀끴꣓Ꝁ결궷쁉꒤ꗟ뻷뉶꓀끴ꪺꗽ엧꓀끴ꅁꛓꕛꕈ뷕뻣ꚨ결궷쁉꒤ꗟ뻷뉶꓀끴ꅆ룓붺ꚡ믹깴ꩫ꒧빁ꗎ꧊덱녠믝끴Ꙙꑀꚳ껄ꪺꖭ럆ꓨꩫꅃꖻ곣ꡳ결뮡ꧺ때ꗀ볆껖끪쉫꒧빁ꗎ꧊ꅁꙝꛓ뿯ꥷ?BreedenLitzenbergerꅝ1978ꅞꓨꩫꡄꕘ4쇴ꝴꙢ껖끪쉫꒧⁂ⵓ璪榴咤꒪몾皤산璡? 결샋ꥷ꣏ꗎ때ꗀ볆껖끪쉫걏ꝟꕩ녎쇴ꝴꩩ둔룪끔ꚳ껄ꙡ신결궷쁉꒤ꗟ뻷뉶꓀끴ꅁꖻ곣ꡳꓱ룻꓀ꝏ쇴ꝴꙢꩩ둔ꚱ뵵뭐 4 덜Ꙩ꛴군궷쁉꒤ꗟ뻷뉶꓀끴ꪺꓨꩫ걏ꯘ멣Ꙣ쇴ꝴꩩ둔ꚱ궱ꑗꅁ꣒꙰DermanKaniꅝ1994ꅞꪺ쇴ꝴꩩ냊뉶ꑇ꒸뻰ꅂDermanꅁKaniChrissꅝ1996ꅞꪺ쇴ꝴꩩ냊뉶ꑔ꒸뻰ꅂꖻ곣ꡳꕈ껖끪쉫꧒꛴녯ꪺꩩ둔귈녡ꑊB-Sꥷ믹볒ꮬ꒤ꕈꡄ녯뿯뻜앶믹껦ꅁ땍ꯡBreedenLitzenbergerꅝ1978ꅞꪺ붺ꚡ믹깴랧꧀ꅁ녎뿯뻜앶믹껦맯뱩곹믹껦낵ꑇ뚥띌꓀ꅁꙁ궼ꑗꑀ뷆ꝑꙝꑬꅁ꛴녯궷쁉꒤ꗟ뻷뉶꓀끴ꅃꗑ꧳ꚹꓨꩫ꽁맯쇴ꝴꩩ둔뙩ꛦꭄ뵵꧊신뒫ꅁꙝꚹꙢ떹꒩곛Ꙑ쇴ꝴꩩ둔ꚱ궱뇸ꗳꑕꅁ꧒꛴녯ꪺ궷쁉꒤ꗟ뻷뉶꓀끴걏ꝟ곛Ꙑꅁ결ꑀ맪쏒쒳썄ꅃꙢ때ꩫ샲노ꖿ뵔ꪺ궷쁉꒤ꗟ꓀끴ꑕꅝꙝ결룪궷쁉낾ꙮꖼꪾꅞꅁꖻ곣ꡳ놵꣼궷쁉꒤ꗟ뻷뉶꓀끴ꪺ닄ꑔꅂꕼ뚥냊깴뭐ꩩ둔ꚱ궱쇴ꝴꪺ낾멁ꅂ깰멁ꭙ볆ꑀ교ꪺ꓀끴ꅃ굙꓀끴꽓꧊뭐쇴ꝴꩩ둔ꮬ멁꒣ꑀ교ꅁꕩ꿠귬ꙝ녎ꕝ걁쇴ꝴꩩ둔ꚱ궱룪끔신결궷쁉꒤ꗟ뻷뉶꓀끴ꪺꭄ뵵꧊신뒫ꓨꩫꙢ룓룪껆듁뚡ꭄ결ꑀꚳ껄ꓨꩫꅃꗑ꧳BreedenLitzenbergerꅝ1978ꅞꪺ붺ꚡ믹깴ꓨꩫꞹꗾꖼ맯볐ꪺ믹륌땻Ꝁꗴ꛳낲덝ꅁ꧒뿠ꪺ뛈결ꑀꚳ껄ꪺ뿯뻜앶ꖭ럆ꖩꞹꗾꖫ돵ꪺ낲덝ꅃꙝꚹꅁꙢꞹꗾꖫ돵낲덝ꑕꅁ껖끪쉫굙결ꑀꚳ껄ꪺꖭ럆ꖩꅁBreedenLitzenbergerꅝ1978ꅞꓨꩫ늣ꗍꪺ궷쁉꒤ꗟ뻷뉶꓀끴꽓꧊삳뭐쇴ꝴꩩ둔ꚱ궱꣣ꚳꑀ교꧊ꅃ 5
궷쁉꒤ꗟ꓀끴ꪺ낾멁뭐깰멁ꭙ볆ꅃ떲ꩇ엣ꗜ궷쁉꒤ꗟ꓀끴룻맯볆녠멁꣣굴낾뭐낪꽕깰꽓꧊ꅁ쁈뗛뙚꒵꣬듁ꓩꪺ뱗ꕛꅁ굴낾낪꽕깰ꪺ놡ꩰꭨ뙖꒣ꧺ엣ꅁꚹ뉻뙈닅Ꙙ껖끪쉫쇴ꝴꩩ둔꒣Ꙑ뙚꒵꣬듁ꓩꑕ꒣맯뫙띌꾺ꮬ멁꒧엜꓆ꅆꕂ껖끪쉫ꩩ둔꣧5볆꧒쇴ꝴ꒧‘낾멁뙋ꓴ’ ꗧ뭐굴낾꒧뻷뉶꓀끴ꑀ교ꅃ 녱궷쁉뫞뉺ꪺꢤꯗꛓꢥꅁꚳ얲꧳ꗦ꧶닟멄ꕈB-S쇴ꝴꩩ둔낵결뿯뻜앶곛맯믹껦ꓴ럇ꅝꙝꛓ쇴ꝴꩩ둔ꝴꚳ싗둉룪끔ꅞꅁꖻ곣ꡳ놴끑걏ꝟ꣏ꗎ때ꗀ볆껖끪쉫ꓨꩫꕩ녎쇴ꝴꙢ뿯뻜앶쇴ꝴꩩ둔룪껆꒧꒺ꪺ룪늣돸륓꓀끴ꚳ껄ꕂꑀ교ꙡꡄꕘꅁ굙ꕛꕈ뫫뵔군뫢궷쁉귈ꅁꭨꕩ륆꣬궷쁉놱뫞ꪺꗘꪺꅃ땍ꛓ믝ꩠ띎ꪺ걏쇴ꝴꙢ뿯뻜앶믹껦꒧볐ꪺ룪늣뻷뉶꓀끴ꭙ쓝꧳궷쁉꒤ꗟ낲덝꒧ꑕꪺ늣ꪫꅁ걇믝뷕뻣룪ꪺ궷쁉뙋ꓴꯡꅁꑾ결맪믚ꪺ뻷뉶꓀끴ꅃꖻꓥ꒺깥ꙷ뇆꙰ꑕꅇ닄ꑇ론꒶닐궷쁉꒤ꗟ뻷뉶꓀끴꒧곛쏶ꓥ쑭ꅃ닄ꑔ론뮡ꧺꖻꓥ꣏ꗎ꒧곣ꡳꓨꩫ뭐맪쏒볒ꮬꅃ닄ꕼ론결룪껆뮡ꧺ뭐맪쏒떲ꩇ꓀꩒ꅃ돌ꯡꑀ론결ꖻꓥ꒧떲뷗ꅃ ㈮₭럀䦤꒥?皤산璤Ɡ?涱뒰儠?뉻ꚳ덜Ꙩ꒣Ꙑꪺ군뙱ꓨꩫꕩ녎쇴ꝴꙢ뿯뻜앶믹껦꒤ꪺ볐ꪺ룪늣궷쁉꒤ꗟ뻷뉶꓀끴ꡄꕘꅃꖩꕝ걁썐롪Black-Scholesꅝ1973ꅞ맯볐ꪺ룪늣믹껦ꩁ녱맯볆녠멁꒧낲덝ꅝ꣒꙰ꅁJarrowRuddꅁ1982ꅆMelickThomasꅁ1997ꅞꅆꧺ엣ꙡ륂ꗎ맪믚뿯뻜앶믹껦뭐B-Sꥷ믹볒ꮬ꒧뚡ꪺ깴늧ꅝ꣒꙰ꅁShimkoꅁ1993ꅆDermanKaniꅁ1994ꅆDumas?et al.ꅁ1998ꅞꅃꯡꓨꩫ꒧쁵쉉결ꕩꪽ놵늣ꗍ쇴ꝴꙢ뿯뻜앶 5 ‘낾멁뙋ꓴ’꒧ꥷ롱뷐ꢣꖻꓥ닄론ꅃ 6
?ꖫ돵믹껦꒤ꪺꪬ멁믹껦꛴군뙱ꅁ뙩ꛓ꛴녯궷쁉꒤ꗟ뻷뉶꓀끴ꅆ₦ﶨ쫂䦬납뾲꒼?ꪺ룪늣껉뚡볆ꙃꪺ꽓꧊ꅁ땍ꛓꙢꞹꗾꖫ돵낲덝ꑕꅁꚹ볐ꪺ룪늣꒧껉뚡볆ꙃ꽓꧊뉺뷗ꑗ삳쓝Ꙩ빬룪끔ꅆꚳ얲꧳ꚹ꿊쉉ꅁꖻ곣ꡳ낲덝룪ꑈꕩ롧ꗑ냊멁룪닕Ꙙ뷆뭳?ꖩꛓ꣏ꖫ돵결ꑀꞹꗾꖫ돵ꅃ₥䢤喻ꆩ瘝涤垦喺?熿?뻜앶믹껦뇀뻉볐ꪺ룪늣궷쁉꒤ꗟ뻷뉶꓀끴ꪺꓨꩫꅝꕝ걁ꚳꗀ볆뭐때ꗀ볆ꓨꩫꅞꅃꚳꗀ볆ꓨꩫ결ꪽ놵뿯ꥷꑀ귓귔뿯ꪺꚳꗀ볆꓀끴ꅁꙢ꿠냷ꖿ뵔ꥷ믹볐ꪺ룪늣뿯뻜앶꒧궭꣮뇸ꗳꑕꅁ귗꒧ꭥ꧒뿯ꥷꪺꚳꗀ볆꓀끴ꅃ곛쏶ꓥ쑭ꚳ맯볆녠멁꒧뉖Ꙙ꓀끴ꅝBahraꅁ1997ꅆMelickThomasꅁ1997ꅞꅂ닄ꑇꮬ멁꒧ꑀ꿫ꢩꖦ꓀끴ꅝBookstaberMcDonaldꅁ1987ꅆMcDonaldꅁ1996ꅞ떥ꅆ맪쏒떲ꩇ엣ꗜ꧒늣ꗍꪺ궷쁉꒤ꗟ꓀끴뭐맯볆녠멁꒣Ꙑꅃꕈ때ꗀ볆ꓨꩫꡄ꣺뻷뉶꓀끴ꪺꗘꪺꅁ걏ꗸ맏둍ꟳ꣣뱵꧊ꪺꑀ꿫ꓨ땻ꚡꅁꛓ꒣릳ꚳꗀ볆ꓨꩫꖲ뚷꣏ꗎꚳꑀꥷ냑볆ꪺ뻷뉶꓀끴ꅃꑀ꿫ꛓꢥꅁ때ꗀ볆ꓨꩫꕝ걁끪쉫꓀꩒ꖭ럆ꩫꅂ돌ꑪ귈ꩫꅂꚱ뵵끴롭ꩫꑔ쏾ꅃꙢ때ꗀ볆끪쉫꓀꩒ꖭ럆ꩫ꒤ꅁꕈ껖끪쉫돌결슲돦ꛓꕂ뱳꩸ꙡ덑꣏ꗎꅃ껖끪쉫ꓨꩫ룕맏녱왛맮룪껆꒤ꕘꑀꙘ빁둹굺ꛛ엜볆뭐ꙝ엜볆쏶ꭙ꒧꣧볆ꅆꛓ뭐뛇닎끪쉫꒣Ꙑꪺ걏껖끪쉫꒣믝굮꽓ꥷꪺ냑볆낲덝ꅃ꣤꧒꣏ꗎ꒧껖꛴군뙱ꕩꕈ곝ꚨ걏ꑀ뫘맯곛엜볆Ꝁ냏냬늾냊ꕛ앶ꖭꞡ꧒녯꣬ꪺ뙱ꅃꗧꝙꅁ껖끪쉫녎ꡃꑀ꛴군쉉뗸결꽵맪꣧볆ꕩ꿠ꕘ뉻ꪺ냏냬꒤ꓟꅁ럭룪껆쉉싷꧒왛맮꣬ꪺ꛴군쉉뙖뮷껉ꅁ맯꽵맪꣧볆ꪺ뱶암뻷뉶ꭨ뙖ꑰꅃꕈ왛맮쇴ꝴꩩ둔맯삳뱩곹믹껦결꣒ꅁ낲덝쇴ꝴꩩ둔결뱩곹믹껦ꪺ꣧볆ꅝσ(X)ꅞꅁꡃꑀ귓룪껆쉉둎걏걙ꑀ꽓ꥷꪺ뱩곹믹껦꧒맯삳ꪺ쇴ꝴꩩ둔ꅃꙝꚹꅁꙢꑀ귓뱩곹믹껦ꖼꪾꪺ쇴ꝴ꾺ꪬꩩ둔꒤ꅁ껖끪쉫룕맏ꕈ룪껆ꖻꢭꪺꮬ멁꣓삱룉덯꿊ꑦꅁꙝꚹ꧒꛴군ꪺ쉉라 6 Rossꅝ1976ꅞ궺ꗽꕘ뿯뻜앶볐ꪺ룪늣ꪺ궷쁉꒤ꗟ뻷뉶꓀끴뭐ꪬ멁믹껦ꚳꡄ쁶앶꒧믹껦ꝥ뉻ꓱ꣒쏶ꭙꅃ 7
걏왛듺냏냬꒺룪껆쉉ꪺꕛ앶ꖭꞡꅁꛓ놱꣮왛듺냏냬ꪺꑪꑰ뫙결녡뱥귈ꅝhꅞꅃAït-SahaliaLoꅝ1998ꅞꝑꗎ껖꛴군뙱꛴군쇴ꝴꙢSꆮP 500믹볆뿯뻜앶믹껦꒤ꪺ궷쁉꒤ꗟ뻷뉶꓀끴ꅁ떲ꩇ땯뉻ꕈ껖꛴군뙱꧒ꡄ녯ꪺ뻷뉶꓀끴뭐B-Sꥷ믹볒ꮬ꧒낲덝믹ꩁ녱맯볆녠멁꓀끴꒣Ꙑꅃ돌ꑪ귈ꓨꩫꅝmaximum-entropy methodꅞ결떹ꥷꑀꗽ엧뻷뉶꓀끴ꑕꅁꕘꑀ때ꗀ볆뻷뉶꓀끴ꅁ꣏꣤몡ꢬ꽓ꥷ궭꣮ꚡꅝ꣒꙰ꅁꕈ룓때ꗀ볆뻷뉶꓀끴ꥷ믹꒧뿯뻜앶믹껦뭐꧒왛맮꣬ꪺ뿯뻜앶ꖫ돵믹껦ꑀ교떥ꅞꅁꣃ뫉ꕩ꿠꣏룓꓀끴꧒뛇뮼ꪺ끔꺧꒺깥뭐ꗽ엧꓀끴돌놵꫱ꅃStutzerꅝ1996ꅞꕈ볐ꪺ룪늣믹껦ꪺ뻺ꕶ꓀끴Ꝁ결ꗽ엧꓀끴ꅁꣃ궭꣮궷쁉꒤ꗟ꓀끴꿠ꖿ뵔ꥷ믹볐ꪺ룪늣뿯뻜앶ꪺ믹껦ꅁ뻉ꕘ궷쁉꒤ꗟꪺ뻷뉶꓀끴ꅁ꣤곣ꡳ땯뉻굴낾낪꽕깰ꪺ쏒뻚ꅁ꣤땻ꯗ뭐꧒꣏ꗎꪺ뻺ꕶ볋ꖻꯗꚳ쏶ꅃꛜ꧳ꚱ뵵끴롭ꩫꅝcurve fitting methodꅞꭙꕈꑀ룻꣣뱵꧊꒧꣧볆꣓끴롭쇴ꝴꩩ둔궷쁉꒤ꗟ뻷뉶꓀끴ꅃ꣒꙰ꅁShimkoꅝ1993ꅞ낲덝쇴ꝴꩩ둔꣧볆결뱩곹믹껦ꪺꑇꚸꓨꙨ뚵ꚡꅆMalzꅝ1997ꅞꕈꑇꚸꓨꙨ뚵ꚡ꣓끴롭쇴ꝴ엜늧맯삳뿯뻜앶ꕎ몸ꖦꅝdeltaꅞ귈ꅝꝙ뿯뻜앶믹껦맯볐ꪺ룪늣믹껦꒧뇓띐ꯗꅞꅆCampa et al.ꅝ1998ꅞ꣏ꗎꑔꚸꗩ볋뒡귈ꩫꅝcubic splineꅞ꣓ꖭ럆쇴ꝴꩩ냊ꯗꅁ꣏꣤ꚨ결뱩곹믹껦뭐껉뚡ꪺ덳쓲꣧볆ꅆRosenberger ?Engleꅝ1997ꅞ결쇗ꝋ굴ꪺ쇴ꝴꩩ둔ꅁ뇄ꗎꙨ뚵ꚡ꣓끴롭꣺맯볆ꯡꪺ쇴ꝴꩩ둔ꅁ떲ꩇ엣ꗜ궷쁉꒤ꗟ꓀끴ꓱ맯볆녠멁꓀끴땹띌굴낾ꕂ깰뎻ꑝ룻ꝃꅃꚹꕾꅁꕈꑀ꿫꣧볆꣓몥꫱궷쁉꒤ꗟ뻷뉶꓀끴ꕝ걁ꕈ뙐ꛌ꽓Ꙩ뚵ꚡꅝHermite-polynomialꅞ꣓꫱궷쁉꒤ꗟ뻷뉶꓀끴ꅝMadanMilneꅁ1994ꅆJondeauRockingerꅁ1998ꅞꅃ결ꑆ뱗ꕛ뱵꧊ꅁ덯Ꙩ뚵ꚡꕩ뭐ꖭ럆뒡룉ꓨꩫ떲ꙘꙢꑀ끟ꅁ꣒꙰Mayhewꅝ1995ꅞꕈꑔꚸꗩ볋뒡귈ꩫ결ꖭ럆ꖩꅁꣃꕈ랥ꑪ꓆궷쁉꒤ꗟ꓀끴꒧ꖭ럆ꯗꪺ랧꧀ꡄꕘ궷쁉꒤ꗟ뻷 7 ꚹꞹꗾꖫ돵꒧낲덝라꣏녯뿯뻜앶ꖫ돵믹껦뭐꣤볐ꪺ룪늣꒧궷쁉꒤ꗟꪬ멁믹껦꓀끴꒧뚡ꪺ쏶ꭙꚨ결ꑀ엩꣢궱ꅃꙝꚹꖻ곣ꡳ꒧ꓨꩫ뭐뻣귓뿯뻜앶맪쏒놴끑ꓥ쑭ꑗ꓀ꙀꙐ꒧ꞹꗾꖫ돵낲덝꒧띶늫ꅁ걏 8
뉶녋ꯗ꣧볆ꅃꖻ곣ꡳ뇄ꗎ때ꗀ볆껖끪쉫ꓨꩫ끴롭쇴ꝴꩩ둔꣧볆ꅁꣃꡄꕘ꧒쇴ꝴꪺ궷쁉꒤ꗟ뻷뉶꓀끴ꅃ ㌮€玤殻傹튼튫갠?맪쏒ꓥ쑭ꑗ엣ꗜ믹볆믹ꕾ뷦앶믹껦ꓱ믹ꖭ뿯뻜앶믹껦꣓녯꧹뙑ꅁꙝꚹꚳ꧒뿗ꪺ‘뱊꾺’ꩩ둔뉻뙈ꅁꚹ뉻뙈‘뉺뷗ꑗ’쇴ꝴ뗛ꑀ귓굴낾ꭰꟀꪺ궷쁉꒤ꗟ뻷뉶꓀끴ꅃꙝꚹꖻ곣ꡳ꒧ꗘꪺꙢ놴끑걏ꝟ꣏ꗎꑀ귓슲돦ꕂ궭꣮룻ꓖꪺ때ꗀ볆껖끪쉫ꓨꩫꕩ녎ꕝꝴꙢFTSE-100뿯뻜앶믹껦꒧쇴ꝴꩩ둔룪끔ꚨꕜꙡ신결곛맯삳꒧궷쁉꒤ꗟ꓀끴ꅃ뒫ꢥ꒧ꅁꙢ낲덝ꖫ돵결냊멁ꙡꞹꗾꖫ돵ꅁꖻ곣ꡳ꣏ꗎ1995꙾2ꓫ8ꓩ8ꓫ23ꓩ뿯뻜앶ꪺ돸믹ꅁ놴끑껖끪쉫쇴ꝴꩩ둔뭐꛴군ꛓ녯꒧궷쁉꒤ꗟ꓀끴걏ꝟ맪쏒ꑗ꒬곛뒧삳ꅁꕈ엧쏒룓뿯뻜앶ꖫ돵믹껦ꪺꙘ뉺꧊뭐껖끪쉫ꓨꩫ꧳룪껆듁뚡ꪺ빁ꗎ꧊ꅃꖻꓥ꣏ꗎ꒧군뙱ꓨꩫ뙽ꥬ꧳때ꗀ볆껖끪쉫꛴군ꕈ뿯뻜앶믹ꛬ뙚꒵꣬듁ꓩ결깹볐뙢ꪺB-S쇴ꝴꩩ둔ꚱ궱ꅆ놵뗛녎ꚹꩩ둔ꚱ궱럭ꝀB-Sꥷ믹꒽ꚡ꒧뿩ꑊ엜볆ꅁꣃ꣏ꗎBreedenLitzenbergerꅝ1978ꅞꪺ붺ꚡ믹깴ꓨꩫ군뫢ꕘ꒣Ꙑ뙚꒵꣬듁ꓩFTSE 100궷쁉꒤ꗟ꓀끴ꅆ곛쏶ꪺꡂ왊뎯굺꙰ꑕꅃ??㌮ㄠ때ꗀ볆껖끪쉫??ꙝ결룪껆ꖻꢭ라뒣꣑곛쏶ꪺ끔꺧ꅁꙝꚹꙢ때ꗀ볆끪쉫꓀꩒꒤ꅁꭙꝑꗎ룪껆꣓뮡ꧺ끪쉫꣧볆ꅃꙢ때ꗀ볆끪쉫꓀꩒꒤ꅁ낣ꑆ굮ꡄ끪쉫꣧볆ꅝmꅞ결ꖭ럆ꪺꚱ뵵 ꝟ맪믚ꖫ돵결ꞹꗾꖫ돵ꭨ쓝ꕴꑀ쒳썄ꅁ꒣ꙁꖻ곣ꡳ꒧놴끑뵤돲꒺ꅃ 9
nꕾꅁꣃ꒣ꭝ궭꣧볆ꅝmꅞꪺꚡꅃ낲덝ꚳꑀ닕룪껆{X,Y}ꅁ꣤ꑀ꿫볒ꮬꕩꕈꫭꗜiii=1꙰ꑕꅇ??Y=m(X)+ε,i=1,Λ,n₡崱ꅞ?iii2꣤꒤m걏ꑀꖼꪾꪺꖭ럆꣧볆ꅁε결듁뇦귈결륳ꕂ엜늧볆결σꪺ끪쉫뭾깴ꅁn결볋iꖻ볆ꅃ때ꗀ볆끪쉫꓀꩒걏ꑀ뫘녱꣼ꑺ쉚ꪺ룪껆꒤ꅁ꛴군끪쉫꣧볆ꕘ귬ꚳ꽓꧊ꪺꖭ럆ꓨꩫꅃꗑ꧳때ꗀ볆끪쉫볒ꮬꡓꚳ덝ꥷmꪺ꣧볆ꮬ멁ꅁ꧒ꕈ꣤쁵쉉Ꙣ꧳엽룪껆ꞹꗾꫭ륆볒ꮬ끔꺧ꅁꛓ꣤꿊쉉Ꙣ꧳ꙝ결ꡓꚳ덝ꥷ끪쉫꣧볆mꪺ꣧볆ꮬ멁ꅁ꧒ꕈ맯꓀꩒떲ꩇꝀ룑쓀껉ꅁ라ꓱꚳꗀ볆끪쉫룻ꡓꚳꪽ왛ꑗꪺ띎롱ꅃꙢ때ꗀ볆끪쉫꓀꩒꒤ꅁꕈ껖꛴군뙱돌결슲돦ꕂ뱳꩸ꙡ덑꣏ꗎꅃ껖꛴군뙱ꕩꕈ곝ꚨ걏ꑀ뫘맯곛엜볆Ꝁ냏냬늾냊ꕛ앶ꖭꞡ꧒녯꣬ꪺ꛴군뙱ꅃ럭끪쉫꣧볆m걏ꑀ귓ꖭ럆꣧볆ꅁꙢ꛴군m(x)ꪺ껉귔ꅁꕩꪾꙢx꫱ꪺX꧒맯삳ꪺYꝴꚳm(x)ꪺ끔꺧ꅁꛓꙢx꫱ꕈꕾꪺiiX꧒맯삳ꪺYꕵꚳꓖ뙱곆ꛜꡓꚳm?x?ꪺ끔꺧ꅃ꧒ꕈ굮꛴군m?x⤠꒧돌슲돦ꓨꩫꅁii둎걏녎덯녡ꚳm?x?끔꺧ꪺ룪껆낵ꕛ앶ꖭꞡꅃ덯귓꫱ꪺꯗꅁ뫙꒧결녡뱥ꖭ럆냑볆ꅁꕈh꣓ꫭꗜꅃꛜ꧳꓀끴떹ꙕ귓왛듺귈Yꪺ앶볆ꅁꭙꗑꑀ귓떹ꥷꪺ껖꣧볆i?ꡍꥷꅆ덯볋ꪺꕛ앶ꖭꞡ꛴군뙱둎ꕳ낵껖꛴군뙱ꅁ돌녠ꢣꪺ껖꛴군뙱결NadarayaWatsonꙢ1964꙾꧒뒣ꕘꪺ닎군뙱ꅆ럭볋ꖻ결쁈뻷덝군껉ꅁNadarayaWatsonꪺ꛴군뙱걏룻빁Ꙙꪺꅃ꣤돦ꑀꛛ엜볆볒ꚡꕩꫭꗜ꙰ꑕꅇ?nx−XiK()Y∑ihi=1?mˆ(x)=₡崲ꅞ?nx−XiK()∑hi=1덯료ꅁxꫭꗜ뇽꛴군삳엜볆꧒맯삳ꪺꛛ엜볆ꅁꛓXꕎꫭꛛ엜볆ꪺ왛듺귈ꅁ삳엜볆iY꧒ꕝꝴꪺ끔꺧ꑪꑰ결K(x)ꅁ꣤꒤K(x)₮효욬낤䂥寅皨욡䆨ꎶ좭溯?ii,n 10
앶볆ꑪꑰꅁꛓꕂ굮꿠엣ꗜ앶볆꣧볆ꪺ꧊뷨ꅁ덱녠뿯ꥷꪺ껖꣧볆결ꑀ덳쓲ꅂꚳ곉ꕂ맯뫙ꪺ맪볆꣧볆ꅃK(x) ꒤ꪺ녡뱥귈hꡍꥷꑆx꒧빆냬ꅁꣃ놱꣮앶볆ꑪꑰꅁꕂꡍꥷ삳ꗑ귾왛듺귈꣓낵ꕛ앶ꖭꞡꅃꕈ뱩곹믹껦X꒧낪뒵껖꣧볆결꣒ꅁ꣤꣧볆ꮬꚡ꙰꒽ꚡꅝ3ꅞ꧒ꗜꅁ결Ꙣ(X−X)쉉ꪺ낪뒵뻷뉶꣧볆낪ꯗꅁ꣤꒤i2(X−X)~ND(0,h)ꅇ?iX2X−X1(X−X)ii?K=exp−₡崳ꅞ?X2h2h2πhXXX?덯료ꅁ뻷뉶꓀끴ꪺ뱥ꯗ걏ꗑ녡뱥귈h꧒놱꣮ꅃꙝ결녠멁꓀끴Ꙣ꣢궿볐럇깴꒧ꕾꅁX꣤뻷뉶귈둎ꑰ꣬ꕩꕈꦿ늤ꅁ꧒ꕈ꣺X±2h뵤돲꒺ꪺ룪껆(X,σ)꣓낵ꕛ앶ꖭꞡꅁXii꣤맏ꫭꗜ꙰맏ㆡ䎦嗆宴輸䦪뫅皭ꮧ妬낹?1꧒맯삳꒧뗪뵵ꪺ낪ꯗꅁ녎X±2h꒺Xꪺ꧒ꚳ왛듺귈σ궼ꑗ앶궫꒧ꯡꕛ셠ꝙꕩꡄ녯곛맯삳꧳Xꪺσ꛴군귈ꅁσˆ(X)ꅃ i ?σi?* **?**X−XikXhX? X ?X− 2 h X+2h xXx맏?돦엜볆껖끪쉫? k(⋅) 결뱩곹믹껦X꒧낪뒵껖꣧볆ꅁ룓뻷뉶꓀끴ꪺ뱥ꯗꭙꗑ녡뱥귈h꧒놱꣮ꅆ룓맏엣ꗜ꣏ꗎX±2h 뵤돲꒺왛XX X 듺귈ꅝXꅁσꅞ꣓꛴군뱩곹믹껦X껉ꅁꙕ왛듺귈꧒샲녯ꪺ앶볆ꑪꑰꅆ꣤꒤σ결X곛맯삳꒧B-S쇴ꝴꩩ둔ꅃ iiii 11
럭ꛛ엜볆결ꑔ귓껉ꅝ꙰ꖻ곣ꡳ결ꡄ궷쁉꒤ꗟ꓀끴꧒꣏ꗎꪺꩩ둔껖끪쉫ꅁꛛ엜볆결SꅂXꅂTꅞꅁ꣺(S±2h)×(X±2h)×(T±2h)뵤돲꒺ꪺB-S쇴ꝴꩩ둔왛듺귈SXTσ(S,X,T)ꅁ궼ꑗ곛맯삳꒧앶볆ꅁꕛ셠ꯡꭋꕩꡄ녯끷맯SꅂXꅂTꪺꩩ둔꛴군귈iiii?ˆσ(S,X,T)ꅁ꣤꒤꧒꣏ꗎꪺ껖꛴군뙱결??????????????₫?겦ꆦ껖炤꛴붦군?뙱ꅁꅝ4ꅞꅃ? nS−SX−XT−Tiiikkkσ∑SXTihhhi=1SXT ꅝ4ꅞ mˆx=σˆ()(S,X,T)=NWnS−SX−XT−Tiiikkk∑FXThhhi=1SXT?(S,X,T)덯료ꅁ결뇽뒡룉꒧ꛛ엜볆룪껆쉉ꅁ꣤꒤S결ꗘꭥ믹볆믹껦ꅁX결뿯뻜앶뱩곹믹껦ꅁT결뙚꒵꣬듁ꓩꅆkk(⋅)ꅂk(⋅)ꅂ(⋅)꓀ꝏ결SꅂXꅂT꒧껖꣧볆ꅁTSXꖻꓥ뇄ꗎ낪뒵꣧볆ꅝꗧꝙ볐럇녠멁꓀끴ꅞꅃ?ꗑ꧳낲덝쇴ꝴꩩ둔꣧볆걏ꖭ럆ꪺꅁꙝꚹ껖꛴군뙱ꕩ덳쓲띌꓀ꪺꚸ볆꒣꿠ꓖ꧳껖꛴군뙱맯ꛛ엜볆띌꓀ꪺꚸ볆ꅁꑝ둎걏맯꧒ꚳ꒶꧳1ꛜd꒧ꛛ엜볆jꅁ꣣ꚳp≥mj꽓꧊ꅁ꣤꒤p결껖꛴군뙱ꕩ덳쓲띌꓀ꪺꚸ볆ꅁm결껖꛴군뙱맯ꛛ엜볆j띌꓀ꪺꚸj볆ꅁd결때ꗀ볆껖끪쉫꒤ꛛ엜볆꒧귓볆ꅃꖻꓥ꒤꧒믝돌Ꙩꚸꪺ띌꓀둎걏Ꙣꡄ궷쁉꒤ꗟ꓀끴껉ꅁ뿯뻜앶믹껦ꖲ뚷맯뱩곹믹껦Ꝁꑇꚸ띌꓀ꅁꙝꚹꙢ꛴군궷쁉꒤ꗟ꓀끴껉ꅁ낲덝쇴ꝴꩩ둔꒧껖꛴군뙱결ꕩꕼꚸ덳쓲띌꓀ꅁ꧒ꕈp=4ꅃꙢ뵔ꥷꞹ껖꛴군뙱ꕩ띌ꚸ볆꒧ꯡꅁ놵ꑕ꣓ꖲ뚷뵔ꥷ껖꣧볆ꪺ뚥볆ꅁꥷ롱껖꣧볆ꅝKꅞꪺ뚥볆ꅝsꅞj 8 Härdleꅝ1990ꅞꅂAït-SahaliaLoꅝ1998ꅁ2000ꅞꅂHärdle, Müller, Sperlich Werwatzꅝ2002ꅞ꣏ꗎNadaraya-Watson껖꛴군뙱꣓룑쓀ꛛ엜볆뭐ꙝ엜볆꒧뚡ꪺ껖끪쉫쏶ꭙꅃ 12
∞l결낸볆뽮꓀ꕂ몡ꢬꑕꙃ쏶ꭙꅇzK(z)dz=0ꅁl=1,3,5,Λ,s−1ꅁꕂj∫−∞∞sjzK(z)dz<∞ꅆ꣤꒤s=p−mꅁj=SꅁXꅁTꅆz결볐럇꓆ꛛ엜볆ꅝꕈ뱩곹jjj∫−∞믹껦X결꣒ꅁz=(x−X)hꅁ꣤꒤x결뇽꛴군ꪺ뱩곹믹껦ꅞꅆp결쇴ꝴꩩ둔껖꣧Xj볆맯닄j귓ꛛ엜볆z덳쓲ꕩ띌꓀ꪺꚸ볆ꅃꑀ꿫ꛓꢥꅁ꣏ꗎ뙖낪뚥껖꣧볆ꅁ라늣ꗍj뙖ꑰꪺ낾깴뚵ꅝbiasꅞꅁꗧꝙꅁ럭꣏ꗎ룻낪뚥ꪺ껖꣧볆껉ꅁ럭볋ꖻ볆ꅝnꅞ뱗ꕛ껉라ꕛꟖ꛴군뙱ꚬ샄꣬꽵ꖿ꣧볆ꪺ덴ꯗꅃꓓ낪뚥ꪺ껖꣧볆Ꙣ군뫢껉ꕩ꿠라ꚳ꒣몡띎ꪺꙡꓨꅁ꣒꙰꧒군뫢ꪺ껖꣧볆귈꒣결ꖿ볆ꅁ꧒ꕈꓥ쑭ꯘ쒳껖꣧볆ꪺ뿯꣺돌ꙮ꒣굮뙗륌ꕼ뚥ꅃꙢꖻꓥ꒤꧒ꗎꪺ껖꣧볆걏낪뒵껖꣧볆ꅁ꣤꒤ꑇ뚥ꪺ껖꣧볆ꚡ결222k(z)=12πexp(−z2)ꅁꕼ뚥껖꣧볆결k(z)=38π(1−z3)exp(−z/2)ꅃꛜ(2)(4)꧳녡뱥귈ꑪꑰꪺ뿯꣺쏶ꭙ뗛껖꛴군뙱ꪺ빁ꗎ꧊ꅆ녡뱥귈꣺ꪺꓓꑰ꧒샲녯ꪺ꛴군뙱라ꖭ럆꒣ꢬꅁ녡뱥귈꣺ꪺꓓꑪ꧒샲녯ꪺ꛴군뙱ꑓꓓ륌ꖭ럆ꅃꑀ꿫ꛓꢥꅁ꙰맏2꧒ꗜꅇ껖꛴군뙱ꪺ낾깴뙱ꅝbiasꅞ뭐엜늧뙱ꅝvarianceꅞ꓀ꝏ쁈뗛녡뱥귈ꪺ뱗ꕛꛓ뱗ꕛ뭐듮ꓖꅁꙝꚹ꛴군뙱꒧ꞡꓨ깴ꅝMSEꅆ결낾깴뙱ꪺꖭꓨ뭐엜늧뙱꒧ꥍꅞꙢ돌빁녡뱥귈ꑕ라ꚳ돌ꑰ귈ꅃ??ꞡꓨ깴ꅝhꅞ 낾깴뙱ꪺꖭꓨꅝhꅞ? 엜늧뙱ꅝhꅞ *h 녡뱥귈ꅝhꅞ ?맏?₮횦炶熤Ʂ?Ꞷ떻傰뺮璶딠p−m−(2m+d)−1jjꙢ맯때ꗀ볆끪쉫꛴군ꚡꪺ닄?귓ꛛ엜볆Ꝁmꚸ띌꓀껉ꅁ라늣ꗍbhꪺ낾깴뚵vnhꪺ엜늧뚵ꅁ꣤꒤?뭐?결jjjꭙ볆뚵ꅁ?결볋ꖻ볆ꅁ?결때ꗀ볆끪쉫꒤ꛛ엜볆꒧볆ꗘꅁ?결쇴ꝴꩩ둔껖꛴군뙱ꕩ덳쓲띌꓀꒧ꚸ볆ꅃꖻꓥꕈ꿠꣏ꞡꓨ깴륆꣬2(p−m)−(2m+d)2−1jj*돌ꑰꪺ녡뱥귈결돌빁녡뱥귈ꅝhꅞꅆꗧꝙ랥ꑰ꓆MSE(h)?bh?vnhꅃ럭낾깴뙱ꪺꖭꓨ뭐엜늧뙱곛떥껉jjj1(d+2p)2(p−m)−(2m+d)2−12−1(d+2p)jjꅝꗧꝙꅁbhꇗvnhꅞꞡꓨ깴라돌ꑰꅁꚹ껉h=(vb)nꅃ?jjj? 13
뻚돌빁녡뱥귈꒽ꚡ뭐Aït-SahaliaLoꅝ1998ꅞꪺꯘ쒳ꅁꖻ곣ꡳ맯꧳ꡃꑀ귓ꛛ엜볆ꪺ녡뱥귈뿯꣺럇ꭨ꙰ꑕꅇ?−1(d+2p)?h=cs(z)n₡崵ꅞ?jjj꣤꒤s(z)결ꛛ엜볆zꪺꭄ뇸ꗳ볐럇깴ꅁj=1ꅁ2ꅁ…ꅁdꅆc=cln(n)ꅁc결ꑀjjjj0j0녠볆ꅆp결껖꣧볆ꕩ띌꓀ꚸ볆ꅆd결ꛛ엜볆볆ꗘꅃꙢ꛴군ꩩ둔꣧볆껉ꅁꖻꓥꭙꕈ꣢귓ꛛ엜볆ꅝd=2ꅞꪺ껖끪쉫볒ꚡ꣓꛴군ꩩ둔ꚱ궱ꅁ꣢ꛛ엜볆꓀ꝏ결믹ꛬꅝ(S−D)Xꅞ뙚꒵꣬듁ꓩꅝTꅞꅆꛓꙢꡄ꣺궷쁉꒤ꗟ꓀끴껉ꅁꭙꕈꑔ귓ꛛ엜볆ꅝd=3ꅞꪺ껖끪쉫볒ꚡ꣓꛴군ꩩ둔ꚱ궱ꅁꛛ엜볆꓀ꝏ결볐ꪺ믹볆ꅝSꅞꅂ뱩곹믹껦ꅝXꅞ뙚꒵꣬듁ꓩꅝTꅞꅃꙝ결Ꙣ꛴군쇴ꝴꩩ둔꣧볆껉ꅁ꒣믝맯ꗴ꛳ꛛ엜볆꣓띌꓀ꅁꙝꚹ낲덝ꩩ둔껖꛴군뙱결ꑇ뚥ꕩ띌ꅝp=2ꅞꅁꕛꑗꡃ귓ꛛ엜볆믝덑띌꓀ꪺꚸ볆m결0ꅁꙝꚹ믹ꛬ뭐뙚꒵꣬듁ꓩꪺ껖꣧볆뇄ꑇ뚥ꮬꚡꅝꗧꝙꅁjk=k=kꅞꅁꚹ껉2ꓫ8ꓩꅝ8ꓫ23ꓩꅞ룪껆꒧믹ꛬ녡뱥귈결(2)ꅝꅞꅁꛓ뙚꒵꣬듁ꓩ녡뱥귈결ꅝꅞꅃꙢ꛴군볆뿯뻜앶ꪺ궷쁉꒤ꗟ뻷뉶꓀끴껉ꅁꖲ뚷녎뿯뻜앶ꥷ믹꒽ꚡ맯뱩곹믹껦Ꝁꑇꚸ띌꓀ꅁꙝꚹ낲덝ꩩ둔껖꛴군뙱결ꕼ뚥ꕩ띌ꅝpꇗ4ꅞꅁꚹꕾ낣ꑆꛛ엜볆Xꪺm결2ꅁ꣤빬ꛛ엜볆ꪺm결0ꅁjjꙝꚹ뱩곹믹껦ꪺ껖꣧볆뇄ꑇ뚥껖꣧볆ꅝs=p−m=4−2=2ꅞꅁꛓ돑ꑕꪺ꣢ꛛXX엜볆ꅝSꅂTꅞꪺ껖꣧볆곒뇄ꕼ뚥껖꣧볆ꅝs=p−m=4−0=4ꅞꅁꗧꝙjjk=k=kꅁꛓk=kꅃꚹ껉2ꓫ8ꓩꅝ8ꓫ23ꓩꅞ꒧볐ꪺ믹볆ꅂ뱩곹믹ST(4)X(2)껦뙚꒵꣬듁ꓩ꒧녡뱥귈꓀ꝏ결ꅝꅞꅂꅝꅞ뭐ꅝꅞꅃꫭ1결뻣뉺ꯡ꒧볆뻚ꅁ엣ꗜꖻꓥ꧳꛴군쇴ꝴꩩ둔ꚱ궱뭐궷쁉꒤ꗟ뻷뉶꓀끴껉ꅁ껖꣧볆뭐녡뱥귈ꪺ뿯꣺ꅃ? 14
?ꫭㄠ꛴군쇴ꝴꩩ둔ꚱ궱뭐궷쁉꒤ꗟ뻷뉶꓀끴껉ꅁ껖꣧볆뭐녡뱥귈ꪺ뿯꣺??p?껖꣧볆?s?m?c?σ?h?d?jjjjj?†?쇴ꝴꩩ둔ꚱ궱??????ㄮ㘴㠴?†〮〷㠷??〮〵㈰?k=k?㈠㈠〠㈠⨪⨪⨪SX(2)ㄮ㤳㠷?†‰⸰㤲?〮〷〰????〮㜷?㠮ㄸ㈶?㐮㘷〰?k=k?㈠㈠〠㈠⨪⨪⨪T(2)〮ㄸ㌶?†㠳⸳㈶?㔮㤶〰??††???궷쁉꒤ꗟ뻷뉶꓀끴?†???㈮㐷㔶?″⸹㌰㔠?㔮㤱?k=k?㐠㐠〠㌠⨪⨪⨪S(4)㐮〴㈷?㌸⸱㠸??㤲⸳????ㄮ㐴㔹?㈲㤮㌰〶?㈰ㄮ㌷?k=k?㈠㐠㈠㌠⨪⨪⨪X(2)ㄮ㔹㤸?㈸㌮㤱㠲?㈷ㄮ㘱????㐮㘴㘲?㠮ㄸ㈶?㌰㔮㈹?k=k?㐠㐠〠㌠⨪⨪⨪T(4)㌮ㄲ㤴?‸㌮㌲㘱?ㄵ㔮㤳??뗹ꅇ??⨪ㄮ?ꫭ뿯뻜앶룪껆ꗦ꧶ꓩ결1995꙾2ꓫ8ꓩꅆꫭ뿯뻜앶룪껆ꗦ꧶ꓩ결1995꙾8ꓫ23ꓩꅃ?㈮₦烁璪榴咮즡?j=(Dꅝ믹ꛬꅁSXꅞꅂT?ꅆ꛴군궷쁉꒤ꗟ꓀끴껉ꅁj㴠SꅂXꅂT ꅃ?S−)X㌮?d결껖꛴군뙱꒤ꛛ엜볆ꪺ볆ꗘꅁ꧳꛴군쇴ꝴꩩ둔껉ꅁd=2ꅆ꧳꛴군궷쁉꒤ꗟ꓀끴껉ꅁd=3ꅃ?㐮?s결닄?귓ꛛ엜볆ꪺ껖꣧볆뚥볆ꅃ?j㔮?p결ꩩ둔껖꛴군뙱ꕩ띌꓀ꪺꚸ볆ꅃ?㘮?m결껖꛴군뙱믝맯닄?귓ꛛ엜볆Ꝁ띌꓀ꪺꚸ볆ꅃ?j㜮?σ결닄?귓ꛛ엜볆ꪺ볋ꖻ볐럇깴ꅃ?j㠮?h결닄?귓ꛛ엜볆ꪺ녡뱥귈ꅃ?j??㌮㈠쇴ꝴꙢ뿯뻜앶믹껦꒤ꪺ궷쁉꒤ꗟ뻷뉶꓀끴??BreedenLitzenbergerꅝ1978ꅞ뒣ꕘ돌ꑀ꿫꓆꛴군궷쁉꒤ꗟ뻷뉶꓀끴ꪺꓨꩫꅃꕌ귌ꕘ꙰ꩇ볐ꪺ룪늣ꪺ꣬듁믹껦ꚳꑀ덳쓲뻷뉶꓀끴ꅁꭨ녎볚ꚡ뿯뻜앶ꥷ믹꒽ꚡ맯뱩곹믹껦Ꝁꑇ뚥띌꓀ꯡꕩ녯꣬볐ꪺ룪늣꣬듁믹껦ꅝSꅞ떥꧳뱩곹믹껦TꅝXꅞꪺꪬ멁믹껦ꅝArrow-Debreu priceꅞꅁꛓꪬ멁믹껦ꙁ궼ꑗꑀ뷆ꝑꙝꑬ 15
ꅝexp(rT)ꅞꝙꕩꡄꕘ럭Sꇗ?ꑕ꒧궷쁉꒤ꗟ뻷뉶귈ꅝf(S)ꅞꅁ꣤ꚡ꙰꒽ꚡt,TTTꅝ㚡庡䌠2∂H(⋅)?f(S)=exp(rT)×₡崶ꅞ?Tt,TS=X2T∂X덯료ꅁt결ꗘꭥ껉뚡ꅁT결뿯뻜앶뙚꒵꣬듁ꓩꅁS결뿯뻜앶꣬듁ꓩ볐ꪺ믹볆믹T껦ꅁH결볚ꚡ뿯뻜앶ꗘꭥ믹껦ꅁr결뙚꒵듁뚡결Tꪺ때궷쁉ꝑ뉶ꓴ럇ꅃ?t,Tꕈ???뿯뻜앶ꥷ믹꒽ꚡ결꣒ꅁ껚뻚꒽ꚡꅝ6ꅞ꧒ꡄꕘꪺ궷쁉꒤ꗟ꓀끴결맯볆녠멁뻷뉶꓀끴ꅁ꙰꒽ꚡꅝ7ꅞ꧒ꗜꅇ?2∂Hˆf(S)=exp(rT)BS,tTt,TS=X2T∂X?2₡崷ꅞ?*2[ln(SS)−(r−σ2)T]1Ttt,T=exp−222σTS2πσTT*덯료ꅁH결B-S뿯뻜앶ꥷ믹꒽ꚡꅆS결꣬듁껉믹볆ꅆS=S−Dꅁ꣤꒤S결Ttttt껉뚡t꒧볐ꪺ룪늣믹껦ꅁD결뿯뻜앶듁뚡꒧볐ꪺ룪늣뉻ꝑ뉻귈ꅆr결때궷tt,T쁉ꝑ뉶ꅆT결뙚꒵꣬듁ꓩꅆσ결껖끪쉫꧒꛴군믹ꖭ뿯뻜앶ꪺ쇴ꝴꩩ둔ꅃ?럭S=X땯ꗍ껉ꅁ꣬듁돸쁶결?$1ꪺꪬ멁믹껦ꕩ롧ꗑꑀ귓붺ꚡ믹깴떦늤꣓뷆T뭳ꅃꗧꝙꅁ뷦ꕘꑇ귓뱩곹믹껦결Sꪺ뙒앶ꣃꙐ껉뙒뙩뱩곹믹껦꓀ꝏ결S−∆STTTS+∆Sꪺ뙒앶ꅆ럭∆S때궭ꑰ껉ꅁ룓붺ꚡ믹깴떦늤라쇍꫱꧳S=Xꪬꩰꑕ궷쁉TTTT꒤ꗟ뻷뉶귈ꪺꗘꭥ믹껦ꅃꙝꚹꅁꖻꓥ뇄붺ꚡ믹깴ꪺ맪Ꝁꓨꩫ꣓ꡄ녯FTSE 100믹볆꒧궷쁉꒤ꗟ뻷뉶꓀끴ꅁ꙰꒽ꚡꅝ㢡庩튥?䜠2∂HH+H−2Hi+1i−1i?=i=1,Λ,N₡崸ꅞ?S=X2T2i∂X∆X 16
꣤꒤X<X<Xꅆ∆X=X−X=X−XꅆN결껖끪쉫뒡꓀ꯡ꒧볋ꖻ볆ꅆi−1ii+1i+1iii−1H결ꯘ멣꧳껖끪쉫쇴ꝴꩩ둔ꑗꪺB-S뿯뻜앶믹껦ꅃ녎ꑗꚡ꧒ꡄ녯ꪺ귈ꙁ궼ꑗ뷆ꝑꙝꑬꅝexp(rT)ꅞꅁꝙꕩꡄꕘ믹돸륓궷쁉꒤ꗟꑕꪺ뻷뉶녋ꯗ꣧볆ꅃ?t,T 㐮₸욻傹튵늪䜠?㐮ㄠ?룪껆??ꖻꓥꕈLIFFE꒧FTSE 100믹볆뿯뻜앶꧳1995꙾2ꓫ8ꓩ뭐8ꓫ23ꓩꪺ뵌꒤돸믹결귬ꥬ룪껆ꅁꚹꗦ꧶ꓩ꒧뿯꣺ꭙ뻚룪껆꒧ꕩ샲녯꧊룓ꓩ꣣ꚳ룻Ꙩ?뿯뻜앶돸믹ꚸ볆ꅃ₨쾥캽䲤꒸욥槁䮦嶨쾥캿?앶ꚬ뵌믹꧒덹ꚨ뭐볐ꪺ믹볆ꭄꙐ껉돸믹꒧낾뭾ꅆꡃꑀ떧뿯뻜앶ꪺ믹껦뇄뙒믹ꅝbidꅞ뭐뷦믹ꅝaskꅞ꒧ꖭꞡꅃꙝ결꣏ꗎ꒧FTSE-100뿯뻜앶결볚ꚡꮴ곹ꅁꙝꚹ볆믹껦ꓴ럇믝ꚩ낣ꖼ꣓뿯뻜앶꣬듁ꓩ꒧ꭥ꒧뉻ꝑ뉻귈ꅁ꣤꒤뉻ꝑꭙꗑ닕ꚨFTSE 100믹볆꒧ꙕ꒧뉻꺧럓꧒볆ꓱ꣒군뫢ꛓ녯ꅃꚹꕾꅁꗦ꧶꒣쁗셣륈깍ꝑ뇸ꗳ꒧뿯뻜앶룪껆ꕩ꿠ꝴꚳ싸끔뱗ꕛ꛴군ꑗ꒧낾뭾ꅁꖻꓥꝒ낣ꚹ뿯뻜앶ꅃꙝꚹ꣏ꗎ꒧뿯뻜앶ꞡ닅Ꙙꛒ뱻쇴ꝴꚨꖻꅝꗧꝙ뙒뷦믹깴ꅞꯡ꒧뉺뷗ꑗꑕ곉ꅁꣃꙢꝒ낣쇴ꝴꩩ둔ꑪ꧳ꅂ꣬듁ꓩꑰ꧳6ꓑꅂ뿯뻜앶믹껦ꑰ꧳8ꭋꑨꪺ룪껆ꯡꅁ?2ꓫ8ꓩꅝ8ꓫ23ꓩꅞꙀꚳ240ꅝ286ꅞ떧룪껆ꅁ꣤꒤ꕝꝴ129ꅝ156ꅞ떧뙒앶111ꅝ130ꅞ떧뷦앶ꅃ꣤꒤ꚳ0ꅝ0ꅞ떧뿯뻜앶뙚꒵꣬듁ꓩꑰ꧳6ꓑꅁ%ꅝ%ꅞ뿯뻜앶륈뉺뷗ꑗꅂꑕ곉ꅁ%ꅝ%ꅞ뿯뻜앶믹껦ꑰ꧳8ꭋꑨꅃꚹꕾꅁꗑ 9 ꣏ꗎ8ꓫ23ꓩ뿯뻜앶믹껦걏결ꑆ뮡ꧺ꒣Ꙑꓩ듁룪껆꒧꣏ꗎꣃ꒣라뱶암맪쏒ꪺ떲ꩇꅃ 17
꧳귛뒰ꕈ굞싩결볐ꪺ꒧볚걷덦맴ꝑ뉶ꅝEuro-currency interest rate for sterling poundsꅞꪺꝑ뉶듁뚡ꥍFTSE-100볆뿯뻜앶ꪺ듁뚡곛쏾ꅁꙝꚹꖻꓥ꣏ꗎ룓ꝑ뉶ꓴ럇결때궷쁉ꝑ뉶ꅁ룪껆꣓랽결Datastreamꅃꫭ2둹굺꒣Ꙑ뙚꒵꣬듁ꓩ뭐믹ꛬꪺ볋ꖻ룪껆꽓꧊ꅁ꣤꒤믹ꛬꅝmoneynessꅞꪺ군뫢ꓨꚡ결ꗘꭥ볆믹껦ꚩ낣뿯뻜앶꣬듁ꓩ꒧ꭥ뉻ꝑ뉻귈ꅁꙁ낣ꕈ뱩곹믹껦ꅝꗧꝙꅁ(S−D)Xꅞꅃ2ꓫ8ꓩꅝ8ꓫ23ꓩꅞ뿯뻜앶ꖭꞡ돸믹뵤돲ꕝ걁ꗑ땵듁믹ꕾ뙒앶믹껦ꭋꑨꅝ땵듁뉠ꯗ믹ꕾ뙒앶믹껦ꭋꑨꅞꛜ듁뉠ꯗ믹꒺뙒앶믹껦ꅝꅞꭋꑨꅁ뙒뷦믹깴ꗑ땵듁믹ꕾ뷦앶믹껦ꅝꅞꭋꑨꛜ듁믹ꖭ뙒앶믹껦듁믹꒺뷦앶ꭋꑨꅝ듁뉠ꯗ믹꒺뷦앶믹깴ꭋꑨꅞꅃ??ꫭ?₼?FꚡTSE 100믹볆뿯뻜앶ꅇ귬ꥬ볋ꖻ꽓꧊?ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ?ꓩ?믹ꛬ†뿯뻜앶?뙒앶?뷦앶??†뙚꒵꣬듁ꓩ?뙚꒵꣬듁ꓩ?뙚꒵꣬듁ꓩ???†㘰?㘰縱㠰??ㄸ㘰〠?㘰縱㠰??ㄸ㘰〠?㘰縱㠰?ꑰ?군ㄸ〠??⸹㐠믹껦?ㄹ㜮〰?ㄱ㠮㘸?ㄴ〮〶??㈶⸹?㘸⸹?ㄹ㜮〰㈴ㄮ〰?㌰ㄮ㔹?₻㌮瑩〰琠㐮㠲㘮㠸??㐮ㄹ㔮㌳㌮〰㔮㘷⸴ㄠ₼ㄴ욶ㄠ?焠㌶??㈵??ㄱ?㔱〮㤴縰⸹㜠믹껦?㔹⸳㔠㤴⸲㈠ㄴ㘮㔶ㄱ⸰?㜷⸶?ㄴ㌮㜹ㄳㄮ㜵ㄲ㜮㈵㌳??ㄵ㘮₻㈮瑩㐵琠?㐮㈲㘮㔶㈮㈵㌮㘷㔮〷㈮㜵㔮㌳?ㄱ⸷㔠₼욶㔠焠?‹?????㈳㈠〮㤷縱⸰〠믹껦?㌲⸵㘠㤮㈰?ㄵㄮ㤲㈹⸰?ㄲ㔮㔰㈱㌮㜵㌸⸱?〰㠴†⸷㔠ㄲㄮ₻㈮瑩ㄲ琠?㔮〰㠮㜵ㄮ㤷㐮㔰ㄱ⸷?㈮㌵㔮㜵?㜮㈵₼욶㐴焠?㔠???????㔵㐠ㄮ〰縱⸰㌠믹껦?㌳⸱㘠㤰⸰〠ㄲ㠮㌰㠵⸵?ㄵ㘮ㄷ㈷㘮〰ㄶ⸶?㔰⸳?〠㤱⸳?₻ㄮ瑩㜲琠?㐮㌸㘮㈮〸㔮ㄷㄱ⸵?ㄮ㘱㌮㤰㐮㜵?₼욶㈵焠㠠??????㐳㠠ㄮ〳縱⸰㘠믹껦?㐲⸷㜠ㄱㄮㄳ?ㄳ㈮㠱ㄴ㌮㌳ㄹ㠮㈵㌴㔮㔰ㄲ⸶?㈴㤲⸰?〠㘱?₻ㄮ瑩㜳琠?㌮㘳㘮㠱㈮㘷㌮㜵ㄱ⸵?ㄮ㐵㌮㔰?㔮㈵₼욶ㄳ焠?㐠???㈵㘠㈠??⸰㘠믹껦?㌵㠮㈹?㈵㈮㤵?㈴㔮㠳㌵㠮㈹㌹㌮㌰㔰㔮㈵??ㄹ⸰㈳㐠⸴㘠₻㈮瑩㜱琠㐮㐸㤮㘳㈮㜱㐮㤰ㄱ⸵???㌮㜹?㜮㤶₼욶ㄴ焠?ㄶ?ㄳㄴ??㐳㜠㘠ꑰ군†㈠㔶?㠲㔳㌲㐴㐹㈴?㌸?㈴?????? ꚹ룪껆꒧뿯꣺ꭙ냑ꛒAït-SahaliaLoꅝ1998ꅞꪺ룪껆뿯꣺럇ꭨꅃ 18
ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ??ꓩ?믹ꛬ†뿯뻜앶?뙒앶?뷦앶??†뙚꒵꣬듁ꓩ?뙚꒵꣬듁ꓩ?뙚꒵꣬듁ꓩ???†㘰?㘰縱㠰??ㄸ㘰〠?㘰縱㠰??ㄸ㘰〠?㘰縱㠰?ꑰ?군ㄸ〠??⸹㐠믹껦?ㄮ㔰?ㄷ㘮㤶?ㄶ㈮㔶㠮〰㈲⸹?㠵⸶?ㄹ㔮〰㈸㐮㜵?㈷㈮㔰?₻㈮瑩㔰琠㐮ㄶ㤮㤱㈮〰㌮㘱㠮㜰㌮〰㐮㔵ㄱ⸶㐠₼ㄷ욶㈠?焠ㄷ????㌶㜠〮㤴縰⸹㜠믹껦?㘹⸲㔠㌮㜷?ㄵ㠮〸ㄶ⸸?㐹⸱?ㄷ㠮㔰ㄲㄮ㘷⸶ㄳ㜠㔮〰?ㄳ?₻㈮瑩ㄷ琠?㌮㜷㠮㤲ㄮ㠳㐮㌸㠮㔰㈮㔰㌮㐳?㤮㌳?₼욶ㄲ焠ㄱ???????㈹㌠〮㤷縱⸰〠믹껦?㌲⸲㘠㌮〰?ㄵ㌮㠹㈳⸰?ㄱㄮ㠸ㄹ㐮㌰㐳⸳?㌸㠸†⸵㘠㌮₻㈮瑩〸琠?㌮〵㜮㔶ㄮ㤴㈮㜳㜮㈮㈳㌮㔶?㠮ㄳ₼욶㌳焠㈱???????ㄵ㘳㐠㠠ㄮ〰縱⸰㌠믹껦?㐱⸰ㄠ㤮㤳?ㄲ㈮㈵㠷⸸?ㄵ㠮㈵㈷〮〰㈲⸲?㔵〠⸵㘠㜳⸰₻㈮瑩㈷琠?㌮㈸㔮ㄷ㈮㘷㌮ㄴ㠮㘷′⸱?㌮㐴?㐮〰?₼욶㈱焠ㄷ?ㄲ??????㔰㤠ㄮ〳縱⸰㘠믹껦?㠮㌶?ㄮ㔷?ㄷㄮ〰ㄸ㘮㈲㠮㜵㌵㌮㜵ㄱ⸱?⸱㜠㈸⸸㤠㐹₻㈮瑩㌱琠?㌮㔷㠮㠰㈮㜰㐮㔰ㄱ⸲?ㄮ㠱㌮〴?㜮ㄷ₼ㄱ욶㤠焠??????㈵㌠??⸰㘠믹껦?㐹㜮㈱?㌷〮〶?㌵㠮㠶㐹㜮㈱㔶㠮㤲㘳㔮㠲??ㄴ⸹㈰㔠⸳㘠₻㈮瑩㜵琠㌮㜴㤮㔹㈮㜵㐮㘰ㄱ⸱???㈮㈰?㜮㘴₼욶㈴焠?㌹?㈰㈴㈵ㄱ?ㄴ?㠳㤠ꑰ군†ㄠㄱ㘠㘹㘰㘲㌴㐱㔴?㌵?㈸?뗹ꅇ?ㄮ₿?皻瑩낫䮤梡䌠㈮₻簾ꞩ瞸熬낥?斫ﲼ욻瑩ꦰꎿ?皨솤Ɜ斲箪톧冲箭좡䆦䆰ꎥ䢼榬僚瑩䌠㌮₻瑩璬낿?皽說嵡獫ꅞ뭐뙒믹ꅝ扩撡庤Ɪ璲ꞡ䌠㐮?NAꫭ때룪껆꧳ꚹ룪껆쏾ꝏꅃ???㐮㈠?귬ꥬ룪껆ꪺ䈭?쇴ꝴꩩ둔??끷맯뿯뻜앶ꪺꡃꑀ떧룪껆ꅁꕩ뇀ꕘB-S쇴ꝴꩩ둔ꅁꫭ3뭐맏3엣ꗜ2ꓫ8ꓩꅂ8ꓫ23ꓩ귬ꥬ룪껆ꪺ믹ꛬꅝ(S−D)Xꅞꅂ뙚꒵꣬듁ꓩꅝTꅞꅂ뭐쇴ꝴꩩ둔꒧뚡ꪺ쏶ꭙꅃ쇴ꝴꩩ둔ꝴꚳꗦ꧶맯ꗘꭥꛜ뿯뻜앶꣬듁ꓩ꒧뚡볐ꪺ룪늣믹껦ꩩ냊ꯗꪺ륷듺ꅆ뒫ꢥ꒧ꅁ꒣Ꙑ꣬듁듁뚡ꪺ쇴ꝴꩩ둔맯볐ꪺꩩ냊ꚳ뗛꒣Ꙑꪺꖫ돵륷듁ꅃꙝꚹꅁ꒣Ꙑ믹ꛬ꒧쇴ꝴꩩ둔띌꾺뉻뙈삳ꗟꢬ꧳곛Ꙑꪺ뿯뻜앶ꗦ꧶ꓩ뭐꣬듁ꓩꅆꗧꝙꅁ쇴ꝴꩩ둔띌꾺ꚱ궱삳ꛒ뱻믹ꛬ뙚꒵꣬듁ꓩ뫻ꯗꅃ맏꒤걐뢹쉉ꫭꗜ뙒앶쇴ꝴꩩ둔귈ꅁ뛪쉉ꫭꗜ뷦앶쇴ꝴꩩ둔귈ꅃ룓맏엣ꗜ녱ꖫ돵ꑗ뿯뻜앶믹껦떥룪껆뇀ꕘ꣓ꪺ쇴ꝴꩩ둔ꅁꣃꭄ꙰B-S볒ꮬ낲덝ꩩ냊ꯗ결녠볆ꅁꛓ걏Ꙣ믹꒺뙒앶ꅝ믹ꕾ 19
뷦앶ꅞꅝ(S−D)X>1ꅞꪺ껉귔ꚳ룻ꑪꪺꩩ둔ꅁꛓꙢ믹ꕾ뙒앶ꅝ믹꒺뷦앶ꅞꅝ(S−D)X<1ꅞ껉ꪺꩩ둔ꭨ룻ꑰꅁꝥ뉻ꕘ‘뱊꾺’ꅝsmirkꅞꪺ뉻뙈ꅁꛓꭄ‘띌꾺’ꅝ???汥ꅞꪺꪬꅁꚹ뭐ꓥ쑭ꑗ맯늼뿯뻜앶곣ꡳ꒧맪쏒떲ꩇꑀ교ꅆ땍ꛓ때뷗걏‘뱊꾺’‘띌꾺’뉻뙈ꅁꑀ꿫닟멄ꑗ덱뫙결‘띌꾺’쇴ꝴꩩ둔ꅃ끷맯믹ꛬ꒧쇴ꝴꩩ둔띌꾺뉻뙈ꕩ엣ꗜꕘꑀ귓뿯뻜앶볒ꮬ꒧뻮쉟궱ꥷ믹꿠ꑏꑪꑰꅆꭄꖭ꒧쇴ꝴꩩ둔띌꾺ꚱ뵵엣ꗜ룓뿯뻜앶ꥷ믹볒ꮬꚳꥷ믹ꑗ꒧낾뭾ꅃ???ꫭ?⁂ⵓ쇴ꝴꩩ둔?FTSE-100뿯뻜앶Ꙣ1995꙾2ꓫ8ꓩ뭐8ꓫ23ꓩꪺ뵌꒤돸믹룪껆ꅁ뇀ꕘ꒣Ꙑ믹ꛬ뭐꣬듁ꓩ꒧B-S쇴ꝴꩩ둔ꅃ ?ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ?ꓩ?믹ꛬ₥ﺳꆿ?瘠뙒앶뷦앶?₶媤떨솤뙚꒵꣬듁ꓩ뙚꒵꣬듁ꓩ??㘰?㘰縱㠰??ㄸ〠?㘰?㘰縱㠰?ㄸ〠?㘰?㘰縱㠰??ㄸ〠??⸹㐠〮〰〰‰⸱㐰ㄠ〮ㄴ㠴???〮ㄵ㈳〮ㄵ㌱〮〰〰〮ㄲ㌸?〮ㄳ㜶〮㤴縰⸹㜠〮ㄲ㐲‰⸱㔴㔠〮ㄶ〸?〮ㄳ㌶〮ㄵ㤸〮ㄶ㈸〮㤹〮ㄴ㌸?ㄵ〮㐰〮㤷縱⸰〠〮ㄳ㌵‰⸱㘲㠠〮ㄶ㈲?〮ㄴ㘰〮ㄷ〲〮ㄶ㘹〮ㄱ㌶〮ㄵㄸ?ㄵ〮㤹ㄮ〰縱⸰㌠〮ㄴ㔳‰⸱㘰㤠〮ㄶ㘷?〮ㄵ㔶〮ㄷ㌹〮ㄷ㈵〮ㄴ㈰〮ㄵ㌱?ㄶ〮㔳ㄮ〳縱⸰㘠〮ㄷ㈰‰⸱㘶㜠〮ㄶ㤱?〮㈲ㄳ〮ㄷ㤰〮ㄷ㠱〮ㄵ㜲〮ㄵ㐴?ㄶ〮㘱??⸰㘠〮㌵㜳‰⸲〶㜠〮ㄸ㌸?〮㌵㜳〮㈲㜵〮ㄹ㐴??〮ㄷ㈰?〮ㄷ㐸 ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ??ꓩ?믹ꛬ₥ﺳꆿ?瘠뙒앶뷦앶?₶媤떨솤뙚꒵꣬듁ꓩ뙚꒵꣬듁ꓩ??㘰?㘰縱㠰??ㄸ〠?㘰?㘰縱㠰?ㄸ〠?㘰?㘰縱㠰??ㄸ〠??⸹㐠〮〹㈵‰⸱ㄷ㤠〮ㄲ㠰?〮㤱〮ㄱ㤳〮ㄳ㐳〮〷㔸〮ㄱ㘹?〮ㄱ㠹〮㤴縰⸹㜠〮〹㌵‰⸱㈰〠〮ㄳ㐹?〮㘹〮ㄲㄷ〮ㄴ㈴〮〸〱〮ㄱ㤰?ㄲ〮㜴〮㤷縱⸰〠〮㔵‰⸱㈸㤠〮ㄳ㠶?〮㔷〮ㄳ〸〮ㄴ㔲〮㔳〮ㄲ㔹?ㄳ〮〳ㄮ〰縱⸰㌠〮ㄱ㜸‰⸱㌳㤠〮ㄴ〳?〮ㄲ㐳〮ㄳ㔳〮ㄵㄳ〮ㄱ㔱〮ㄳ㈴?ㄳ〮㘷ㄮ〳縱⸰㘠〮ㄳ㜶‰⸱㐲〠〮ㄴ㜷?〮ㄴ㘰〮ㄴ㔶〮ㄵ㠳〮ㄲ㜱〮ㄳ㤹?ㄴ〮〷??⸰㘠〮㈸ㄱ‰⸱㠳㠠〮ㄷ㜱?〮㈸ㄱ〮ㄹ㠸〮ㄹ㠰??〮ㄵ㘹?〮ㄵㄵ ???? 20
ꗦ꧶ꓩꅇ?1995꙾2ꓫ8ꓩ???ꗦ꧶ꓩꅇ1995꙾8ꓫ23ꓩ 맏?⁆呓䔭?뿯뻜앶귬ꥬ룪껆Bꪺ-S쇴ꝴꩩ둔ꚱ궱?FTSE-100뿯뻜앶ꪺ믹ꛬꅝ(S−D)/Xꅞꅂ뙚꒵꣬듁ꓩꅝTꅞꅂ뭐B-S쇴ꝴꩩ둔꒧뚡ꪺ쏶ꭙꅃ ??㐮㌠?껖끪쉫꛴군ꪺ쇴ꝴꩩ둔ꚱ궱??럭꣏ꗎ껖끪쉫꣓꛴군덳쓲ꩩ둔ꚱ궱껉ꅁꖻꓥꕈ꣢귓ꛛ엜볆ꅝd=2ꅞꪺ껖끪쉫볒ꚡ꣓꛴군룓쇴ꝴꩩ둔ꚱ궱ꅁ꣤꒤꣢ꛛ엜볆결믹ꛬꅝ(S−D)Xꅞ뙚꒵꣬듁ꓩꅝTꅞꅃꫭ4뭐맏4걏ꕈ때ꗀ볆껖끪쉫ꓨꚡ꛴군ꕘ꣓ꪺꩩ둔ꚱ궱ꅝvolatility surfaceꅞꅁ결믹ꛬ뙚꒵꣬듁ꓩꪺ꣧볆ꅃꗑ맏ꕩ곝ꕘꚳ엣뗛ꪺꭄ맯뫙꾺ꪬꩩ둔ꅁꗧꝙ믹ꛬ뙖낪늣ꗍꪺꩩ둔ꑝ뙖ꑪꅃꕩ꿠룑쓀귬ꙝ꒧ꑀ결룪ꑈ결ꑆꢾꓮꖼ꣓ 21
볆믹껦ꪺꑕ뙞ꛓ쇊뙒믹ꕾ뷦앶ꅁ꣏녯믹ꕾ뷦앶꒧ꕘ믹룻낪ꅁ뻉교쇴ꝴꩩ둔ꝥ뉻‘뱊꾺’꒧ꪬꅃꙢꥍ귬ꥬ룪껆ꪺ쇴ꝴꩩ둔ꅝꫭ3뭐맏3ꅞꓱ룻ꯡꅁꕩꪾ때ꗀ볆껖끪쉫꧒꛴군ꕘ꣓ꪺꩩ둔ꚱ궱ꥍ귬ꥬ룪껆ꪺ쇴ꝴꩩ둔ꚱ궱ꭄ녠곛ꅃ??ꫭ?₵䲥삼욮횰櫂殤ꟁ璪榴咦炭젠룓ꫭ꣏ꗎꑇ귓ꛛ엜볆ꅝ믹ꛬ뭐뙚꒵꣬듁ꓩꅞꪺ때ꗀ볆껖끪쉫ꖩ꣓꛴군FTSE-100뿯뻜앶믹껦꧒쇴ꝴꪺB-Sꩩ냊뉶ꅃ ?ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ?ꓩ?믹ꛬ₥ﺳꆿ?瘠뙒앶뷦앶?₶媤떨솤뙚꒵꣬듁ꓩ뙚꒵꣬듁ꓩ??㘰?㘰縱㠰??ㄸ〠?㘰?㘰縱㠰?ㄸ〠?㘰?㘰縱㠰??ㄸ〠??⸹㐠〮ㄱ㜶‰⸱㐱㈠〮ㄴ㘷?〮ㄴ㌶〮ㄵ㔶〮ㄵ㐵〮〹㠲〮ㄲ㠶?〮ㄴ〶〮㤴縰⸹㜠〮ㄳ㘳‰⸱㔲㤠〮ㄵ㐸?〮ㄴ㤰〮ㄶ㈰〮ㄶㄵ〮ㄲ㘸〮ㄴ㐹?ㄴ〮㤵〮㤷縱⸰〠〮ㄴ㈴‰⸱㔷㘠〮ㄵ㠶?〮ㄵ㌸〮ㄶ㘲〮ㄶ㐳〮ㄳ㌹〮ㄵ〲?ㄵ〮㐱ㄮ〰縱⸰㌠〮ㄴ㤴‰⸱㘳〠〮ㄶ㈸?〮ㄶ㌲〮ㄷ㈶〮ㄶ㠱〮ㄳ㤰〮ㄵ㐵?ㄵ〮㠷ㄮ〳縱⸰㘠〮ㄵ㤵‰⸱㘹㌠〮ㄶ㜱?〮ㄸ㈱〮ㄸㄹ〮ㄷ㌱〮ㄴ㈵〮ㄵ㠲?ㄶ〮㈵??⸰㘠〮㈲㈹‰⸱㤲㈠〮ㄷ㤳?〮㌰㌳〮㈱㔲〮ㄸ㠷〮ㄴ㜶〮ㄶ㜰?〮ㄷ〱 ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ??ꓩ?믹ꛬ₥ﺳꆿ?瘠뙒앶뷦앶?₶媤떨솤뙚꒵꣬듁ꓩ뙚꒵꣬듁ꓩ??㘰?㘰縱㠰??ㄸ〠?㘰?㘰縱㠰?ㄸ〠?㘰?㘰縱㠰??ㄸ〠??⸹㐠〮㔱‰⸱㈳〠〮ㄳ㈵?〮ㄱ〴〮ㄲ㔳〮ㄳ㠸〮〹㤱〮ㄲㄲ?〮ㄲ㔵〮㤴縰⸹㜠〮ㄱ〱‰⸱㈷ㄠ〮ㄳ㘸?〮ㄱ㔹〮ㄳ〲〮ㄴ㌰〮㐲〮ㄲ㐵?ㄳ〮〹〮㤷縱⸰〠〮ㄱ㌹‰⸱㌰㐠〮ㄳ㤶?〮ㄲㄷ〮ㄳ㐱〮ㄴ㘳〮㘵〮ㄲ㘸?ㄳ〮㌶ㄮ〰縱⸰㌠〮ㄱ㤶‰⸱㌴㤠〮ㄴ㈸?〮ㄳ〹〮ㄳ㤶〮ㄵ〷〮㠶〮ㄲ㤵?ㄳ〮㘴ㄮ〳縱⸰㘠〮ㄲ㠴‰⸱㐱㈠〮ㄴ㘷?〮ㄴ㔱〮ㄴ㜴〮ㄵ㘶〮ㄱ〴〮ㄳ㈵?ㄳ〮㤳??⸰㘠〮㈷㌴‰⸱㤷㌠〮ㄸ?〮㈸㔳〮㈰㌸〮ㄹ㔸〮ㄱ㈷〮ㄳ㘰?〮ㄴ㘴 ??ꗦ꧶ꓩꅇ1995꙾2ꓫ8ꓩ??? 22
?ꗦ꧶ꓩꅇ1995꙾8ꓫ23ꓩ ?맏?₵䲥삼욮횰櫂殩튦炪뫁璪榴咦놭넠ꗦ꧶ꓩ결1995꙾2ꓫ8ꓩꅇ믹ꛬ껖꣧볆꒧녡뱥귈결ꅁ뙚꒵꣬듁ꓩ껖꣧볆꒧녡뱥귈결ꅁ돌ꑪ껖끪쉫쇴ꝴꩩ둔꛴군귈결ꅁ돌ꑰ껖끪쉫쇴ꝴꩩ둔꛴군귈결ꅃꗦ꧶ꓩ결1995꙾8ꓫ23ꓩꅇ믹ꛬ껖꣧볆꒧녡뱥귈결ꅁ뙚꒵꣬듁ꓩ껖꣧볆꒧녡뱥귈결ꅁ돌ꑪ껖끪쉫쇴ꝴꩩ둔꛴군귈결ꅁ돌ꑰ껖끪쉫쇴ꝴꩩ둔꛴군귈결ꅃ???결ꑆꟳ뙩ꑀꡂ왛맮ꩩ둔ꪬ쁈껉뚡엜ꪺ땻ꯗꅁ귌녎뙚2ꓫ8ꓩꅝ8ꓫ23ꓩꅞ꣬듁듁뚡ꥷ결ꅂꅂꅂꅂꓑꅝꅂꅂꅂꅂꓑꅞꅁꛓ꓀ꝏ땥ꕘ맯삳믹ꛬ땻ꯗꪺꩩ둔ꪬꅁꡃ귓꣬듁ꓩꗑ꒣Ꙑꮬꚡꪺ뵵걱ꕎꫭꅃꗑ맏5ꕩ곝ꕘ뙚꒵꣬듁ꓩ뙖땵ꪺꩩ둔ꪬ뙖끾깫ꅁꛓ뙚꒵꣬듁ꓩ뙖ꭨ뙖ꖭ뵷ꅃꛓꕂꙢ믹ꕾ뷦앶ꅂ믹꒺뙒앶ꪺꩩ둔ꭨ걏쁈뿯뻜앶꣬듁ꓩꪺ뱗ꕛꛓ듮ꓖꅆ믹꒺뷦앶ꅂ믹ꕾ뙒앶ꪺꩩ둔ꚳ쁈뗛뿯뻜앶꣬듁ꓩꪺ뱗ꕛꛓ뱗ꕛꪺ뛉Ꙗꅃ????? 23
ꗦ꧶ꓩꅇ1995꙾2ꓫ8ꓩ ??ꗦ꧶ꓩꅇ1995꙾8ꓫ23ꓩ ?맏?₥䢵䲥삼욮횰櫂殩튦炤ꎦ储솤뫁璪榴吠ꗦ꧶ꓩ결1995꙾2ꓫ8ꓩꅇ믹ꛬ껖꣧볆꒧녡뱥귈결ꅁ뙚꒵꣬듁ꓩ껖꣧볆꒧녡뱥귈결ꅃꗦ꧶ꓩ결1995꙾8ꓫ23ꓩꅇ믹ꛬ껖꣧볆꒧녡뱥귈결ꅁ뙚꒵꣬듁ꓩ껖꣧볆꒧녡뱥귈결ꅃ? 㐮㐠 FTSE 100믹볆꒧궷쁉꒤ꗟ뻷뉶꓀끴??ㄱꖻꓥꕈ1995꙾2ꓫ8ꓩꅝ8ꓫ23ꓩꅞ10쉉30꓀₤?FTSE 100믹볆ꓴ럇3070ꅝ3525ꅞ결ꗘꭥ믹볆ꓴ럇ꅁꛓ군뫢쇴ꝴꙢ룓ꓩ뿯뻜앶믹껦꒤꣤뙚꒵곹 11₼??FTSE-100뿯뻜앶돌ꯡꗦ꧶껉뚡결꣬듁ꓫꗷ닄ꑔ귓걐듁꒭ꚭꑗꑑ쉉ꕢꅃ? 24
ꑀ꙾꒺ꪺ믹볆ꪺ궷쁉꒤ꗟ뻷뉶꓀끴ꅁ꣤꒤군뫢ꙕ꣬듁ꓩ꧒믝ꪺ때궷쁉ꝑ뉶걏ꕈ뒡룉ꓨꚡ샲녯ꅁꛓ꧒믝ꪺ뉻ꝑ뉻귈걏럓맪믚낣꺧ꓩꝑꓴ럇꣓군뫢ꅃ맏6결ꕈ때ꗀ볆껖끪쉫ꓨꩫ꧒ꡄ녯ꪺ꒣Ꙑ꣬듁ꓩ꒧FTSE 100믹볆궷쁉꒤ꗟ뻷뉶꓀끴ꅝPDFꅞꅃ룓맏엣ꗜꕘ땵듁궷쁉꒤ꗟ뻷뉶꓀끴곛맯꧳듁궷쁉꒤ꗟ뻷뉶꣣ꚳ룻ꑪ꒧깰멁ꅁꕂꭄꝥ맯뫙꒧ꮬ멁ꅃ??ꗦ꧶ꓩꅇ1995꙾2ꓫ8ꓩ??ꗦ꧶ꓩꅇ1995꙾8ꓫ23ꓩ???맏‶₵䲥삼욮횰櫂殩튦炤Ꞥꎦ储솤F?TSE 100믹볆궷쁉꒤ꗟ뻷뉶꓀끴?ꗦ꧶ꓩ결1995꙾2ꓫ8ꓩꅇ볐ꪺ믹볆껖꣧볆꒧녡뱥귈결ꅁ뱩곹믹껦껖꣧볆꒧녡뱥귈결ꅁ뙚꒵꣬듁ꓩ껖꣧볆꒧녡뱥귈결ꅃꗦ꧶ꓩ결1995꙾8ꓫ23ꓩꅇ볐ꪺ믹볆껖꣧볆꒧녡뱥귈결ꅁ뱩곹믹껦껖꣧볆꒧녡뱥귈결ꅁ뙚꒵꣬듁ꓩ껖꣧볆꒧녡뱥귈결ꅃ??결ꓱ룻꛴녯꒧궷쁉꒤ꗟ뻷뉶꓀끴뭐B-S볒ꮬ낲덝ꪺ맯볆녠멁꓀끴ꪺ꒣Ꙑꅁ귌ꗧꡄꕘ맯볆녠멁ꪺ뻷뉶귈ꅁ꣤Ꝁꩫ결녎ꙕ뫘ꕩ꿠ꪺ꣬듁믹ꓴ럇ꅂꗘꭥ믹ꅂ때궷쁉ꝑ뉶ꓴ럇ꅂ뙚꒵꣬듁ꓩꅂ뭐믹ꖭ뿯뻜앶ꪺ껖끪쉫ꩩ둔꛴군귈ꅁ녡ꑊ맯볆녠멁뻷뉶꓀끴ꪺ꒽ꚡꅝ꒽ꚡꅝ㞡庡庡䎭좱澪悷亪몬価䆦嶬?B-S볒ꮬ낲덝ꩩ냊ꯗ결ꑀ 25
녠볆ꅁ꧒ꕈ귌ꕈ껖끪쉫꧒꛴군믹ꖭ뿯뻜앶ꪺ쇴ꝴꩩ둔ꅁ꣓ꕎ듀뉺뷗ꪺ맯볆녠멁궷쁉꒤ꗟ뻷뉶꓀끴꒤ꪺꩩ냊ꯗꅃ맏7ꝙ결럓B-Sꥷ믹볒ꮬꪺ궷쁉꒤ꗟ뻷뉶꓀끴ꅃ ꗦ꧶ꓩꅇ1995꙾2ꓫ8ꓩ ??ꗦ꧶ꓩꅇ1995꙾8ꓫ23ꓩ ??맏㜠꒣Ꙑ꣬듁ꓩ꒧FTSE 100믹볆맯볆녠멁궷쁉꒤ꗟ뻷뉶꓀끴?꒣Ꙑ꣬듁ꓩꩩ둔냑볆ꓴ럇결쇴ꝴꙢ믹ꖭ뿯뻜앶믹껦꒤꒧껖꛴군귈ꅃ ?결ꑆꟳ뉍랡ꓱ룻꧒ꡄ녯ꪺ궷쁉꒤ꗟ뻷뉶꓀끴뭐B-S볒ꮬ꧒낲덝ꪺ맯볆녠멁꓀끴ꪺ깴늧ꅁꖻ곣ꡳ꓀ꝏꡄꕘ뙚꒵꣬듁ꓩ결100ꓑꅂ200ꓑꅂ300ꓑꪺ뻷뉶꓀끴ꅆ맏8결꒣Ꙑ꣬듁ꓩꪺFTSE 100궷쁉꒤ꗟ뻷뉶꓀끴ꅁ꣤꒤ꕈ때ꗀ볆껖끪쉫꧒ꡄꕘꪺ뻷뉶ꗑ맪뵵꧒ꕎꫭꅁꛓ뗪뵵ꭙB-Sꥷ믹볒ꚡ낲덝ꪺ맯볆녠멁궷쁉꒤ꗟ뻷뉶꓀끴ꅃ맏9ꭨꓱ룻쁈껉뚡롧륌쇴ꝴꩩ둔꙰꛳뱶암뻷뉶꓀끴ꪺꪬꅃ뙚꒵꣬듁ꓩ결100ꅂ200300ꓑꪺ쇴ꝴꩩ둔ꝥ뉻‘뱊꾺’ꪺ뉻뙈ꅁꗧꝙ쁈뗛껉뚡뙖땵ꅁ믹ꕾ뷦앶ꅂ믹꒺ 26
뙒앶ꪺ쇴ꝴꩩ둔뙖ꑪꅁꛓ믹꒺뷦앶ꅂ믹ꕾ뙒앶ꭨ걏쁈뗛껉뚡뙖땵쇴ꝴꩩ둔뙖ꑰꅆ곛맯삳ꪺ궷쁉꒤ꗟ뻷뉶꓀끴ꭨ럭뙚꒵꣬듁ꓩ띕땵ꅁ꓀끴쇍꫱꧳굴낾ꅂ낪꽕깰ꪺ놡ꭨ뙖ꧺ엣ꅁ곆ꛜꖪꟀ뻷뉶ꚳ빭깰뉻뙈늣ꗍꅃRubinsteinꅝ1994ꅞ뒣룪ꑈꙢ1987꙾ꡡ땯ꗍꯡꅁ라쇊뙒믹ꕾ뷦앶꣓덗쇗ꖼ꣓믹ꑕ뙞ꪺ궷쁉ꅁꙝꚹꕛ궫ꖪꟀ뻷뉶귈ꪺ앶볆ꅁ늣ꗍ믹꓀끴ꖪꟀ빭깰뉻뙈ꅃꫭ5결꒣Ꙑ꣬듁ꓩ궷쁉꒤ꗟ뻷뉶꓀끴ꪺ뇔굺닎군꓀꩒ꅁꑔ귓꒣Ꙑ꣬듁ꓩꪺ낾멁ꭙ볆곒ꑰ꧳0ꅁꝥ뉻굴낾ꪺ뉻뙈ꅁꕂ쁈뗛꣬듁껉뚡뙖굴낾ꪺ뉻뙈뙖꒣ꧺ엣ꅁꚹ뉻뙈뭐쇴ꝴꩩ둔ꪺ뇗뉶쁈뗛꣬듁ꓩꪺ뱗ꕛꝥ뉻땹띌룻ꖭ뵷ꪺ쇍뛕ꑀ교ꅁ쇴ꝴ뗛B-S꒽ꚡ맯듁뿯뻜앶믹껦룻땵듁뿯뻜앶믹껦땹띌룻꒣꣣낾뭾ꅃꛜ꧳깰멁ꭙ볆ꅁꑔ귓꒣Ꙑ꣬듁ꓩꪺ깰멁ꭙ볆곒ꑪ꧳3ꅁꝥ뉻낪꽕깰ꪺ놡ꩰꅁꛓꕂ쁈뗛껉뚡ꪺ뱗ꕛꅁ낪꽕깰ꪺ놡ꩰ뙖꒣ꧺ엣ꅁ꣤뉻뙈뭐쇴ꝴꩩ둔ꪺꕙ꧊쁈뗛꣬듁ꓩꪺ뱗ꕛꝥ뉻룻뵷ꥍꪺ쇍뛕곛ꑀ교ꅁꑝ둎걏쁈뗛껉뚡ꪺ뱗ꕛꅁ쇴ꝴꩩ둔뇗뉶엜냊ꪺ덴ꯗ룻멃ꅃꙝꚹꅁ꣏ꗎ껖끪쉫ꓨꩫꕩ녎ꕝꝴꙢ?FTSE-100?뿯뻜앶믹껦꒧쇴ꝴꩩ둔룪끔ꚨꕜꙡ신결곛맯삳꒧궷쁉꒤ꗟ꓀끴ꅃ ꫭ??FTSE 100믹볆궷쁉꒤ꗟ뻷뉶꓀끴ꪺ뇔굺닎군꓀꩒??ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ?ꓩ?₮횰櫂殩맯튦볆녠炪멁몤꓀산끴琠䈭匠뙚꒵꣬듁ꓩ‱〰ꓑ㈰?ꓑ㌰?ꓑ?ꓑ㈰?ꓑ㌰?ꓑ듁뇦귈?†㌱㈷⸵?†″ㄹ㈮㌴†″㈶㐮ㄶ†㌱㈷⸵?†㌱㤲⸲㜠†㌲㘲⸵?볐럇깴?㈶㌮㔴㌷㠮㈱‴㘶⸰?′㔱⸱?㌷㠮㜰?㐷㤮㐵낾멁ꭙ볆?††−〮㘸†−†〮?㔸†−†〮?㐱††‰⸲?††‰⸳㔠††‰⸴?깰멁ꭙ볆?††㐮㘵†††㐮㌵†††㌮㤸††″⸱?††″⸲ㄠ††″⸱???ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ??ꓩ?₮횰櫂殩맯튦볆녠炪멁몤꓀산끴琠䈭匠뙚꒵꣬듁ꓩ‱〰ꓑ㈰?ꓑ㌰?ꓑ?ꓑ㈰?ꓑ㌰?ꓑ듁뇦귈?†㌵㤰⸸?†″㘶〮㈲†″㜳ㄮ㠹†㌵㤰⸸?†㌶㘰⸱〠†㌷㌰⸹?볐럇깴?㈴㘮㐵㌶㈮㐹‴㔵⸴?′㐴⸴?㌴㐮㐷?㐴㔮〴낾멁ꭙ볆?††−〮㘹†−†〮?㘶†−†〮?㌲††‰⸲?††‰⸲㠠††‰⸳?깰멁ꭙ볆?††㔮㤸†††㔮㘴†††㐮ㄱ††″⸰?††″⸱㐠††″⸰?? 27
ꅝㆡ庶媤떨솤?100ꓑ?ꗦ꧶ꓩꅇ1995꙾2ꓫ8ꓩ₥?1995꙾8ꓫ23ꓩ???ꅝ㊡庶媤떨솤?200ꓑ?ꗦ꧶ꓩꅇ1995꙾2ꓫ8ꓩ₥?1995꙾8ꓫ23ꓩ???ꅝ㎡庶媤떨솤?300ꓑ?ꗦ꧶ꓩꅇ1995꙾2ꓫ8ꓩ₥?1995꙾8ꓫ23ꓩ???맏?₤ꎦ储솤Ɪ횰櫂殻?䈭?궷쁉꒤ꗟ뻷뉶꓀끴?맪뵵ꕎꫭꗑ때ꗀ볆껖끪쉫ꓨꩫ꧒꛴녯꒧꒣Ꙑ뙚꒵꣬듁ꓩFTSE 100믹볆궷쁉꒤ꗟ뻷뉶꓀끴ꅆ뗪뵵ꕎꫭ맯볆녠멁궷쁉꒤ꗟ뻷뉶꓀끴ꅃ? 28
ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ? ꓩ??ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ???ꓩ?맏?₵䲥삼욮횰櫂殩튦炤ꎦ傶媤떨솤? FTSE 100 쇴ꝴꩩ둔뭐궷쁉꒤ꗟ뻷뉶꓀끴???결ꑆ뮡ꧺ껖끪쉫쇴ꝴꩩ둔ꚱ궱뭐붺ꚡ믹깴궷쁉꒤ꗟ뻷뉶꓀끴꣣ꚳꑀ교꧊ꅁꖻ곣ꡳ군뫢쇴ꝴꙢ껖끪쉫ꩩ둔ꚱ궱꒤꒣Ꙑ뙚꒵꣬듁ꓩꑕx%믹ꕾFTSE-100뙒ꅂ뷦앶곛맯믹껦ꓱ뉶꣓ꫭꗜ껖끪쉫ꩩ둔ꚱ궱꧒쇴ꝴꪺ꓀끴낾멁땻ꯗꅃBatesꅝ1997ꅞꥷ롱‘낾멁뙋ꓴ’ꅝskewness premium; SKꅞ꙰ꑕꅁ C(S,T;X)c?SK(x%)≡−1†P(S,T;X)pFt덯료ꅁX=<F<X=F(1+x%),x%>0ꅆ꣤꒤F결볐ꪺ볆뮷듁믹껦ꅆptctt1+x%C(S,T;X)결뱩곹믹껦Xꅂ뙚꒵꣬듁ꓩTꓑꪺ믹ꕾ뙒앶껖끪쉫꛴군귈ꅆccP(S,T;X)결뱩곹믹껦Xꅂ뙚꒵꣬듁ꓩTꓑꪺ믹ꕾ뷦앶껖끪쉫꛴군귈ꅁꕩ꣏ꗎ믹pp 29
꒺뙒앶ꅝC(S,T;X)ꅞ뙒뷦앶ꖭ믹꒽ꚡꅝput-call parityꅞꡄ녯ꅃ굙pSK(x%)=x%ꅁꭨ믹꓀끴결맯볆녠멁ꅆ굙SK(x%)>x%ꅁꭨ꓀끴룻맯볆녠멁꣣ꖿ낾멁ꅆ굙SK(x%)<x%ꅁꭨ꓀끴룻맯볆녠멁꣣굴낾멁ꅃ‘낾멁뙋ꓴ’ꭙꓱ룻믹ꕾ뙒앶뭐믹ꕾ뷦앶믹껦ꅁꪽ쒱ꑗꅁꕵꚳ럭볐ꪺ룪늣믹껦ꑪꅝꑰꅞ꧳뱩곹믹껦껉ꅁ믹ꕾ뙒앶ꅝ믹ꕾ뷦앶ꅞꑾꚳꖿꪺ돸쁶ꅆꙝꚹꅁ믹ꕾ뙒ꅂ뷦앶믹껦ꪽ놵걍뻷뉶꓀끴ꕫꅂꖪꟀꪺ꽓꧊ꅁ싇ꗑꓱ룻믹ꕾ뿯뻜앶믹껦ꕩꙝꚹ샲노꓀끴낾멁땻ꯗꅃ맏10엣ꗜ꒣Ꙑ뙚꒵꣬듁ꓩꑕx%‘낾멁뙋ꓴ’ꅃ맏꒤x%ꪺ뵤돲ꗑꛜꅁ뚡껦결ꅆ룓맏엣ꗜSK(x%)결굴귈ꅁꫭꗜ쇴ꝴꙢ껖끪쉫ꩩ둔ꚱ궱ꑕꪺFTSE 100궷쁉꒤ꗟ꓀끴결굴낾ꅁꕂ쁈뗛뙚꒵꣬듁ꓩꪺ뱗ꕛꅁ굴낾ꪺ땻ꯗ뮼듮ꅁ뭐붺ꚡ믹깴ꩫꡄꕘꪺ뻷뉶꓀끴맏ꮬ꣣ꑀ교꧊ꅝ맏6ꅞꅃ 30
ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ? ꓩ??ꗦ꧶ꓩꅇㄹ㤵꙾?ꓫ???ꓩ???맏璦抮횰櫂殪榴咦놭놤꒤ꎦ傶媤떨솤?x%믹ꕾ䙔卅ⴱ〰뙒ꅂ뷦앶곛맯믹껦ꓱ뉶?뻮뙢결꒣Ꙑ뙚꒵꣬듁ꓩꅁ셡뙢결Batesꅝ1997ꅞꙕ뫘x%ꪺ‘낾멁뙋ꓴ’ꭙ볆SK(x%)ꅁꥷ롱결믹ꕾ뙒앶뭐믹ꕾ뷦앶믹껦깴늧ꪺꓱ뉶ꅁꗧꝙSK(x%)=C(S,T;X)P(S,T;X)−1ꅁ꣤꒤C(S,T;X)ꅂP(S,T;X)ꪺ껖끪cpcp쉫ꩩ둔결Ꙣ뱩곹믹껦X=F(1+x%)ꅂX=F(1+x%)ꅁ꣬듁ꓩ결Tꪺ껖끪쉫꛴군귈ꅁ꣤꒤F결볐ꪺctptt볆뮷듁믹껦ꅃ맏꒤ꗑꑗ꣬ꑕx%ꪺ뵤돲결ꛜꅁ뚡껦결ꅆ룓맏엣ꗜSK(x%)결굴귈ꅁꫭꗜ䙔卅?〧궷쁉꒤ꗟ꓀끴꣣굴낾멁ꅁꕂ쁈뗛뙚꒵꣬듁ꓩꪺ뱗ꕛꅁ굴낾ꪺ땻ꯗ뮼듮ꅃ ??㔮₵늻礠?볐ꪺ믹볆ꩩ냊꧊맯꧳룪ꑈꪺꡍ떦걏ꑀ뚵ꯜ궫굮ꪺ끔꺧ꅁ땍ꛓ룓ꩩ냊꧊라쁈뗛껉뚡롧륌ꛓ엜냊ꅁꗘꭥꥼꖼꚳ뱳결ꑪ깡뭻Ꙑꪺ돌꣎ꩩ냊ꯗ꛴군볒ꮬꅃꙝ 31
ꚹꅁꖻ곣ꡳ링룕ꕈ때ꗀ볆껖끪쉫ꓨꚡ꣓꛴군ꩩ둔꣧볆ꅁ엽룪껆ꝥ쑭ꛛꑶꪺ귬뮪ꅁꛓ꒣ꕛꕈ궭꣮꣧볆ꚡꅃ싇ꗑ꣏ꗎ1995꙾2ꓫ8ꓩ8ꓫ23ꓩ뿯뻜앶믹껦ꅁ놴끑꣏ꗎ때ꗀ볆껖끪쉫걏ꝟꕩ녎쇴ꝴꩩ둔룪끔ꚳ껄ꙡ신결궷쁉꒤ꗟ뻷뉶꓀끴꣓샋ꥷ껖끪쉫ꓨꩫ꒧ꚳ껄꧊ꅁ꣤꒤쇴ꝴꙢ때ꗀ볆껖끪쉫ꩩ둔ꚱ궱꒤ꪺ볐ꪺ룪늣믹껦뻷뉶꓀끴ꭙ꣏ꗎ붺ꚡ믹깴ꓨꩫꛓ꛴녯ꅁ룓ꩫ꒧ꚳ껄꧊ꡍꥷ꧳꣏ꗎꪺ껖끪쉫걏ꝟ결ꑀ빁럭ꪺ룪껆ꖭ럆볒ꮬꅃꙢ맪쏒떲ꩇꓨ궱ꅁ땯뉻볚ꚡ?FTSE-100 믹볆뿯뻜앶ꪺ룪껆꧒ꡄꕘꪺ껖끪쉫쇴ꝴꩩ둔꣣ꚳ‘뱊꾺’ꪺ뉻뙈ꅁꕂ꣬듁ꓩ뙖땵ꅁ꣤쇴ꝴꩩ둔ꚱ뵵뙖끾깫ꅃꚹꕾꅁ룓믹볆닅Ꙙ믹쉘뒲뉺뷗ꅁ싇ꗑ왛맮꒣Ꙑ뙚꒵꣬듁ꓩꪺ뻷뉶꓀끴ꅁ땯뉻꣬듁ꓩ뙖뮷듁뇦귈뙖ꑪꅁꕂ쁈뗛꣬듁껉뚡꧔믹꓀끴볐럇깴뙖ꑪꅁ뮡ꧺꖼ꣓믹ꕩ꿠륆꣬ꪺ뵤돲녎쁈껉뚡ꪺ뱗ꕛꛓ쉘ꑪꅃꙁꅁ믹볆ꪺ궷쁉꒤ꗟ뻷뉶꓀끴꒣결맯볆녠멁꓀끴ꅁ꣤꒤꒣Ꙑ뙚꒵꣬듁ꓩꪺ궷쁉꒤ꗟ뻷뉶꓀끴곒룻맯볆녠멁꣓녯굴낾낪꽕깰ꅁ쁈뗛꣬듁ꓩꪺ뱗ꕛꅁ굴낾낪꽕깰ꪺ놡ꩰꭨ뙖꒣ꧺ엣ꅃꚹꕾꅁꗑ꧳궫ꑪ끔꺧ꪺꯅꝇꅂꝑꪺ땯꧱ꅂꑈ결ꪺ뻞셡떥ꛓ꣏녯ꖫ돵믹껦엜냊ꚳ룵아뉻뙈ꅁ룪ꑈ깠꧈믹ꑕ뙞ꛓ쇊뙒믹ꕾ뷦앶꣓쇗쁉ꅁ덯곒라꣏녯믹꓀끴싹Ꟁꪺ뻷뉶뱗ꕛꅁ곆ꛜ뻷뉶Ꟁ뫝ꚳ빭깰놡늣ꗍꅝ꙰맏㦡庡䎳첫䆥뮹?떲ꩇꓤ꯹껖끪쉫ꓨꩫꙢ룪껆듁뚡ꪺꚳ껄꧊ꅁꗧꝙ껖끪쉫ꓨꩫꕩ녎ꕝꝴꙢ FTSE-100?뿯뻜앶믹껦꒧쇴ꝴꩩ둔룪끔ꚨꕜꙡ신결곛맯삳꒧궷쁉꒤ꗟ뻷뉶꓀끴ꅃ뒫ꢥ꒧ꅁ껖끪쉫ꩩ둔ꚱ궱쇴ꝴꪺ믹꓀끴룪끔ꅝ꣒꙰맏9꒧‘뱊꾺’쇴ꝴꩩ둔ꪺ듁뚡떲멣ꅁ맏10꒧굴귈‘낾멁뙋ꓴ’ꅞ뭐ꗑ붺ꚡ믹깴ꩫꡄꕘꪺ궷쁉꒤ꗟ뻷뉶꓀끴꽓꧊ꅝ꣒꙰맏㦤Ɬ?낾ꅂ낪꽕깰ꅞꑀ교ꅃꚹ곣ꡳ떲ꩇ꒣뛈뛈ꕵ걏궫ꗓFTSE-100뿯뻜앶믹껦꣣ꚳ띌꾺ꮬ멁꒧쇴ꝴꩩ둔ꚱ뵵ꅁꛓꕂ쏒ꧺꕘ껖끪쉫쇴ꝴꩩ둔꒧띌꾺ꚱ뵵뉻뙈뭐꣤볐ꪺ믹볆꒧궷쁉꒤ꗟ뻷뉶꓀끴꣣ꚳ맪쏒ꑗ꒧ꑀ교꧊ꅃ? 32
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