롧샧뫞뉺뷗쉏 , , 2005 닄93-116궶 ?믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ Jump Diffusion and Optimal Hedging StrategyꇐAn Application of Dow Jones Index and Futures ????ꫴ귵귗 ꩌꣴꗁ 걸럧ꚨ 걟ꓫ뗘 (ReceivedꅇMar. 25, 2005ꅆFirsr RevisionꅇAug. 23, 2005ꅆAcceptedꅇSep. 20, 2005) 멋굮 ꖻꓥꕈ과냪늼ꖫ돵결곣ꡳ맯뙈ꅁꝑꗎ륄쎣ꑵ띾ꖭꞡ볆듁덦꣓덗쇗꣤볆뉻덦ꩩ냊꒧궷쁉ꅃ곛쏶룪껆꣺ꛛBloomberg룪껆깷ꅁ룪껆ꮬ멁결ꓩ룪껆ꅁ꣺볋듁뚡결1998꙾1ꓫ2ꓩ꣬2003꙾7ꓫ25ꓩꅁ볋ꖻ볆Ꙁ1399떧ꅃ Ꙣ끬ꡄ궷쁉랥ꑰ꓆꒧ꭥ뒣ꑕꅁꖻꓥ룕맏ꝑꗎGARJI볒ꮬ꣓꺷꺻ꖫ돵ꙝ곰땯꧊궫ꑪ롧샙ꗳ꧒덹ꚨ룪늣돸륓뉶꒧쁈뻷룵아꒣덳쓲뉻뙈ꅁꝑꗎ늾냊뗸떡ꅁꕈ륄쎣ꑵ띾믹볆결곣ꡳ맯뙈ꅁ놴끑볋ꖻꕾ꒧쇗쁉셚껄ꅁꙐ껉삳ꗎOLS볒ꮬꅂGARJI볒ꮬGARCH볒ꮬ뙩ꛦ쇗쁉셚껄땵ꓑ듁ꥍꓑ듁꒧쇗쁉셚껄깴늧꧊꓀꩒ꅃ맪쏒떲ꩇ땯뉻ꕈGARJI볒ꮬ뙩ꛦ쇗쁉ꪺ셚껄ꖼ굙륷듁꒤뉺띑ꅃ꒣뷗뇄ꗎ꛳뫘쇗쁉볒ꮬ뙩ꛦ뉻덦뎡ꛬ꒧쇗쁉ꅁ곒꿠ꑪ둔ꙡ궰ꝃ꯹ꚳ뉻덦꒧궷쁉ꅁ맪쏒엣ꗜ믹볆듁덦ꮴ곹결ꑀꙮꪺ쇗쁉ꑵ꣣ꅃ 쏶쇤꙲ꅇGARJIꅂGARCHꅂ볋ꖻꕾ쇗쁉ꅂ늾냊뗸떡 Abstract This study investigates the optimal hedge strategies between Dow Jones index futures and its spot market by using OLS, GARJI, and GARCH models. The daily data are collected from Bloomberg Data Base; there are 1399 observations from Jan. 2, 1998 to July 25, 2003. Under the assumption of minimizing the risk, we use GARJI to capture the price jumps phenomena that result from the impact of sudden economic changes upon asset returns. Rolling windows are adopted and the out of sample hedging performance with different hedging horizons are compared among OLS, GARJI, and GARCH models. Despite the results of GARJI do not standout as we expected, the underlying hedging models in futures can indeed reduce the spot’s holding risks. Empirically evidence shows the stock index future is a good hedging utility. KeywordsꅇGARJI, GARCH, Out of Sample Hedging, Rolling Window 1맪뷮ꑪ뻇끝냈뿄꡴뇐뇂 2삭ꩆ곬ꑪ뻇끝냈뿄꡴냆뇐뇂 3꒸냶곬뻇덎뻇끼끝냈뿄꡴솿깶 4뉈ꚿꑪ뻇끝냈뿄꧒뫓ꑨ 93
롧샧뫞뉺뷗쉏 , , 2005 돼ꅂꭥꢥ 뻚Markowitz(1952)꧒뒣꒧룪닕Ꙙ뉺뷗(Portfolio Selection)ꅁ룪닕Ꙙ꒧궷쁉ꕩ꓀결엜늧볆궷쁉ꅝꭄ꡴닎꧊궷쁉ꅞꙀ엜늧볆궷쁉ꅝ꡴닎꧊궷쁉ꅞꅁꭥꕩ싇ꗑꙨ꒸꓆룪(Diversification)꣓덗쇗ꅁꙀ엜늧볆궷쁉때ꩫꙝꚹꛓ궰ꝃꅃꚹ껉ꅁ냟ꚳ덺륌듁덦ꮴ곹꒧쇗쁉ꕜ꿠ꅁꕈ냲깴궷쁉꣺ꕎ믹껦궷쁉ꅁ녎궷쁉늾신떹뻷ꅁ꣓덗쇗꡴닎꧊궷쁉(Systematic Risk)ꅃꛓꗑ꧳듁덦뭐뉻덦ꖫ돵뚡꒧낪ꯗ곛쏶ꅁ믹볆듁덦ꙝꛓꕩ결늼룪꒧쇗쁉ꑵ꣣ꅁꛓꙢ녱듁덦쇗쁉ꗦ꧶꒤ꅁ쇗쁉맯꧳쇗쁉ꓱ뉶(Hedge Ratio)ꪺ꛴군쏶뻣귓쇗쁉륌땻꒧셚껄ꫭ뉻ꅁꙢ쇗쁉떦늤ꪺ곣ꡳ꒤ꅁ꙰꛳빁럭꛴군쇗쁉ꓱ뉶ꗧꙨ결뻇꧒쏶ꩠꅃ Black and Scholes(1973)뭻결Ꙣꞹ과ꖫ돵ꪺ낲덝ꑕꅁꙝꥷ엜늧꒧둘꛳ꖬ껔륂냊ꭙ삳ꡃ돦ꛬ껉뚡ꖫ돵띳룪끔맯룪늣믹껦꒧쏤믚뱶암(Marginal Effect)ꅁ뭻결믹돸륓꒧엜냊녎쇍꧳덳쓲ꕂꖭ럆꒧껉뚡Ꟈꙃꅁ냊멁믹꒧뷕뻣ꭙ꣣ꚳ덳쓲룴깼(Continuous Sample Path)꒧쁈뻷륌땻ꅃꗘꭥ걊ꚳ꒧ꓥ쑭ꅁ맯룪늣돸륓뉶ꙝꛓꙨ낲덝꣤ꩁ녱덳쓲ꪺ쉘뒲쁈뻷륌땻ꅃ놩맪ꑗꅁ뿄ꖫ돵쉁ꚳ꙳Ꙣ덳쓲껉뚡Ꟈꙃ꒧뉻덦냓ꭾꅁ럭땯ꗍ쏶믹껦꒧궫ꑪ늧녠ꗳꅁꚹꖫ돵ꭄ륷듁ꙝ꿀맯룪늣믹껦꒧뱶암낣삳꧳꽓ꥷ싷뒲껉쉉ꕾꅁ꣤띳룪끔뷄삻ꪺ땻ꯗꗧꙨ뙗륌ꖿ녠ꪺ쏤믚뱶암ꅃꙝꚹꅁꖻꓥ녎ꕄ굮놴끑럭뉻덦믹껦땯ꗍ꒣덳쓲ꪺ룵아뉻뙈껉ꅁ꙰꛳꛴군돌빁쇗쁉ꓱ뉶ꅁꣃ뙩ꑀꡂ뇄ꗎ멵냊(Rolling)곣ꡳꩫ륂ꗎ꧳ꙕ귓볒ꮬꑗꅁꙁ놴끑꧳꒣Ꙑ쇗쁉볒ꮬ뭐쇗쁉듁뚡ꑕ꒧쇗쁉셚껄ꅃ Ederington(1979)뻚쇗쁉뉺뷗꒧꓀쏾ꓨꚡꅁ뭻결듁덦꒧쇗쁉뉺뷗ꕩ냏꓀ꚨꑔ뫘ꅁ1.뛇닎쇗쁉뉺뷗 2.뿯뻜꧊쇗쁉뉺뷗 3.돌ꑰ엜늧쇗쁉뉺뷗ꅃꙢ뛇닎쇗쁉꒤ꅁꕄ녩ꞹꗾ쇗쁉ꅁꙝꚹ쇗쁉ꓱ뉶결1ꅃꙢ뿯뻜꧊쇗쁉뉺뷗꒤ꅁ뭻결굙꒣쇗쁉ꅁꭨ쇗쁉ꓱ뉶결0ꅆ굙뙩ꛦ쇗쁉ꅁꭨ쇗쁉ꓱ뉶결1ꅁꕈ륆ꞹꗾ쇗쁉ꅃ돌ꑰ엜늧쇗쁉뉺뷗ꅁꭨꝑꗎ룪ꑈ꧒꯹ꚳ꒧뉻덦뎡ꛬ뭐듁덦뎡ꛬ닕ꚨꑀ룪닕Ꙙꅁ녪뷕룪닕Ꙙ쇗쁉뉺뷗꒧쇗쁉ꓱ뉶ꣃ꒣걏ꭄ0ꝙ1ꪺ뿯뻜ꅁꛓ걏ꕈꑀ꛴군꒧돌빁쇗쁉ꓱ뉶꣓뙩ꛦ쇗쁉ꅁꣃꙐ껉ꛒ뱻룪닕Ꙙ꒧돸륓뭐궷쁉ꅁ꣓뮡ꧺ곛쏶꒧쇗쁉ꗘꪺꅃ껚뻚돌ꑰ엜늧쇗쁉뉺뷗군뫢쇗쁉ꓱ뉶껉ꅁ꣤꧒끴빁ꪺ군뙱볒ꮬꖲ뚷꿠ꖿ뵔둹쎸돸륓뉶꓀끴ꪺꮬ멁ꅁ뛇닎낲덝믹ꩩ냊ꭙ닅Ꙙꑀ쉘뒲륌땻(Diffusion Process)ꅁꙢꚹ낲덝ꑕ믹돸륓뉶ꝥ녠멁꓀끴ꅃ껚뻚Fama(1965)뭐Mandelbrot(1967)ꪺ곣ꡳ엣ꗜ믹돸륓뉶ꪺ꓀끴ꚳ낾멁낪깰멁ꭙ볆ꅁ뭐녠멁꓀끴ꣃ꒣곛닅ꅃ뇸ꗳ늧뷨엜늧(Conditional Heteroskedasticity)뭐룵아-쉘뒲륌땻(Jump-diffusion Process)ꙝꛓꚨ결Ꙣ놴끑믹돸륓뉶꓀끴ꮬ멁껉꒧꣢ꑪ뷒썄ꅃ 륄쎣ꑵ띾ꖭꞡ볆(Dow Jones Industrial Averageꅁ슲뫙DJIA)걏ꕀꑗ돌꣣뱶암ꪺ믹볆꒧ꎸꅁꛜ꒵ꑷꚳꑀꛊꙨ꙾ꪺ뻺ꕶꅁꕄ굮ꭙꗑ30ꓤ늼닕ꚨꅃꖻꓥ녎ꕈ륄쎣ꑵ띾ꖭꞡ믹볆결ꕄ굮곣ꡳ볐ꪺꅁ놴끑Ꙣ쁙쇗쁉ꑕꅁ삳ꗎGARJI볒ꮬ뭐GARCH볒ꮬ뙩ꛦ쇗쁉꒧셚껄ꅃ 94
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?뙌ꅂꓥ쑭Ꙟ압 ꑀꅂ냪ꕾ곛쏶ꓥ쑭 Ederington(1979)Ꙣ끬ꡄ돌ꑰ엜늧볆ꑕꅁꕈ뉻덦믹깴맯듁덦믹깴꒧뒶덱돌ꑰꖭꓨꩫ(Ordinary Least Squares, OLS)꣓꛴뫢쇗쁉ꓱ뉶ꅁ꓀ꝏ맯T-BillꅂGNMAꑇ듁덦ꖫ돵쇗쁉껄ꩇꝀꓱ룻ꅆ떲ꩇ땯뉻ꅁ돌빁쇗쁉ꓱ뉶ꑀ꿫ꞡꑰ꧳1ꅁꚹ뭐뛇닎쇗쁉뉺뷗꒧뭻ꪾ꒣Ꙑꅁꕂ쇗쁉셚껄ꥍ쇗쁉듁뚡결ꖿꙖ쏶ꭙꅁꗧꝙ쇗쁉듁뚡띕ꅁ쇗쁉셚껄띕꣎ꅃFiglewski(1984)ꭨꕈ궷쁉랥ꑰ결끬ꡄꗘ볐ꅁ낲덝ꝑ꒧땯꧱결쁈뻷뉻뙈ꅁ놴끑Value LineꅂS&P 500NYSEꑔ뫘믹볆듁덦맯과냪믹뉻덦ꖫ돵꒧쇗쁉곣ꡳꅁ떲ꩇ땯뉻뺨뫞ꕈꑀꓑ결쇗쁉듁뚡꒧쇗쁉껄ꩇ룻ꕈꑀ뙧결쇗쁉듁뚡깴ꅁꚹꣃꭄ띎뿗때궭듁ꦵ쇗쁉듁뚡ꭋ꿠뱗뙩쇗쁉껄뉶ꅆ곛Ꙑꙡꅁ뙚듁덦ꮴ곹꣬듁ꓩꪺ뮷꫱ꑝ삳꒣뙗륌꣢귓ꓫꅁ꙰ꚹꑾ꿠녯꣬돌꣎ꪺ쇗쁉껄ꩇꅃ Kroner and Sultan(1993)Ꙣ끬ꡄ궷쁉랥ꑰ꓆ꑕꅁꕈ꣺ꛛ냪믚뿄ꖫ돵ꗦ꧶꒧굞싩ꅂꕛ꺳ꑪ맴ꅂ뱷냪남Ꝋꅂꓩ뛪럧ꑨꩫ궦떥꒭뫘ꕾ뛗뉻덦뭐듁덦뛗뉶ꅁꗑ1985꙾2ꓫꛜ1990꙾2ꓫꅁꕈ슲돦쇗쁉ꅂ뛇닎OLS볒ꮬꅂOLSꙀ뻣Ꙙ싹엜뙱GARCHꅝ1,1ꅞ볒ꮬ뙩ꛦ볋ꖻ꒺볋ꖻꕾ꒧꓀꩒ꅁ맪쏒떲ꩇ엣ꗜ싹엜뙱GARCHꅝ1,1ꅞ볒ꮬ꒧쇗쁉셚껄곒ꓱ꣤ꕌ볒ꮬ꣎ꅁꚹꕾꅁꙢꛒ뱻ꗦ꧶ꚨꖻꯡꅁ싹엜뙱GARCHꅝ1,1ꅞ볒ꮬ꒴꿠떽뛇닎ꪺ쇗쁉떦늤셚껄ꅁ뱗녪룪맯ꕾ뛗뎡ꛬꪺ쇗쁉뫞뉺꿠ꑏꅃ Lindahl(1992)ꕈMMIS&P500믹볆듁덦결곣ꡳ맯뙈ꅁ꣤곣ꡳ떲ꩇ땯뉻Ꙣ돌ꑰ엜늧볆쇗쁉ꑕꅁ쇗쁉셚껄ꚳ쁈쇗쁉듁뚡뱗ꕛ쇍뛕ꅁꗧ녯꣬쁈쇗쁉듁뚡ꪺ뱗ꕛ쇗쁉셚껄띕꣎ꪺ떲뷗ꅃBaillie and Myers(1991)ꝑꗎ싹엜뙱GARCH볒ꮬ꛴뫢돌빁쇗쁉ꓱ뉶ꅁ맪쏒땯뉻GARCH볒ꮬ꛴뫢꒧돌빁쇗쁉ꓱ뉶꣣껉뚡엜냊꧊ꅁꕂ꣤쇗쁉ꫭ뉻쁵꧳륂ꗎ끪쉫ꓨꩫ꛴군ꪺꥷ쇗쁉ꓱ뉶볒ꮬꅃ Park and Switzer(1995)ꕈS&P 500뭐Toronto 35꣢뫘믹볆뉻덦듁덦ꅁ놴끑뇸ꗳ엜늧볒ꮬꙢ믹볆듁덦쇗쁉ꓨ궱꿠ꝟꚳ껄떽뛇닎OLSꪺ쇗쁉껄꽱ꅁ곣ꡳ듁뚡결1988꙾6ꓫꛜ1991꙾12ꓫꅁ쉞꣺ꡃ뙧ꑔꚬ뵌믹룪껆ꅁ맪쏒떲ꩇ땯뉻때뷗걏귾ꑀ뫘볆ꅁ싹엜뙱GARCHꪺ쇗쁉셚껄쁵꧳ꓑ꽵쇗쁉ꅂOLSꅂOLS-CIꅃ Ghosh(1993)ꭨꝑꗎꩫ냪ꪺCAC40믹볆뉻덦뭐듁덦ꅂ굞냪ꪺ귛뒰뿄껉돸볆(FTSE100)뉻덦뭐듁덦ꅂꓩꖻꪺꓩ롧225믹볆뉻덦뭐듁덦ꕈ뱷냪DAX믹볆뉻덦뭐듁덦떥꒣Ꙑꪺꖫ돵ꅁ룕맏둍ꡄꑀ귓돌빁ꪺ군뙱볒ꮬꕈ뇀꛴쇗쁉ꓱ뉶ꅃ땯뉻ꙕꖫ돵ꪺ뉻덦뭐듁덦뚡곒꙳Ꙣ뗛Ꙁ뻣Ꙙ쏶ꭙꅁ꣤꧒뗻꛴꣢뫘군뙱볒ꮬ(OLS & ECM)ꪺ쇗쁉셚껄꒧떲뷗뭐Ꙣꗽꭥ꧒녯ꪺ떲뷗곛Ꙑꅁꝙ뭾깴귗ꖿ볒ꮬ(ECM)쁵꧳뒶덱돌ꑰꖭꓨꩫ(OLS)ꅃ Gagnon and Lypny(1997)ꓱ룻쁒멁쇗쁉떦늤싹엜뙱GARCHꅝ1,1ꅞ냊멁쇗쁉떦늤꒧쇗쁉ꚳ껄꧊ꅁ떲ꩇ땯뉻냊멁볒ꮬ꒧룑쓀꿠ꑏ엣뗛쁵꧳쁒멁볒ꮬꅃKoutmos and Pericli(1999)ꕈꑔꑑ꙾ꥷꝑ뉶꒧과냪GNMA뛅꣩결뉻덦볐ꪺꅁꣃꕈꑑ꙾듁ꪺ과냪꒤듁꒽뛅결듁덦쇗쁉볐ꪺꅁ곣ꡳ듁뚡결1992꙾7ꓫꛜ1995꙾8ꓫꅁꓱ룻냊멁뭾깴귗ꖿGARCH볒ꮬ(ECMꇐGARCH)뭐뛇닎끪쉫볒ꮬꑇ꒧볋ꖻ꒺볋ꖻꕾꪺ쇗쁉셚껄ꅁ떲ꩇꗧ땯뉻냊멁싹엜뙱뭾깴귗ꖿGARCH볒ꮬ꒧쇗쁉셚껄ꓱ뛇닎쁒멁끪쉫볒ꮬ꣎ꅃ Lien and Tse (1999)ꭨꝑꗎ뛇닎끪쉫ꚡ(OLS)ꅂꕛꑊꑆ뎡꓀Ꙁ뻣Ꙙ쏶ꭙꪺ뭾깴귗ꖿ볒ꮬ(FIEC)ꅂ뭾깴귗ꖿ볒ꮬ(ECM)ꅂꙖ뙱ꛛ끪쉫볒ꮬ(VAR)ꅁꣃ꓀ꝏꙁꕛꑊ뇸ꗳ엜늧볆늧뷨꧊껄ꩇ 95
롧샧뫞뉺뷗쉏 , , 2005 (GARCH)ꅁ곣ꡳ볐ꪺ결ꙢSIMEXꗦ꧶ꪺꓩ롧225볆뉻덦뭐듁덦ꅁ샋엧ꑗ굺볒ꮬꪺ쇗쁉ꓱ뉶꣤쇗쁉닕Ꙙ꒧셚껄ꅆ떲ꩇ엣ꗜꕛꑊGARCHꕩ뱗ꕛ쇗쁉셚껄ꅁOLS결돌깴ꪺ쇗쁉떦늤ꅃ Yeh and Gannon(2000)ꅁꙢꛒ뱻ꗦ꧶ꚨꖻꪺ놡ꩰꑕꅁ륂ꗎ냊멁볒ꮬ꛴뫢돌빁쇗쁉ꓱ뉶(OHR)ꅁꣃꙢ룪닕Ꙙ띬꽱ꪺ냲슦ꑗ뭐ꥷ쇗쁉볒ꮬ(Constant Hedge Model)뙩ꛦꓱ룻ꅆ곣ꡳ맯뙈결뎷뇹듁덦ꗦ꧶꧒(SFE)꒧Share Price Index(SPI)듁덦ꮴ곹ꅁ땯뉻ꕈ룪닕Ꙙ띬꽱결ꓱ룻냲슦ꅁGARCH볒ꮬ돐덹ꕘ돌ꑪꪺꝑ볭ꅁꛓꓑ꽵볒ꮬ(Naïve Model)ꭨ돌깴ꅆ곛룻꧳ꥷ쇗쁉ꓱ뉶볒ꮬꅁGARCH쇗쁉ꓱ뉶라쁈껉뚡ꪺ뇀늾ꛓ엜냊ꅁꛓꥷ쇗쁉ꓱ뉶덑뭻결걏GARCH쇗쁉ꓱ뉶꒧듁ꖭꞡꅆGARCH볒ꮬꪺ볋ꖻꕾ륷듺셚껄ꕇ꿠꺷꺻땵듁(weekly)ꪺ깍ꝑ뻷라ꅃ Das(2002)ꅂJorion(1988)떲ꙘARCH볒ꮬ뭐룵아ꇐ쉘뒲볒ꮬꅁ놴끑과냪뛅꣩ꅂ늼뭐ꕾ뛗ꖫ돵ꅁ떲ꩇ땯뉻ꚹ쏾볒ꮬꪺ떲Ꙙ곒뒣ꑆ볒ꮬꪺ끴빁꿠ꑏꅃChan and Maheu(2002)ꭨ떲ꙘGARCH볒ꮬ뭐룵아ꇐ쉘뒲볒ꮬ꧳늼ꖫ돵ꅁꣃ녎룵아녪ꯗ(Jump Intensity)덝ꥷ결뭐ARMA볒ꮬ곛Ꙑ볒ꚡꅁ꣏룵아녪ꯗ라쁈뗛껉뚡ꛓ엜냊ꅁꛓꙢ룵아ꑪꑰ(Jump Size)ꪺ덝ꥷꑗꅁꑝ녎꣤ꩁ녱꓀끴ꪺ냑볆ꅁ덝ꥷ결꣣ꚳ쁈껉뚡ꩩ냊ꪺ꽓꧊ꅆꙢꚹ덝ꥷꑕꅁ때뷗Ꙣ볋ꖻ꒺ꪺ끴빁걏볋ꖻꕾꩩ냊꧊ꪺ륷듺곒ꚳ룻꣎ꪺ떲ꩇꅃ ꑇꅂ냪꒺곛쏶ꓥ쑭 쉏ꞻꓥ(1996)ꕈ슲돦쇗쁉ꅂ뛇닎OLSꅂOLSꙀ뻣Ꙙ볒ꮬ싹엜뙱GARCH볒ꮬ꓀ꝏ놴끑띳ꕛ냪믚뿄ꗦ꧶꧒(SGX)ꓩꖻꑪꣁ듁덦ꗦ꧶꧒(OSE)ꪺNikkei 225믹볆듁덦삳ꗎ꧳ꓩꖻꕸ왗ꖫ뉻덦꒤쇗쁉ꪺ껄ꩇꅃꚿꓥ녪(1997)ꓱ룻뛇닎OLS볒ꮬꅂ뭾깴귗ꖿ볒ꮬBivariate GARCH꒧쇗쁉껄ꩇꅁꣃ뙩ꑀꡂ놴끑ꛒ뱻ꗦ꧶ꚨꖻꯡ꒧쇗쁉껄뉶ꚳ꛳뱶암ꅃꕈꫛꕛ귴냓띾ꗦ꧶꧒꒧S&P 500듁덦ꮴ곹ꅂ궻들듁덦ꗦ꧶꧒꒧꯭ꗍ믹볆듁덦ꅂ띳ꕛ냪믚덦맴ꗦ꧶꧒꒧ꓩ롧믹볆듁덦결맪쏒맯뙈ꅃꩌ롱늻(1998)껚뻚Johnson(1960)꧒뒣ꪺ돌ꑰ엜늧쇗쁉떦늤ꅁꕈ냪꒺뙽꧱ꮬꙀꙐ냲ꝑꗎ벯껚ꕶꝑꕸ듁덦쇗쁉결꣒ꅁ꓀ꝏ륂ꗎ뛇닎OLS볒ꮬꅂECMꅂ돦엜뙱GARCHꅝ1,1ꅞ뭐싹엜뙱GARCHꅝ1,1ꅞ볒ꮬ꣓샋듺ꙕꙀꙐ냲ꪺ쇗쁉셚껄ꅁꕈꙢ뿯꣺꒣Ꙑ군뙱볒ꮬ꧒샲녯ꪺ쇗쁉ꓱ꣒ꑕꅁ맯꧳걙꽓ꥷꙀꙐ냲ꛓꢥꅁ걏ꝟ라덹ꚨ쇗쁉셚껄ꪺ깴늧꧊ꅃ빇뽰(1998)녎꒣맯뫙ꮬꪺGARCH(Asymmetric Generalized Autoregressive Conditional HeteroscadascityꅁAGARCH)볒ꮬꗎ꧳꛴군S&P 500ꅂ꯭ꗍꅂꓩ롧225ꅂꙎ뚩볆벯껚ꕸ떥꒭귓듁덦ꖫ돵ꪺ쇗쁉ꓱ꣒ꑗꅃꓽ쑒Ɪ(1999)ꕈJump Diffusion Model끴빁뭻쇊앶쏒ꪺꖫ믹ꅁꝑꗎ돌ꑪ랧ꩫ(Maximum Likelihood Estimation)꛴군Merton볒ꮬꪺ냑볆ꅁꣃꕈ믹껦뭾깴ꅂꛊ꓀ꓱ뭾깴ꛊ꓀ꓱ뭾깴ꖭꓨ낵결뗻꛴볐ꅃꝅꥼꅂ뿠꧷Ꝁ(2000)뇄ꗎ뛇닎슲돦쇗쁉볒ꮬꅂOLS볒ꮬꅂOLS-CI볒ꮬ냊멁쇗쁉GARCH볒ꮬꅁ끷맯과냪ꫛꕛ귴냓띾ꗦ꧶꧒(CME)ꪺS&P500볆듁덦ꅂꓩꖻꑪꣁ쏒꣩ꗦ꧶꧒(OSE)ꪺNikkei225볆듁덦ꅂ궻들듁덦ꗦ꧶꧒(HKFE)ꪺHang Seng볆듁덦ꅂ띳ꕛ냪믚뿄ꗦ꧶꧒(SIMEX)ꪺ벯껚ꕸ볆듁덦ꕸ왗듁덦ꗦ꧶꧒(TAIFEX)ꪺꕸ왗ꕛ앶믹볆듁덦떥꒭뫘ꮴ곹꣓Ꝁ맪쏒ꅃ썑ꟓ(2001)륂ꗎ뛇닎OLS볒ꮬꅂ뭾깴귗ꖿ볒ꮬꅂ돦엜뙱GARCHꅝ1,1ꅞꅂ싹엜뙱GARCHꅝ1,1ꅞ뭐롧ꕤ냒쉯뉢뺹냊멁뷕뻣떥쇗쁉볒ꮬ꛴군쇗쁉ꓱ뉶ꅁ꓀ꝏꕈꕸ왗ꅂ과냪ꅂꓩꖻꩫ냪떥 96
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?ꕼ귓냪깡꒧믹볆듁덦ꅁꓱ룻꒣Ꙑ볒ꮬ꒧쇗쁉껄ꩇꅃ뛀뒺ꧺ(2001)끷맯ꕸ왗ꕛ앶믹볆뉻덦뭐듁덦ꅂꑰꮬꕸ듁덦결곣ꡳ볐ꪺꅁ놴끑볆듁덦쁒멁쇗쁉떦늤ꅝꕝꝴOLSꅂNear-VARꅂECMꅞꥍ냊멁쇗쁉떦늤(GARCH)꒧쇗쁉셚껄ꅁ 냑ꅂ곣ꡳꓨꩫ Ꙣ끬ꡄ궷쁉랥ꑰ꓆꒧ꭥ뒣ꑕꅁꖻꓥ룕맏ꝑꗎGARJI볒ꮬ꣓꺷꺻ꖫ돵ꙝ곰땯꧊궫ꑪ롧샙ꗳ꧒덹ꚨ룪늣돸륓뉶꒧쁈뻷룵아꒣덳쓲뉻뙈ꅁꣃ뭐OLSꅂGARCH떥Ꙣ꒣Ꙑ쇗쁉듁뚡ꑕꅁꝑꗎ늾냊뗸떡(Rolling Window)놴끑볋ꖻꕾ(Out of Sample)ꓱ룻맪믚뙩ꛦ쇗쁉ꯡꅁ꧳쇗쁉듁뚡듁ꖽ꒧쇗쁉셚껄ꅃ ꑀꅂ뛇닎OLS쇗쁉볒ꮬ 결놱뫞ꣃ궰ꝃ룪닕Ꙙꪺ궷쁉ꅁ쇗쁉ꖲ뚷ꡍꥷꑀ돌빁쇗쁉ꓱ뉶ꅁꑀ꿫ꝑꗎ룪닕Ꙙ돸륓ꪺ엜늧볆꣓뿅뙱궷쁉ꅁꡄ녯돌ꑰ엜늧쇗쁉ꓱ뉶ꅃ굙쇗쁉Ꙣ닄t−1듁뻖ꚳ1돦ꛬ꒧뉻덦뎡ꛬꅝ믹껦Sꅞꅁꣃꡍꥷ꧳닄t듁뷦ꕘꅝ믹껦Sꅞꅁꭨꖼ쇗쁉뉻덦뎡ꛬ꒧륷듁돸t−1t륓뭐엜늧볆꓀ꝏ꙰닄ꅝ1ꅞ닄ꅝ2ꅞꚡꅇ E(U)=E(∆S) ꅝ1ꅞ t Var(U)=Var(∆S) ꅝ2ꅞ t ꣤꒤ꅁ∆S=S−S결뉻덦믹껦Ꙣt듁ꪺ엜냊ꅁꕂUꫭꗜꖼ쇗쁉ꪺ룪뎡ꛬ(Unhedged ttt−1position)ꅃ굙쇗쁉꧳닄t−1듁뷦ꕘb돦ꛬꪺ듁덦뎡ꛬ뙩ꛦ쇗쁉ꅁꭨ쇗쁉룪닕Ꙙ꒧륷듁돸륓뭐엜늧볆꓀ꝏ꙰닄ꅝ3ꅞ닄ꅝ4ꅞꚡꅇ E(H)=E(∆S)−bE(∆F) ꅝ3ꅞ tt 2Var(H)=Var(∆S)−2bCov(∆S,∆F)+bVar(∆F) ꅝ4ꅞ tttt ꣤꒤ꅁ∆F=F−F결듁덦믹껦Ꙣt듁ꪺ엜냊ꅁꕂHꫭꗜ쇗쁉ꯡꪺ룪뎡ꛬ(Hedged ttt−1position)ꅃ굙꣏쇗쁉룪닕Ꙙ륷듁돸륓꒧엜늧볆돌ꑰ결쇗쁉꧒쏶ꓟ꒧쇗쁉ꗘꪺꅁꭨ맯*닄ꅝ4ꅞꚡ꒧bꑀ뚥띌꓀ꅁꣃꕏꓨ땻ꚡ결륳ꅁꝙ녯꣬돌ꑰ엜늧쇗쁉ꓱ뉶b결 Cov(∆S,∆F)*ttb= ꅝ5ꅞ Var(∆F)t 쇗쁉셚껄ꪺ뿅뙱결궰ꝃꖼ쇗쁉뉻덦뎡ꛬ륷듁돸륓ꪺ엜늧볆꒧땻ꯗꅁ궰ꝃ땻ꯗ띕ꑪꅁ 97
롧샧뫞뉺뷗쉏 , , 2005 ꕎꫭ쇗쁉껄ꩇ띕꣎ꅃ뿅뙱ꓨꚡ꙰닄ꅝ6ꅞꚡ Var(U)−Var(H)HE= ꅝ6ꅞ Var(U) ꣤꒤ꅁHEꫭꗜ쇗쁉ꭥꯡ룪뎡ꛬꪺ궷쁉궰ꝃ땻ꯗꅁꝙ쇗쁉셚껄(Hedging Effectiveness)*녎닄ꅝ5ꅞꚡ녯꣬ꪺ돌빁쇗쁉ꓱ뉶bꕎꑊ닄ꅝ4ꅞꚡꅁꣃ녎떲ꩇ닄ꅝ2ꅞꚡꪺꖼ쇗쁉뉻덦륷듁돸륓꒧엜늧볆ꕎꑊ닄ꅝ6ꅞꚡꅁ군뫢쇗쁉껄ꩇꅇ 2Cov(∆S,∆F)ttHE= ꅝ7ꅞ Var(∆S)Var(∆F)tt Ꙣꪽ놵쇗쁉ꑕꅁꗑ꧳듁덦볐ꪺ룪늣뭐뉻덦걏곛Ꙑꪺꅁ꣤믹껦꣼곛Ꙑꙝ꿀꧒뱶암ꅁꙝꚹꅁ듁덦믹껦뭐뉻덦믹껦삳꣣ꚳ듁ꞡ뿅쏶ꭙꅁꕈ돸륓뉶끪쉫볒ꚡ꒧끪쉫ꭙ볆뭐Ꝑꥷꭙ볆꧒꛴군꒧돌빁쇗쁉ꓱ뉶뭐쇗쁉껄ꩇ삳결쎭ꥷꅃ ꑇꅂ돦엜뙱GARCH볒ꮬ ꚭ듁껉뚡Ꟈꙃ볒ꮬꅁꭙꯘ멣Ꙣ득깴뚵엜늧볆꣣믴뷨꧊꒧뇸ꗳꑗꅆ땍ꛓꅁ맪쏒ꑗ덜Ꙩ끝냈꣤ꕌ낪쁗뉶ꪺ룪껆ꣃ꒣닅Ꙙꭥ굺ꪺ낲덝ꅁꛓ걏꣣ꚳ낾멁(Skewness)깰멁(Kurtosis)ꅁꕂ득깴뚵엜늧볆ꣃꭄꥷ꒣엜ꅁꛓ걏라쁈뗛껉뚡ꪺ롧륌ꛓ엜ꅃ뻚ꚹꅁEngle(1982)ꕈ띳ꪺꓨꙖꯤꛒꅁ뒣ꕘARCH(Autoregressive Conditional Heteroscedasticity)볒ꮬꅁ꣤ꗘꪺ걏Ᶎ뇦떽뛇닎볒ꮬ맯꧳엜늧볆ꥷꪺ꒣Ꙙ뉺낲덝ꅁ냲ꖻꑗꭙ삳ꗎ뇸ꗳ뻷뉶녋ꯗ꣧볆ꕛꕈꥷ롱ꅁ꒹덜뇸ꗳ엜늧볆쁈뗛껉뚡ꪺ롧륌ꛓ엜ꅁꣃꕂ걏륌ꕨ뭾깴뚵ꖭꓨꪺ꣧볆ꅃARCHꅝpꅞ끪쉫볒ꮬ덝ꥷ꙰ꑕꅇ s=α+βf+ε ttttεΩ~N(0,h) tt−1tp2h=α+αε t0∑it−ii=1 ꣤꒤ꅁΩꫭꗜ꣬t−1듁결ꓮ꧒ꚳꕩꝑꗎꪺ룪끔뚰Ꙙꅁh결껉뚡ꟇꙃS꒧뇸ꗳ엜늧볆ꅁt−1tt결ꑆꭋ꧳꛴군볒ꮬ꣏뇸ꗳ엜늧볆h栗결ꖿ귈ꅁ걇ꖲ뚷궭꣮α>0ꅁα≥0(i=1,L,p)ꅃꗑt0i꧳볒ꮬ꒤뇸ꗳ엜늧볆꣼ꭥp듁뭾깴뚵ꪺ뱶암ꅁꙝꚹ럭듁ꪺ엜냊녎꣼ꭥ듁꧒뱶암ꅃꑓꗑ꧳α≥0ꅁ꧒ꕈꭥ듁늣ꗍꑰ둔ꯗ엜냊껉ꅁ럭듁ꑝ라늣ꗍꑰ둔ꯗꪺꙐꙖ엜냊ꅆꭥ듁늣ꗍꑪ둔iꯗ엜냊껉ꅁ럭듁ꑝ라늣ꗍꑪ둔ꯗꪺꙐꙖ엜냊ꅆꚹꝙ걏Mandelbrot(1963)뭐Fama(1976)꧒ꩩ냊쉏뭅ꪺ뉻뙈ꅃꚹꕾꅁARCH볒ꮬꑝ꣣ꚳ낪꽕깰ꪺ꽓꧊ꅁꙝꚹꟳ꿠꣣엩둹굺뿄꧊룪늣ꩩ냊ꪺ꽓꧊ꅃ 98
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?ARCH볒ꮬ쇶땍꿠꺷꺻꣬뿄꧊룪늣믹껦ꪺꛦ결ꅁ꣤ꛛ끪쉫듁볆덱녠ꯜꅁ꒣닅Ꙙ껉뚡Ꟈꙃ볒ꮬ덝ꥷ꧒굮ꡄꪺ냑볆뫫슲(Parsimonious)귬ꭨꅁꕂ굮ꡄα곒결ꖿꅁꦹꦹ믝i굮싇ꝕ곛럭ꗴ띎ꪺ뵵꧊뮼듮뢨ꯡ듁떲멣ꅃ꧳걏Bollerslev(1986)삳ꗎ뇸ꗳ뻷뉶녋ꯗ꣧볆ꅁ녎ARCH볒ꮬꕛꕈ쉘깩ꅁ뒣ꕘꑆꑀ꿫꓆ꛛ끪쉫뇸ꗳ엜늧볆(Generalized ARCH)볒ꮬꅁꚹ볒ꮬꪺ뮼ꦵ떲멣ꟳ꣣뱵꧊ꅁ꒹덜뇸ꗳ엜늧볆꒣뛈꣼꣬ꭥ듁뭾깴뚵ꖭꓨ꧒뱶암ꅁꑝ라꣼꣬ꭥ듁뇸ꗳ엜늧볆꧒뱶암ꅃꗑ꧳GARCH볒ꮬ꒣꿠둸뒤ARCH볒ꮬꪺ꽓꧊ꅁꕂꙢ뇸ꗳ엜늧볆ꪺ뢨ꯡ떲멣(Lag Structure)덝ꥷꑗꟳ꣣뱵꧊ꅆꕴꕾꅁ낪뚥ꪺARCH볒ꮬꕩꕈꝃ뚥GARCH볒ꮬ꣓둹굺ꅆGARCHꅝp,qꅞ끪쉫볒ꮬꕩꫭꗜꚨꅇ s=α+βf+ε tttεΩ~N(0,h) tt−1tpq2h=α+αε+δh t0∑it−i∑it−ii=1i=1 ꗑ꧳끝냈껉뚡Ꟈꙃꅁ뒶륍뭻결룓뇸ꗳ엜늧볆ꅝhꅞ결ꑀ뫘ARMAꅝ1,1ꅞ볒ꮬꅁꙝtꚹꖻꓥ껚뻚Holmes(1996)뇄ꗎ돦엜뙱GARCHꅝ1,1ꅞ쇗쁉볒ꮬꅁꕩꫭꗜ꙰ꑕꅇ s=a+bf+ε tttεΩ~N(0,h) tt−1t2h=α+αε+δh t01t−11t−1sꅇ뉻덦돸륓뉶 tfꅇ듁덦돸륓뉶 taꅇ멉뙚뚵 bꅇ뇗뉶뚵ꅁꝙ결꣏ꗎ듁덦쇗쁉ꓱ뉶 *ꑗꚡꝑꗎ돌ꑪ랧ꩫꅁꙁ롧싐땻Ꟈ(Iterative Procedure)ꝙꕩ녯ꕘ쇗쁉ꓱ뉶ꅝbꅞꅃ ꑔꅂGARJI볒ꮬ Chan and Maheu(2002)뒣ꕘ꒧ARJI볒ꮬꅁ꣤녎뇸ꗳ룵아녪ꯗ덝결꣣ꚳ쁈껉뚡엜냊ꪺ꽓꧊ꕂ닅ꙘARMAꚡꅁꣃꕂꛒ뱻룪늣돸륓뉶ꪺGARCH껄ꩇꅃꙢꝙꥷ돸륓뉶룪끔뚰ꙘΩ=R,L,Rꑕꅁꖻꓥ룪늣돸륓뉶ꪺ군뙱볒ꮬ뇄Maheu and McCurdy(2004)꒧덝{}t−11t−1ꥷꅁꣃ녎ꚹ볒ꮬ뫙결GARJIꅁ꣤ꕩꫭꗜ꙰ꑕꅇ 99
롧샧뫞뉺뷗쉏 , , 2005 pR=µ+φR+ε+ε ꅝ8ꅞ ∑tit−1,=1 qp2ε=hzꅁz~NID0,1 ꕂ h=ω+αε+βh ꅝ9ꅞ ()1,tttt∑∑tit−it−i=1i=1 εꩁ녱ꑀ듁뇦돸륓결륳ꪺ녠멁쁈뻷륌땻ꅁꝙE[ε|Ω]=0ꅁꛓε결룑쓀룵아꧒덝ꥷꪺ1,t1,tt−12,t쁈뻷륌땻ꅁ꣤뇸ꗳꖭꞡ볆결륳ꅁꝙE[ε|Ω]=0ꅆꙢꚹε뭐εꡃ듁ꞡ곛꒬뽗ꗟꅃ 2,tt−11,t2,tꗑꚡꅝ8ꅞꕩꪾ돸륓뉶ꕝꝴ꣢귓쁈뻷륌땻ꙝꑬꅁ꣤ꑀꩁ녱녠멁쁈뻷륌땻ꅁꕴꑀ결룵아ꪺ쁈뻷륌땻ꅁ꣤ꗑ냑볆λꅁꆣ뫙결룵아녪ꯗ(Jump Intensity)ꅆ꣣껉뚡엜늧ꪺPoissont꓀끴놱꣮돦ꛬ껉뚡꒺ꙝ결ꭄꖿ녠룪끔꧒늣ꗍꪺ룵아ꚸ볆ꆤ꧒놱꣮ꅃ낲덝ꙢΩꑕꅁ돦ꛬt−1껉뚡t−1,t꒺ꪺ룵아ꚸ볆결n∈0,1,2,Lꅁꭨnꪺ뇸ꗳ뻷뉶꓀끴꙰ꑕꅇ []{}jt −λjteλtP(n=j | Ω)= j=0,1,2,L ꅝ10ꅞ tt−1j ! ꣤꒤λ≡En|Ωꅁ뫙결뇸ꗳ룵아녪ꯗꅁ결Ꙣ룪끔뚰ꙘΩꑕꅁ룵아ꪺ듁뇦ꚸ볆ꅃBates []ttt−1t−1(1991)뭻결ꖫ돵룵아ꪺ뻷뉶ꕩ꿠라쁈뗛껉뚡ꛓ엜ꅁꝙ걏녎룵아ꪺ뻷뉶ꥍ룵아ꑪꑰ꧒쓝꓀끴꒤ꪺ냑볆ꅁ덝ꥷ결꣣ꚳ쁈껉뚡엜냊ꪺ꽓꧊ꅃDas(1998)ꥍFortune(1999)뇄ꗎ뗪샀엜볆녎룵아녪ꯗ덝ꥷ결라쁈껉뚡뇀늾ꛓ엜ꅃChernov et al.(1999) ꭨ녎룵아녪ꯗ덝결꓀ꝏ꣼륌ꕨ룵아ꑪꑰ꒧뱶암쁈뻷ꩩ냊ꪺꙝ꿀ꅃꕴꕾꅁEraker et al.(1999)뇄ꗎ돸륓뉶ꥍꩩ냊뉶덝ꥷ룵아ꪺꛦ결ꅃꖻꓥ녎룵아녪ꯗꪺ냊멁륌땻덝ꥷ결ARMAꅝ1,1ꅞꅁ뭐Chan and Maheu(2002)ꪺARJIꅝ1,1ꅞ볒ꮬ곛Ꙑꅁꫭꗜ꙰ꑕꅇ λ=λ+ρλ+γξ ꅝ11ꅞ t0t−1t−1 굙ρ=γ=0ꭨ결Jorion(1988)ꪺConstant Jump Intensity볒ꮬꅃ꣤꒤ξ뫙결룵아녪ꯗꪺt−1뭾깴뚵ꅁꥷ롱꙰ꑕꅇ ∞ξ≡En|Ωλj Pn=j|Ωλ ꅝ12ꅞ []()t−1t−1t−1t−1∑t−1t−1t−1j=0 ꣤꒤Pn=j|Ω뫙결쉯뱌(Filter)ꅁ결Ꙣ껉뚡결t-1ꑕ맯nꪺꯡ(Ex Post)뻷뉶뇀()t−1t−1t−1 100
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?뷗ꅃEn|Ω결t-2꣬t-1룵아듁뇦ꚸ볆ꪺꯡ뗻꛴ꅁλ결Ꙣ끔꺧뚰ꙘΩꑕꪺ룵[]t−1t−1t−1t−2아ꪺ뇸ꗳ듁뇦ꚸ볆ꅃꙢ떹ꥷ끔꺧뚰Ꙙ결Ωꑕꅁξ결닅Ꙙꖭ뷤꧊뷨ꪺꟇꙃ(Martingale t−1tDifference Sequence)ꅁꝙEξ|Ω=0ꅁꕂEξ=0ꥍCovξ,ξ=0ꅁi>0ꅃꙝꚹ룵[][]()tt−1ttt−i아녪ꯗꪺ뭾깴뚵삳룓꒣꣣ꚳꟇꙃ곛쏶ꪺ꧊뷨ꅃ ꗑꚡꅝ12ꅞꕩ녯ꭄ뇸ꗳꪺ룵아녪ꯗꅁꕩꫭꗜ꙰ꑕꅇ λ0Eλ= ꅝ13ꅞ []t1−ρ ꗑꑗꕩꪾARJI볒ꮬꪺ쎭ꥷ뇸ꗳ결ρ<1ꅁꕂꕩ녎룵아녪ꯗꪺ룳듁륷듺ꫭꗜ꙰ꑕꅇ λ i=0tEλ|Ω= ꅝ14ꅞ []t+it−1i−1iλ1+ρ+L+ρ+ρλ i≥1()0t ARJI볒ꮬꕩꕈ궫띳ꫭꗜ결ꅇ λ=λ+ρ−γ λ+γ En|Ω ꅝ15ꅞ ()[]t0t−1t−1t−1 ꣤꒤맯꧳꧒ꚳꪺtꅁλ>0ꕂλ>0ꅁρ≥γꅁγ≥0ꅃ t0룵아ꑪꑰπ낲덝결녱녠멁꓀끴꒤뽗ꗟꧢ꣺꒧쁈뻷엜볆ꅁꚹ룵아ꑪꑰꪺ꓀끴꙰ꑕ t,k 2π~NID θ,δ ꅝ16ꅞ ()t,k 낲덝Ꙣ껉뚡t-1꣬t껉ꅁ뱶암돸륓뉶ꪺ룵아ꙝꑬꫭꗜ결ꅇ ntJ=π ꅝ17ꅞ ∑tt,kk=1 ꙝꚹꅁ룵아ꪺ쁈뻷륌땻εꅁꙢt껉쉉껉ꕩꫭꗜ결ꅇ 2,tntε=J−EJ|Ω=π−θλ ꅝ18ꅞ []2,tttt−1∑t,ktk=1 101
롧샧뫞뉺뷗쉏 , , 2005 돸륓뉶ꪺ뇸ꗳ엜늧볆ꕩ꓀룑결꣢귓뎡꓀ꅁꑀ결쉘뒲륌땻꒤걍륌ꕨ껸꺧뷄삻꧒녡꣓룻ꖭ뵷ꪺ뇸ꗳ엜늧볆ꅁꝙGARCH볒ꮬ꒤ꪺ뇸ꗳ늧뷨엜늧볆ꅆꕴꑀ뎡꓀결걍늧뷨룪끔륌땻ꪺ뇸ꗳ엜늧볆ꅁꝙ룵아ꙝꑬ꧒끞쑭ꪺ뇸ꗳ늧뷨엜늧볆ꅃꙝꚹꅁ돸륓뉶ꪺ뇸ꗳ늧뷨엜늧볆꙰ꑕꅇ VarR|Ω=Varε|Ω+Varε|Ω ()()()tt−11,t−1t−12,t−1t−122=h+θ+δ λ ꅝ19ꅞ ()tt ꚡꅝ19ꅞ꒤ꪺ닄ꑀ뎡꓀결GARCH볒ꮬ꒤ꪺ늧뷨엜늧볆ꅁꝙꚡꅝ9ꅞꅁ귈녯ꩠ띎ꪺ걏ꖻꓥ맯꧳GARCHꪺ뇸ꗳ늧뷨엜늧볆ꣃ때ꛒ뱻ꖿ굴껸꺧뷄삻ꪺ꒣맯뫙껄ꩇꅃꛓ닄ꑇ뎡꓀결룵아ꪺ뇸ꗳ늧뷨엜늧볆ꅁ꣤결 22Varε|Ω=θ+δ λ ꅝ20ꅞ ()()2,t−1|t−1t Ꙣꚡꅝ8ꅞꪺ덝ꥷꑕꅁ돸륓뉶ꪺꑀ꣬ꕼ뚥냊깴ꕩꫭꗜ꙰ꑕꅇ ER|Ω=µ ꅝ21ꅞ []tt−1 22VarR|Ω=h+θ+δ λ ꅝ22ꅞ []()tt−1tt 32λθ+3θδ()tSkR|Ω= ꅝ23ꅞ []tt−13222h+λδ+λθttt 4224λθ+6θδ+3δ()tKuR|Ω=3+ ꅝ24ꅞ []tt−122h+λδ+λθttt 걇ꕝꝴ룵아쉘뒲륌땻ꪺ룪늣돸륓뉶ꅁ꣤깰멁ꅂ낾멁라쁈껉뚡엜꓆ꚳ꧒엜ꅁ꒣뛈룻꿠꺷꺻랥뫝ꗳ땯ꗍ껉꧒늣ꗍꪺ띬꽱놡ꩰꅁꟳꕩ꽵맪걍룪늣믹귈냊멁ꩩ냊엜꓆놡ꅃ Ꙣ맯볆랧꣧볆ꪺ덝ꥷꑗꅆ궺ꗽꖲ뚷ꗽꯘꗟꕘ돸륓뉶Ꙣ돦ꛬ냏뚡ꕝꝴj귓룵아ꑕꪺ녠멁뇸ꗳ녋ꯗ뻷뉶꣧볆ꅁꙢꚡꅝ8ꅞꪺ덝ꥷꑕꅁ꣤ꕩꫭꗜ꙰ꑕꅇ 102
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?2pR−µ−R+θλ−θj∑tt−it−12i=12fR|n=j , Ω=2πh+jδexp−ꅝ25ꅞ ()()ttt−1t22h+jδ()t ꕴꕾꅁ룵아뻷뉶ꪺꯡ뇀뷗ꅁChan and Maheu(2002)뒣ꕘꝑꗎꢩꓳꥷ뉺(Bayes rule)ꅁꙢ왛맮꣬t듁룪끔Rꯡꅁꕩ뇀뷗t듁ꪺꯡ뇸ꗳ뻷뉶ꅁꚹ뻷뉶뇀뷗ꫭꗜ꙰ꑕꅇ t fR|n=j,ΩPn=j|Ω()()ttt−1tt−1Pn=j|Ω= ꅝ26ꅞ ()tt−1fR|Ω()tt−1 뻣Ꙙ돦ꛬ냏뚡꧒ꚳ룵아ꚸ볆ꯡꅁ돸륓뉶ꪺ뇸ꗳ뻷뉶녋ꯗ꣧볆ꕩꫭꗜ꙰ꑕꅇ ∞fR|ΩfR|n=j,ΩPn=j|Ω ꅝ27ꅞ ()()()tt−1∑ttt−1tt−1j=0 Ꙣꑗ굺ꪺ덝ꥷꑕꅁ맯볆랧꣧볆ꕩꫭꗜ결ꅇ TL(Ψ)=log f(R|Ω;Ψ) ꅝ28ꅞ ∑tt−1t=1 ꣤꒤Ψ=(µ,φ,ω,α,β,θ,δ,λ,ρ,γ)결ꯝ꛴냑볆Ꙗ뙱ꅃ iii0ꗑ꧳ꖻꓥ뇄ꗎ늾냊뗸떡ꪺꓨꩫ뙩ꛦ볋ꖻꕾ냑볆ꪺ꛴군ꅁ녎GARJI볒ꮬꪺ냑볆뙩ꛦ궭꣮ꅁꕈ뒣꛴군ꪺ껄뉶꧊뭐럇뵔꧊ꅁꙝꚹꅁ굙녎GARJI꒤ꪺ냑볆Ꙗ뙱Ψ뙩ꛦ궭꣮ꅁꝙθ=δ=λ=ρ=γ=0ꅁꭨꕩ녯꣬GARCH볒ꮬꅃꗑ꧳GARCH볒ꮬ걏녎GARJI꧒쓝0냑볆ꕛꕈ궭꣮ꛓ녯ꅁ걇뫙꣤결궭꣮볒ꮬꅃꕴꕾꅁꖻꓥ녎꧒뇄ꗎꪺꑇ뫘볒ꮬ뇔굺꙰ꑗꅁ녎ꚳꝑ꧳땻ꚡꪺ뵳뵘뭐냑볆ꪺ꛴군ꅃ Ꙣ귓ꝏ냑볆ꪺ샋ꥷꅁ뇄ꗎ랧ꓱ뉶샋ꥷ(LR-test)꓀ꝏ맯꧳꣼궭꣮볒ꮬꪺ냑볆θꅁꥍ0ꖼ꣼궭볒ꮬꪺ냑볆θ뙩ꛦ샋ꥷꅁ꣤샋ꥷ닎군뙱결 1 LR=−2 LR|θ−LR|θ ()()t0t1 ꣤ꩁ녱ꛛꗑꯗ결Kꪺꕤꓨ꓀끴ꅁ꣤꒤K=nθ−nθꅁnθꫭꗜθ꒤ꪺ냑볆귓볆ꅃ ()()()10Ꙣ볒ꮬ끴빁꿠ꑏꪺꝐ쉟ꑗꅁJorion(1988)뭐Chahal and Wang(1997)곒뇄ꗎSchwarz 103
롧샧뫞뉺뷗쉏 , , 2005 criterionꝀ결뿯꣺볒ꮬꪺ럇ꭨꅁ걇ꖻꓥꗧ뇄ꚹ럇ꭨ꙰ꑕꚡ SC=−2 LR|θ+nθ lnT ꅝ29ꅞ ()()t ꣤꒤LR|θ결맯볆랧꣧볆귈ꅁnθꫭꗜθ꒤ꪺ냑볆귓볆ꅁT결왛듺귈귓볆ꅃ ()()t ꕼꅂ냊멁룵아녪ꯗꑕꪺ돌빁쇗쁉볒ꮬ 뻚Johnson(1960), Stein(1961)Ederington(1979)녎Markowitz(1952)꒧ꖭꞡ볆ꇐ엜늧볆ꩫꅁꕈ룪닕Ꙙ돸륓ꪺ엜늧볆꣓뿅뙱궷쁉ꅁ삳ꗎ꧳뉻덦뎡ꛬꪺ쇗쁉ꅁꕩ녯꣬엜늧볆랥ꑰ꓆꒧쇗쁉ꓱ뉶ꅃ낲덝ꑀ쇗쁉룪닕ꙘꕝꝴC돦ꛬꪺ뉻덦ꥍC돦ꛬꪺ듁덦ꅁꕂ뉻sf덦ꥍ듁덦Ꙣt껉쉉ꪺ믹껦꓀ꝏ결SꥍFꭨꚹ쇗쁉룪닕Ꙙꪺ돸륓뉶ꕩꫭꗜ꙰ꑕꅇ tt R=R−hR ꅝ30ꅞ hsf 굙쇗쁉뷦ꕘh돦ꛬꪺ듁덦뎡ꛬ뙩ꛦ쇗쁉ꅁꭨ쇗쁉룪닕Ꙙ꒧돌ꑰ돌엜늧볆ꓨ땻ꚡ꙰ꑕꅇ 2minVarR=VarR+hVarR−2hCovR,R ꅝ31ꅞ ()()()()hsfsfh 녎ꅝ31ꅞꚡ맯쇗쁉ꓱ뉶h꣺ꑀ뚥띌꓀ꅁꙁꕏ꣤떥꧳륳ꅁꝙꕩ녯꣬돌ꑰ꓆쇗쁉룪닕Ꙙ엜늧ꑕꪺ돌빁쇗쁉ꓱ뉶ꅁ뫙결돌ꑰ엜늧쇗쁉ꓱ뉶(Minimum Variance hedge ratio; MV hedge ratio)꙰ꑕꅇ CovR,Rσ()σsfMVsfsh===ρ ꅝ32ꅞ 2σσVarR()fff ꣤꒤ꅁρꅂσ꓀ꝏ결R뭐Rꪺ곛쏶ꭙ볆뭐Ꙁ엜늧볆ꅁꛓσ뭐σ꓀ꝏ결R뭐Rꪺ볐럇sfsfsfsf깴ꅃ ꖻꓥ뇄ꗎMaheu and McCurdy(2004)ꪺGARJI볒ꮬꅁ녎돸륓뉶덝ꥷ결ꕩꕈ꺷꺻꣤꒣덳쓲ꪺ룵아ꅁꣃꕂ꿇ꑊ쇗쁉ꓱ뉶ꪺ군뫢ꅁ녎ꚹꑀ돸륓뉶ꕝꝴ룵아ꪺ쇗쁉ꓱ뉶ꫭꗜ꙰ꑕꅇ 104
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?222Cov(R,R)σ+(θ+δ) λsfssssJh==ρ ꅝ33ꅞ 222Var(R)fσ+(θ+δ) λffff 22꣤꒤θꅂθꅂδ뭐δ꓀ꝏ결뉻덦ꥍ듁덦룵아ꑪꑰ꒤ꪺꖭꞡ볆뭐엜늧볆ꅁλꅂλ꓀ꝏ결sfsfsf뉻덦ꥍ듁덦ꪺ룵아녪ꯗꅃ Ꙣꅝ33ꅞꚡ꒤ꅁ굙꒣ꛒ뱻룵아ꪺ놡ꩰꑕλ=λ=0ꅁꭨ돌빁쇗쁉ꓱ뉶녎슲꓆ꚨ결ꚡsfꅝ32ꅞꪺMV쇗쁉ꓱ뉶ꅃ ꛜ꧳쇗쁉셚껄ꪺ뿅뙱ꅁꕩꕈ덺륌ꖼ쇗쁉뉻덦뎡ꛬ륷듁돸륓ꪺ엜늧볆듮ꓖ꒧땻ꯗꕛꕈ뿅뙱ꅁ궰ꝃ땻ꯗ띕ꑪꅁꕎꫭ쇗쁉껄ꩇ띕꣎ꅃ뿅뙱쇗쁉셚껄ꪺ쇗쁉셚껄볐ꅝ돦ꑀ듁ꅞ꙰ꑕꚡꅇ Var(R)−Var(R)shpHE= ꅝ34ꅞ Var(R)s ꗑ꧳ꖻꓥ꒧륷듺뭐쇗쁉뇄ꗎ늾냊뗸떡ꪺꓨꚡꅁꕈ볋ꖻꕾꪺ꛴군ꓨꚡꅁ맯볋ꖻ룪껆뙩ꛦnꚸ끪냩군뫢ꅁ걇뻣엩룪껆뵤돲ꪺ쇗쁉껄ꩇꕩꗑꖭꞡꪺ쇗쁉셚껄볆뿅뙱ꅇ nHE∑ii=1HEI= ꅝ35ꅞ n 쇗쁉셚껄볆띕낪ꅁꫭꗜ냊멁쇗쁉셚껄띕꣎ꅃ뉺뷗ꑗꅁ쇗쁉셚껄ꪺ낪ꝃꅁꡍꥷ꧳Var(R)꧒듮ꓖꪺ땻ꯗꅁ굙꒣ꛒ뱻룵아ꪺ놡ꩰꑕꅁꝙλ=λ=0ꅁꭨꗑꚡꅝ31ꅞ쇴ꝴhpsfVar(R)듮ꓖ꒧땻ꯗꕄ굮꣼쇗쁉ꓱ뉶뭐σꑪꑰ꧒ꡍꥷꅃꛓ꒣ꛒ뱻룵아놡ꩰꑕꪺ쇗쁉ꅁhpsf떲뷗결쇗쁉듁뚡띕ꅁ쇗쁉셚껄띕꣎(Figlewski, 1984; Lindahl, 1992)ꅁ꣤귬ꙝ결듁덦뭐뉻덦꧳땵듁뚡ꪺꕩ꿠ꝥ뉻굴곛쏶ꅁ뻉교쉘ꑪ띬ꖢꛓꖢꕨ쇗쁉꒧ꗘꪺꅁ쑙궫뱶암쇗쁉셚껄ꅃ굙ꖫ돵꙳Ꙣ곰땯ꪺ롧샙ꗳ꧒ꓞ끟ꪺꭄ륷듁꧊룵아ꅁꛓ꣏땵듁뚡Ꙣ꒣ꞹ과ꖫ돵떲멣꒤ꅁ듁덦뭐뉻덦ꢫ뛕꒣ꑀ교ꪺ뉻뙈ꅁꖻꓥ듁뇦싇ꗑGARJI볒ꮬꪺ덝ꥷꕛꕈ꺷꺻쁈뻷룵아ꪺ뉻뙈ꅃꙝꚹꅁ굙룪ꑈꚳ땵듁ꪺ쇗쁉믝ꡄ껉ꅁ쇗쁉ꓱ뉶ꪺ군뫢ꓨꚡꕩꛒ뱻뇄ꗎꕝꝴ룵아ꩩ냊ꪺ쇗쁉ꓱ뉶ꅁꕈ뫻꯹룪닕Ꙙ돌빁ꪺꙨ뎡ꛬꅃ 105
롧샧뫞뉺뷗쉏 , , 2005 롶ꅂ맪쏒떲ꩇ뭐꓀꩒ ꑀꅂ룪껆꣓랽뭐덂뉺 ꖻꓥꕈ과냪늼ꖫ돵결곣ꡳ맯뙈ꅁꝑꗎ륄쎣ꑵ띾ꖭꞡ볆듁덦꣓덗쇗꣤볆뉻덦ꩩ냊꒧궷쁉ꅃ곛쏶룪껆꣺ꛛBloomberg룪껆깷ꅁ룪껆ꮬ멁결ꓩ룪껆ꅁ꣺볋듁뚡결1998꙾1ꓫ2ꓩ꣬2003꙾7ꓫ25ꓩꅁ볋ꖻ볆Ꙁ1399떧ꅃ륄쎣ꑵ띾ꖭꞡ볆듁덦ꪺ꣬듁ꓫꗷ뇄ꑔꓫ둠샴ꅁꝙ꣬듁ꓫꗷ결ꑔꓫꅂ꒻ꓫꅂꑅꓫꅂꑑꑇꓫꅆ륄쎣ꑵ띾ꖭꞡ볆듁덦ꪺ돌ꯡꗦ꧶ꓩ결꣬듁ꓫꗷꪺ닄ꑔ귓걐듁꒭ꅃꗑ꧳Ꙑꑀꓩ꒺ꚳ꒣Ꙑ꣬듁ꓩꪺ듁덦ꮴ곹뙩ꛦꗦ꧶ꅁꖻꓥ녎뛈ꛒ뱻럭ꓩꗦ꧶뙱돌ꑪꪺꮴ곹ꅃ덱녠ꗦ꧶뙱결돌ꑪꪺ듁덦ꮴ곹결꫱ꓫꮴ곹ꅁ걇뿯뻜싷왛맮ꓩ돌꫱듁ꪺ듁덦ꮴ곹믹껦결듁덦믹껦ꅁꣃꙢ꫱ꓫ듁덦Ꙙ곹꣬듁ꭥ뿯ꥷꗦ꧶뙱돌ꑪꓩꝀꙘ곹신뒫ꅃ걇녎ꡃꓩ믹볆꣤ꡃꓩ듁덦볆ꅁꕈ맯볆깴꓀ꚡ신뒫결돸륓뉶ꪺꓨꚡ꣓ꫭꗜꅆ닄t듁ꪺ믹뉻덦뭐듁덦ꪺ돸륓뉶ꕩꥷ롱결ꅇ R=(lnP−lnP)×100 ꅝ36ꅞ ttt−1 ꣤꒤ꅁR결닄t듁믹볆뉻덦듁덦ꪺꓩ돸륓뉶 tP결닄t듁ꪺ믹볆뉻덦듁덦ꚬ뵌믹 tP결닄t−1듁믹볆뉻덦듁덦ꪺꓩ돸륓뉶 t−1lnP뭐lnPꫭꗜ꣺ꛛ땍맯볆ꯡꪺꚬ뵌믹 tt−1 ꑇꅂ냲ꖻ닎군뙱 ꫭ1ꙃꕘꑆ륄쎣ꑵ띾믹볆뉻덦듁덦ꪺ냲ꖻ닎군뙱ꅁꗑ꧳믹볆듁덦걏ꕈ믹볆결볐ꪺꪫꪺ뿄냓ꭾꅁꙝꚹ믹볆뉻덦뭐믹볆듁덦꒧냲ꖻ닎군뙱삳랥결쏾ꅁꗑꫭ1꒤ꅁꕩꕈꧺ엣곝꣬덯볋ꪺ떲ꩇꅁ듁덦뭐뉻덦ꪺꖭꞡ귈둘ꕇꑀ교ꅁ듁덦ꪺꩩ냊꧊룻뉻덦결ꑪꅃꚹꕾꅁ늼뭐듁덦ꖫ돵곒ꝥ뉻낪꽕깰ꪺ놡ꅁꑝ둎걏꧒뿗ꪺꅵꭰꟀꅶ(Fat Tail)뉻뙈ꅁꛓ롧ꗑJarque–Bera녠멁꓀끴샋ꥷꑝꕩ땯뉻ꅁꖫ돵ꪺꓩ돸륓뎣엣뗛떴녠멁꓀끴ꪺ낲덝ꅃ맏1결귬ꥬ껉뚡Ꟈꙃ맏ꅁ셡뙢ꕎꫭ믹볆ꅁ뻮뙢ꕎꫭ볋ꖻ듁뚡ꅃ ꫭ 1 륄쎣ꑵ띾볆뉻덦뭐듁덦돸륓뉶꒧냲ꖻ닎군뙱 닎군뙱 ꖭꞡ볆 볐럇깴 낾멁ꭙ볆깰멁ꭙ볆돌ꑰ귈 돌ꑪ귈 JB 엜볆 믹볆뉻덦 % ***% % *** 믹볆듁덦 % ***% % *** 뗹ꅇ1. *ꅂ*****꓀ꝏꫭꗜ10%ꅂ5%1%꒧엣뗛ꓴ럇ꅃ 2. JB결Jarque-Bera꒧녠멁꓀끴샋ꥷꅃ 106
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?Panel 1 : DownJones 뉻덦120001100010000900080007000JFMAMJJASONDJFMAMJJASONDJFMAMJJASONDJFMAMJJASONDJFMAMJJASONDJFMAM199819992000200120022003Panel 2 : DownJones 듁덦120001100010000900080007000JFMAMJJASONDJFMAMJJASONDJFMAMJJASONDJFMAMJJASONDJFMAMJJASONDJFMAM199819992000200120022003맏 1 엜볆귬ꥬ껉뚡Ꟈꙃ쇍뛕맏 롧돦껚샋ꥷꅁ녯ꪾ륄쎣ꑵ띾믹볆뉻덦ꥍ볆듁덦껉뚡Ꟈꙃ룪껆곒결I(1)ꥷ멁ꅁ꣣ꚳ돦껚뉻뙈(Ghosh 1993, Sephton 1993a, Sephton 1993b)ꅃꙢ뇄ꗎGARCH볒ꮬ꒧ꭥꅁ믝ꗽ샋ꥷ륄쎣ꑵ띾믹볆ꥍ믹볆듁덦믹깴롧ꗑ볒ꮬ끴빁꧒늣ꗍꪺ득깴뚵ꅁ걏ꝟ꣣ꚳARCH뉻뙈ꅁꕈꝑꖻ곣ꡳ꒧뇄ꗎGARCH볒ꮬ뙩ꛦ맪쏒곣ꡳꅆꖻꓥ뇄ꗎLM샋ꥷꩫ꣓맯득깴뚵뙩ꛦ샋ꥷꅁ샋엧걏ꝟ꙳Ꙣ엜늧볆늧뷨꧊ꅃꗑꫭ2꒤ꪺLM샋ꥷ엣ꗜ룪껆꙳ꙢARCH껄ꩇꅃ ꑔꅂ볒ꮬ꒧쇗쁉껄ꩇ꓀꩒?ꅂ볋ꖻ꒺쇗쁉껄ꩇ꒧뿅뙱 껚뻚Park(1995)뿅뙱쇗쁉껄ꩇꪺ랧꧀ꅁꖻ곣ꡳ녎ꓱ룻ꙕ뫘꒣Ꙑ쇗쁉볒ꚡ룻꒣쇗쁉ꪬ멁ꑕ꧒듮ꓖꪺ엜늧볆ꛊ꓀ꓱ결쇗쁉껄ꩇ뿅뙱ꪺ볐럇ꅃ궺ꗽꯘꗟ듁덦뭐뉻덦ꪺ쇗쁉룪닕Ꙙꅁꣃ꛴뫢ꕘ돌빁쇗쁉ꓱ뉶꙰ꑕꅇ 2*Var(π)ꇗσ(s−bf) ꅝ37ꅞ tt ꫭ 2 륄쎣ꑵ띾볆뉻덦뭐듁덦볆듁덦ARCH껄ꩇ샋ꥷ 엜볆 믹볆뉻덦 믹볆듁덦 LM test *** *** 뗹ꅇ1. ***ꫭꗜ꣣1%ꪺ엣뗛ꓴ럇ꅃ 107
롧샧뫞뉺뷗쉏 , , 2005 **꣤꒤b결돌빁쇗쁉ꓱ뉶ꅃ군뫢b꧒믝ꪺ냑볆ꕩ꓀ꝏ싇ꗑGARCHꅂGARJI꒧꛴군ꅃꕈGARCH볒ꮬ꧒군뫢꒧돌빁쇗쁉ꓱ뉶ꕩꫭꗜ결ꅇ Cov(R,R)σσsfsf*sb===ρ ꅝ38ꅞ 2Var(R)σσfff 굙ꛒ뱻믹껦룵아놡ꑕꅁꕈGARJI볒ꮬ꧒군뫢꒧돌빁쇗쁉ꓱ뉶녎꙰ꑕꅇ σ+J(t)δρ(σσ+J(t)δδ)sfsfsfsf*b== ꅝ39ꅞ 2222σ+J(t)δσ+J(t)δffff ꙕ볒ꚡ쇗쁉껄ꩇ꒧쁵Ꙉꅁ뫝뗸꣤꿠꣏꒣쇗쁉ꑕ꒧엜늧볆듮ꓖꙨꓖꛊ꓀ꓱꛓꥷꅆ꣤볆뻇ꚡ꙰ꑕꅁ룓귈띕ꑪꅁꫭꗜ쇗쁉셚껄띕ꙮꅃꅇ 22σ−σno−hedgehedgedHEꇗ ꅝ40ꅞ 2σno−hedge ꅂ볋ꖻꕾ쇗쁉맪쏒떲ꩇ Ꙣ뎡꓀ꓥ쑭꒤ꕄ녩쇗쁉ꓱ뉶쇗쁉셚껄ꕩꕈꙢꙐꑀ듁뚡ꡍꥷꅁ덯Ꙣ맪믚ꪺ쇗쁉뻞Ꝁ걏쏸ꕈ뙩ꛦꪺꅁꚹ쉉ꝙ녠ꓞ땯뻇ꪺꪧ쒳ꅃ맪믚뙩ꛦ쇗쁉뻞Ꝁ껉ꅁꑪ뎣꣏ꗎ륌ꕨ걙ꑀ걱듁뚡ꪺ룪껆뙩ꛦ쇗쁉ꓱ뉶꒧꛴군ꅁꙁ낲덝ꚹ쇗쁉ꓱ뉶ꕩꕈ쎭ꥷ뫻꯹꧳걙ꑀꓴꖭꑕꅆꕈꚹ쇗쁉ꓱ뉶뙩ꛦ쇗쁉ꅁꙁ샋엧맪믚쇗쁉ꕩ꿠ꪺ껄ꩇꅃBenet(1992)ꕈꕾ뛗듁덦결꣒ꅁꯘ쒳뇄ꗎ볋ꖻꕾ걏ꭥ(Ex-ante)ꪺ왛쉉꣓뗻꛴쇗쁉껄ꩇꅁ뭻결ꚹ맯꧳륷듺쇗쁉꒧궷쁉궰ꝃ땻ꯗꅁ룻꿠ꚳꚳ껄꒧뮡ꧺꅃ 볋ꖻꕾꪺ쇗쁉껄ꩇ뿅뙱ꅁꖲ뚷ꗽꕈ쇗쁉듁뚡꒧ꭥꪺꑀ걱룪껆꣓군뫢꒣Ꙑ볒ꚡꪺ쇗쁉ꓱ뉶ꅁꙁ녎꣤ꕎꑊ쇗쁉듁뚡ꡄ뫢ꕘ쇗쁉ꯡ룪닕Ꙙꪺ엜늧볆ꅁ군뫢뇄ꗎ꒣Ꙑ쇗쁉볒ꚡ껉ꅁ꒣쇗쁉껉엜늧볆듮ꓖꪺꛊ꓀ꓱꅁ군뫢ꓨꚡꙐꚡꅝ40ꅞꅃ ꙁꕈ늾냊뗸떡꒧ꓨꚡꅁꡃꚸ늾냊ꑀ떧껉뚡Ꟈꙃ룪껆ꅁ궫뷆ꑗꙃ꒧군뫢ꯡ꣺꣤쇗쁉껄ꩇ꒧ꖭꞡ귈ꅁ룓귈띕ꑪꅁꫭꗜ쇗쁉껄ꩇ띕ꙮꅃ ꖻꓥꕈ볋ꖻꕾ꒧왛쉉꣓뗻꛴쇗쁉셚껄ꅁ쇗쁉ꓱ뉶꛴군듁뚡ꥷ결1000ꓑꅁꛛ1998꙾1ꓫ2ꓩ끟ꣃꝑꗎ늾냊뗸떡꒧ꓨꩫ꣓꓀꩒꣢뫘쇗쁉볒ꮬ꒤쇗쁉듁뚡꒧땵맯꧳쇗쁉셚껄꒧뱶암ꅃꖻꓥ뙩ꛦ맪쏒꒧꯹ꚳ쇗쁉듁뚡꓀ꝏ결10ꓑꅂ20ꓑꅂ30ꓑꅂ50ꓑꅁ끪냩ꪺꚸ볆꓀ꝏ결30ꚸꅂ15ꚸꅂ10ꚸꕈ6ꚸꅁ맏2걏ꕈ꯹ꚳ쇗쁉듁뚡결10ꓑꅁ쇗쁉ꓱ뉶꛴군듁뚡1000ꓑ결꣒ꅁ뮡ꧺꖻꓥ뇄늾냊뗸떡ꓨꩫꪺ꛴군듁뚡뭐쇗쁉듁뚡꒧늾냊륌땻ꅁ꧒뿗꛴군듁뚡닄ꑀꚸ끪냩ꭙꝑꗎꭥ1000ꓑ꒧믹뉻덦뭐듁덦룪껆ꗽ꛴군쇗쁉ꓱ뉶ꅁ땍ꯡ 108
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ? 10ꓑ10ꓑ 닄1ꚸ끪냩 ꛴군듁뚡(1000ꓑ) 쇗쁉듁뚡 ꛴군듁뚡(1000ꓑ) 쇗쁉듁뚡 닄2ꚸ끪냩 ꅇ닄3ꚸ끪냩 ꅇ맏 2 ꛴군듁뚡(1000ꓑ)뭐쇗쁉듁뚡(10ꓑ)꒧늾냊뗸떡ꓨꩫ 맯쇗쁉듁뚡ꅝꝙ놵ꑕ꣓10ꓑꅞꅁ맪믚뙩ꛦ쇗쁉ꅁꙢ쇗쁉듁뚡듁ꖽ뗻꛴꣤쇗쁉셚껄ꅁ꣤빬쏾뇀ꅃ 롧ꗑꚹꩫꅁ볋ꖻꕾ꒧맪쏒곒ꕈꡃ듁돌띳룪끔꣓꛴군ꑕ듁ꪺ쇗쁉ꓱ뉶ꅁꣃꝑꗎꑕ듁ꪺ맪믚룪껆군뫢볋ꖻꕾ꒧쇗쁉셚껄ꅁ걇ꖻ곣ꡳ꣢뫘쇗쁉볒ꮬ볋ꖻꕾ꒧쇗쁉ꓱ뉶곒뇄냊멁뷕뻣ꅁꛓꭄꥷ꒧쇗쁉ꓱ뉶ꅃ ꗑ꧳ꖫ돵곰땯꧊궫ꑪ롧샙ꗳ꒧땯ꗍ덹ꚨ룪늣돸륓뉶쁈뻷룵아ꅁ룵아ꑪꑰꕩ결굴ꖿꅁꑪꑰꅁꕂ라뱶암돸륓뉶꓀끴꒧낾멁ꅃ걇ꖻꓥ샀녎뇸ꗳ엜늧볆ꪺ볒ꮬ덝ꥷ결ꕝꝴ덳쓲꧊ꖭ쎭ꪺ쁈뻷륌땻꒣덳쓲ꪺ룵아쉘뒲륌땻ꅁꛓGARCH볒ꮬ걏녎GARJI꧒쓝냑볆ꕛꑗ궭꣮ꛓ녯ꅃꖻꓥ뿯꣺GARCHꅝ1,1ꅞꥍGARJIꅝ1,1ꅞ뙩ꛦ볋ꖻ꒺냑볆ꪺ꛴군ꅆ5꧳GARJIꅝ1,1ꅞ꒤ꅁ돦ꛬ껉뚡ꪺ룵아ꚸ볆덝ꥷ결5귓ꅃꫭ3ꙃꕘGARJIꅝ1,1ꅞ볒ꮬ뭐GARCHꅝ1,1ꅞ볋ꖻ꒺냑볆꒧꛴군떲ꩇꅁꛓꫭ4결ꕈ볋ꖻꕾ꒧왛쉉ꅁ껚뻚쇗쁉듁뚡꒧땵꒣Ꙑ꧒군뫢ꕘ꒧ꖭꞡ쇗쁉ꓱ뉶ꅃꕩꕈ땯뉻Ꙣꗴ꛳쇗쁉듁뚡ꅁ쇗쁉ꓱ뉶곒ꑰ꧳1ꅁꚹ뭐Ederington(1979), Lindahl(1992), Park and Switzer(1995)떥맪쏒곣ꡳꪺ떲ꩇ곛Ꙑꅁꝙ꒣뚷녎뉻덦ꪺ뎡ꛬ뙩ꛦꛊ꓀꒧ꛊꪺ쇗쁉ꅁꕩ론곙룪ꑈ뎡꓀꒧쇗쁉ꚨꖻꅃꙢ쇗쁉듁뚡결40ꓑꕈꯡꅁ쇗쁉ꓱ뉶ꑪ꧳1ꅁꚹꕩ꿠걏쇗쁉뚡ꪺ꧔ꅁ맯ꖫ돵ꢫ뛕ꪺ꒣뵔ꥷ뻉교쇗쁉ꓱ뉶ꪺ뱗ꕛꅃ ꫭ5ꕈ볋ꖻꕾ꒧왛쉉Ꙣ꒣Ꙑ쇗쁉ꑵ꣣뭐쇗쁉볒ꮬꑕꅁ껚뻚쇗쁉듁뚡꒧땵꒣Ꙑꅁꝑꗎ꛴군듁뚡꧒군뫢ꕘ꒧쇗쁉ꓱ뉶ꅁꕈ늾냊뗸떡꒧덎군뫢쇗쁉셚껄볆(HEI)ꅃ ? Chan and Maheu(2002)녎룵아귓볆덝ꥷ결20귓ꅁ땍ꛓꖻ곣ꡳ땯뉻룵아귓볆덝ꥷ결5귓뭐20귓꧒꛴군ꕘꪺ냑볆깴늧꒣ꑪꅁꕂBall and Torous(1985b)뒣꣬룵아귓볆덝ꥷ결10귓ꟳꑰꅁꕩ륆꣬꛴군ꪺ뫫뵔ꯗꅃ 109
롧샧뫞뉺뷗쉏 , , 2005 ꫭ 3 GARJIꅝ1,1ꅞ볒ꮬ뭐GARCHꅝ1,1ꅞ볒ꮬ꒧꛴군떲ꩇ 믹볆 볆듁덦 GARCH(1,1) GARJI(1,1) GARCH(1,1) GARJI(1,1) µ µ ω ω **** ****** α α *** ****** β β *** *** ****** η *** η *** 00ς **ς *00λ *** λ ** 00ρ ρ ******γ γ *** *** Q (15) Q (10) 22Q(15) Q(10) (15) (15)ξξttSC SC LR-test *** LR-test *** 랧꣧랧꣧ 볆귈 볆귈 뗹ꅇ1. *ꅂ**ꅂ***꓀ꝏꫭꗜ꣣10%ꅂ5%1%ꪺ엣뗛ꓴ럇ꅃ 2. 볒ꮬ덝ꥷꅇ GARJI(1,1)ꅇ ꅁ ꅁ ꅁ R=µ+ε+εε=hzz~NID(0,1)t1,t2,t1,ttttnt ε=π−θλ2,t∑t,ktk=12꣤꒤ , λ=λ+ρλ+, γξh=ω+αε+βhπ~N(η,ς)t01t−11t−1tt−1t−1t,k002GARCH(1,1) : , , h=ω+αε+βhR=µ+εε=hzz~NID(0,1)tt−1t−1t1,t1,tttt3. SC결Schwarz Criterion(1978)ꅃ ꫭ 4 Ꙣ꒣Ꙑ볒ꮬꑕ꒧ꖭꞡ쇗쁉ꓱ뉶 쇗쁉듁뚡 OLGARCHꅝ1,1ꅞGARJIꅝ1,1ꅞ S 10ꓑ 20ꓑ 30ꓑ 50ꓑ 110
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?맏″₨즶ꇅ?Ɦ몱쪱檫휠 ꫭ 5 Ꙣ꒣Ꙑ볒ꮬꑕ꒧쇗쁉셚껄볆(HEI) 쇗쁉듁뚡 OLGARCHꅝ1,1ꅞGARJIꅝ1,1ꅞ S 10ꓑ 20ꓑ ꓑ 50ꓑ ꗑꚹ맪쏒떲ꩇꕩꕈ땯뉻ꅇGARCH볒ꮬ꒧쇗쁉셚껄엣뗛쁵꧳GARJI볒ꮬOLS볒ꮬꅁ엣ꗜ꒣꣼룵아ꪺꙝ꿀꒧뱶암ꅁꚹ쉉ꕩ꿠ꙝ결과냪ꖫ곛맯ꞹ뻣낷ꗾꅁꕂꖫ돵룻꣣껄뉶ꅃꛓ꒣뷗뇄ꗎ꛳뫘군뙱볒ꮬꅁ쇗쁉듁뚡맯꧳쇗쁉셚껄꒧뱶암곒꣣ꚳꖿꙖ쏶ꭙꅁꗧꝙ쇗쁉듁뚡띕ꅁ쇗쁉셚껄띕꣎ꅁꚹ뭐Ederington(1979), Figlewski(1984), Lindahl(1992)꧒녯 111
롧샧뫞뉺뷗쉏 , , 2005 ꣬꒧곣ꡳ떲뷗곛ꅁꕄ굮ꙝ꿀결쇗쁉셚껄ꪺ낪ꝃꗑ쇗쁉룪닕Ꙙ꒧엜늧볆듮ꓖ꒧땻ꯗ꧒ꡍꥷꅃ쇴ꝴVar(R)듮ꓖ꒧땻ꯗꕄ굮꣼쇗쁉ꓱ뉶뭐뉻덦듁덦꒧Ꙁ엜늧볆ꑪꑰ꧒ꡍꥷꅁꗧhpꝙ듁덦돸륓뭐뉻덦돸륓꒧곛쏶ꯗ띕낪ꅁꭨ쇗쁉ꓱ뉶띕낪ꅁ쇗쁉셚껄ꙝꛓ녎ꑗꅁ땵듁뚡뉻덦ꖫ돵뭐듁덦ꖫ돵꒧곛쏶꧊룻ꑰꅆ듁ꛓꢥꅁ뉻덦뭐듁덦뚡꙳Ꙣ뗛Ꙁ뻣Ꙙ쏶ꭙ(Ghosh, 1993)ꅁ곛쏶ꭙ볆ꯜ낪ꅁ꧒ꕈ쇗쁉듁뚡ꪺ땵ꅁ녎ꡍꥷ뉻덦뭐듁덦ꪺ곛쏶ꯗꅁ뙩ꛓ뱶암쇗쁉셚껄ꅃꙝꚹꖻ맪쏒떲ꩇꕩꗑ꣢ꓨ궱룑쓀ꅇ닄ꑀꅂ뉺뷗ꑗꅁ쁈뗛쇗쁉듁뚡ꪺ뱗ꅁꗑ꧳듁덦뭐뉻덦꒧곛쏶ꭙ볆쁈꒧뱗ꕛꅁ쇗쁉셚껄ꑝ삳쁈꒧뒣낪ꅃ닄ꑇꅂ녱맪냈ꑗ뻞Ꝁꛓꢥꅁꗑ꧳쁙쇗쁉Ꙣ듁덦뭐뉻덦ꩩ냊ꓨꙖ곛Ꙑ껉ꑾ걏ꚳ껄ꪺ쇗쁉떦늤ꅁ땵껉뚡꒺듁덦뭐뉻덦꒧ꩩ냊ꓨꙖ꒣ꞹꗾ곛Ꙑꅁ곆ꛜ라곛ꅁ쁙쇗쁉ꛓ라쉘ꑪ띬ꖢꛓꖢꕨ쇗쁉꒧ꗘꪺꅃꕈ껉뚡꣓곝ꅁꗑ꧳듁덦뭐뉻덦꒧곛쏶꧊ꭄ녠낪ꅁ쁙쇗쁉떦늤ꕩꕈꚳ껄ꪺ놱꣮궷쁉ꅁ쇗쁉셚껄럭땍ꑝ룻ꙮꅃ걇ꕈ믹볆듁덦Ꝁ결쇗쁉볐ꪺ껉ꅁ삳ꕈꓑ듁쇗쁉떦늤뒣낪쇗쁉셚껄ꅃꅝ꙰맏4꧒ꗜꅞ ꗮꅂ떲뷗뭐ꯘ쒳?듁덦ꗦ꧶Ꙣ롧샙겡냊끝믢냬ꅁꚳ꣤ꣴ뙖꒧끞쑭뭐ꖲ굮꧊ꅃꗑ꧳꣤꣣ꚳ쇗쁉뭐믹껦땯뉻꒧ꕜ꿠ꅁ륅ꭐꚨ냓띾뭐뿄겡냊꒧뾳늱ꅆꗧꙝ꣤꒧뻷ꕜ꿠ꅁ꣏쇗쁉녯ꕈ싇ꗑ듁덦ꖫ돵신뛹궷쁉ꅃꛓ쁈뗛ꗾ뉹꓆뿄엩꡴ꪺ깩ꅁ룪닕Ꙙꗧ쁈꒧Ꙩ볋꓆ꅁ맯룪ꛓꢥꅁꙢ끬ꡄ낪돸륓ꪺꭥ뒣ꑕ꙰꛳ꚳ껄궰ꝃ룪닕Ꙙ궷쁉걏곛럭궫굮ꪺ뷒썄ꅃ듁덦Ꙣ냓ꭾꖫ돵뭐뿄ꖫ돵걏곛럭궫굮ꪺ쇗쁉ꑵ꣣ꅁ꙰꛳Ꞵ빁ꪺ덝군ꣃꚳ껄ꝑꗎ듁덦ꮴ곹덗쇗ꖫ돵뉻덦믹껦엜냊꒧뷄삻ꅁ맯룪ꑈꙢꭏ꯹ꚬ꽱ꓨ궱꣣ꚳ쏶쇤ꪺ뱶암ꑏꅃ ꅝ1,1ꅞꅝ1,1ꅞꓑ20ꓑ30ꓑ50ꓑ 맏 4 ꒣Ꙑ볒ꮬꑕ륄쎣ꑵ띾볆듁덦쇗쁉셚껄꒧ꓱ룻 ?? 112
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?ꖻꓥꝑꗎOLSꅂGARCHꅝ1,1ꅞGARJI(1,1)떥ꅁ룪껆뇄ꛛ1998꙾1ꓫ2ꓩ꣬2003꙾7ꓫ25ꓩ꒧륄쎣ꑵ띾믹볆듁덦ꅁ놴끑Ꙣ쁙쇗쁉ꑕ꒧쇗쁉셚껄ꅁꣃꕈ늾냊뗸떡꒧ꓨꩫꝑꗎ볋ꖻ꒺꧒꛴군꒧쇗쁉ꓱ뉶ꅁ꓀꩒볋ꖻꕾ쇗쁉듁뚡꒧땵맯꧳쇗쁉셚껄꒧뱶암ꅃ 맪쏒떲ꩇ땯뉻ꅁꓑ듁ꪺ쇗쁉떦늤ꕩ샲녯룻꣎ꪺ쇗쁉셚껄ꅁꚹ떲뷗뭐냪꒺ꕾ곛쏶ꓥ쑭꧒녯꣬ꪺ떲뷗ꑪ교곛Ꙑꅃꖻ곣ꡳ뭐꣤ꕌ곛쏶곣ꡳ꒣Ꙑ꒧덂Ꙣ꧳Ꙑ껉놴끑삳ꗎOLS볒ꮬꅂGARJI볒ꮬGARCH볒ꮬ뙩ꛦ땵ꓑ듁ꥍꓑ듁꒧쇗쁉셚껄깴늧꧊ꅁꗑ꧳과냪ꖫ룻낷ꗾꕂ꣣껄뉶꧊ꅁꝙ꣏땵ꓑ듁꒧쇗쁉떦늤ꗧꕩ꒣뚷ꛒ뱻믹껦룵아꒧ꙝ꿀ꅃ뺨뫞쇗쁉볒ꮬ꒣Ꙑꅁ꒣뷗뇄ꗎ꛳뫘쇗쁉볒ꮬ뙩ꛦ뉻덦뎡ꛬ꒧쇗쁉ꅁ곒꿠ꑪ둔ꙡ궰ꝃ꯹ꚳ뉻덦꒧궷쁉ꅁ맪쏒엣ꗜ믹볆듁덦ꮴ곹결ꑀꙮꪺ쇗쁉ꑵ꣣ꅃ 113
롧샧뫞뉺뷗쉏 , , 2005 냑ꛒꓥ쑭?1. ꓽ쑒Ɪ(1999)ꅁꅵꕈ룵아ꇐ쉘뒲볒ꮬ뗻믹돦ꑀꮬ뭻쇊앶쏒꒧맪쏒곣ꡳꅶꅁ낪뚯닄ꑀ곬ꑪ뻇뿄샧륂곣ꡳ꧒뫓ꑨ뷗ꓥꅃ 2. ꚿꓥ녪(1997)ꅁꅵ믹볆듁덦쇗쁉껄ꩇ꒧곣ꡳꅶꅁꗦ덱ꑪ뻇뫞뉺곬뻇곣ꡳ꧒뫓ꑨ뷗ꓥꅃ 3. ꝅꥼꅂ뿠꧷Ꝁ(2001)ꅁꅵ믹볆듁덦꒧쇗쁉ꓱ뉶뭐쇗쁉껄꽱ꅶꅁ뫞뉺곣ꡳ뻇돸ꅁ-31 4. ꩌ롱늻(1998)ꅁꅵꙕ군뙱볒ꮬ꒧쇗쁉셚껄ꓱ룻-뙽꧱ꮬꙀꙐ냲륂ꗎ벯껚ꕶꝑꕸ볆듁덦ꅶꅁ뉈ꚿꑪ뻇뿄곣ꡳ꧒뫓ꑨ뷗ꓥꅃ 5. 뛀뒺ꧺ(2001)ꅁꅵꕸ왗믹볆듁덦돌빁쇗쁉떦늤꒧곣ꡳꅶꅁ뉈ꚿꑪ뻇끝냈뿄뻇꡴곣ꡳ꧒뫓ꑨ뷗ꓥꅃ 6. 빇뽰(1998)ꅁꅵ믹볆듁덦ꖫ돵ꑗꪺ냊멁쇗쁉떦늤곣ꡳꅶꅁ뉍뗘ꑪ뻇닎군뻇곣ꡳ꧒뫓ꑨ뷗ꓥꅃ 7. 썑ꟓ(2001)ꅁꅵ냪믚믹볆듁덦뭐뉻덦ꪽ놵쇗쁉떦늤꒧곣ꡳꅶꅁ뉈ꚿꑪ뻇끝냈뿄뻇꡴곣ꡳ꧒뫓ꑨ뷗ꓥꅃ 8. 쉏ꞻꓥ(1998)ꅁꅵꓩ롧믹볆듁덦쇗쁉껄ꩇ꒧맪쏒곣ꡳꉷ䝁剃?볒ꮬ꒧삳ꗎꅁꅶ쏒꣩멛듁덦뫞뉺ꅁ16:7ꅁ1-23궶ꅃ 9. Baillie, R. T. and R. J. Myers(1991), “Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge”, Journal of Applied Econometrics, Vol. 6, 109-124. 10. Bates, D. S.(1991), “The Crash of ’87: Was it Expected? The Evidence from the Options Markets”, Journal of Finance. 46: 1009-1044. 11. Black, F. and M. Scholes(1974), “From Theory to a New Financial Product”, The Journal of Finance, , . 12. Bollerslev, T.(1986), “Generalized autoregressive heteroskedasticity”, Journal of Econometrics 31, 307-327. 13. Chahal, M. S. and J. Wang(1997), “Jump Diffusion Processes and Emerging Bond and Stock Markets: An Investigation Using Daily Data”, Multinational Finance Journal, , -98 14. Chan, W. H. and J. M. Maheu(2002), “Conditional Jump Dynamics in Stock Market Return”, Journal of Business & Economic Statistics, 20(3): 377-389. 15. Chernov, M., A. R. Gallant, E. Ghyels and G. Tauchen(1999), “A New Class of Stochastic Volatility Models With Jumps: Theory and Estimation”, working paper, CIRANO. 16. Das, S. R.(1998), “Poisson-Gaussian Processes and the Bond Market”, Working Paper 6631, National Bureau of Economic Research. 17. Das, S. R.(2002), “The Surprise Element: Jumps in Interest Rates”, Journal of Econometrics, 106: 27-65. 18. Ederington, L. H.(1979), “The Hedging Performance of The New Futures Markets”, The Journal of Finance, No1, March. 114
믹껦룵아뭐쇗쁉떦늤꒧놴끑ꇐꕈ륄쎣ꑵ띾볆뉻덦뭐듁덦결꣒ ?19. Engle, R. F.(1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation”, Econometrica, 50(4), -1007 20. Fama, E. F.(1976), “Forward Rates as Predictors of Future Spot Rates”, Journal of Financial Economics, 3(4), -77 21. Fama, E. F.(1965), “The Behavior of stock prices”, Journal of Business, 38, pp34-105. 22. Figlewski, S.(1984), “Hedging Performance and Basis Risk in Stock Index Futures”, Journal of Finance, Vol. 39(3), 657-669. 23. Fortune, P.(1999), “Are Stock Returns Different Over Weekends? A Jump Diffusion Analysis of the Weekend Effect”, New England Economic Review, September/October, 3-19. 24. Ghosh, A.(1993), “Hedging with Stock Index Futures: Estimation and Forecasting with Error Correction Model”, The Journal of Futures Markets, Vol. 13(7), 743-752. 25. Ghosh, A.(1993), “Cointegration and Error Correction Models: Intertemporal Causality between Index and Futures Prices”, The Journal of Futures Markets, Vol. 13(2), 193-198. 26. Holmes, P.(1996), “Stock Index Futures Hedging: Hedge Ratio Estimation, Duration Effects, Expiration Effects and Hedge Ratio Stability”, Journal of Business Finance and Accounting, 23(1), 63-77. 27. Johnson, L.(1960), “The Theory of Hedging and Speculation in Commodity Futures”, Review of Economic Studies, Vol. 27, 139-151. 28. Jorion, P.(1988), “On Jump Processes in the Foreign Exchange and Stock Markets”, The Review of Financial Studies. 1(4): 427-445. 29. Kroner, F. K. and S. Jahangir(1993), “Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures”, The Journal of Financial and Quantitative Analysis, Vol. 4, 535-551. 30. Koutmos, G. and A. Pericli(1999), “Hedging GNMA Mortgage-Backed Securities with T-Note Futures: Dynamic versus Static Hedging”, Real Estate Economics, Vol. 27(2), 335-363. 31. Lien, D. and Y. K. Tse(1999), “Fractional Cointegration and Futures Hedging”, Journal of Futures Markets, Vol. 19, , pp457-474. 32. Lindahl, M.(1992), “Minimum Variance Hedge Ratios for Stock Index Futures : Duration and Expiration Effects”, The Journal of Futures Markets, 33-51. 33. Louis, G. and L. Greg(1997), “The Benefits of Dynamically Hedging the Toronto 35 Stock Index”, Canadian Journal of Administrative Sciences, Vol. 14(1), 69-78. 34. Markowitz, H.(1952), “Portfolio Selection”, Journal of Finance, 7(1): 77-91. 35. Maheu, M. J. and H. T. McCurdy(2004), “New Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns”, Journal of Finance, 59(2): 755 – 793. 36. Mandelbrot, B.(1963), “The Variation of Certain Speculative Prices”, Journal of Business, 36, pp. 394-419. 115
롧샧뫞뉺뷗쉏 , , 2005 37. Mandelbrot, B.(1967), “The Variation of Some Other Speculative Price”, Journal of Business, 40, pp. 393-413. 38. Park, T. H. and L. N. Switzer(1995), “Bivariate GARCH Estimation of the Optimal Hedge Ratios for Stock Index Future: A Note”, Journal of Futures Markets, Vol. 15, 61-67. 39. Sally C. Y. and L. G. Gerard(2000), “Comparing Trading Performance of the Constant and Dynamic Hedge Models: A Note”, Review of Quantitative Finance and Accounting, Vol. 14, 155-160. 40. Sephton, P. S.(1993), “Hedging Wheat and Canola at the Winnipeg Commodity Exchange”, Applied Financial Economics, , -73 41. Sephton, P. S.(1993), “Optimal Hedge Ratios at the Winnipeg Commodity Exchange”, The Canadian Journal of Economics, , -94 42. Stein, J. L.(1961), “The simultaneous determination of spot and futures prices”, American Economic Review, Vol. 51, 1012-1025. 116
