A Study on Volatility Forecasting Models

2008 ڣ 6 ִΔรԶཚΔ62-77

ፕਐᙇᖗᦞ࣍լٵൣቼՀᔞشհं೯৫ᑓী։࣫

A Study on Volatility Forecasting Models

under Dif f erent ScenariosЁCase ofTAIEX Option

࿓ߢॾ

ഏم೏ႂᚨشઝݾՕᖂ ८ᘜᇷಛઔߒࢬ ܗ෻ඒ඄

ຫ֟ဉ

ഏم೏ႂᚨشઝݾՕᖂ ८ᘜᇷಛઔߒࢬ

Abstract

In orderto evaluate the price ofTAIEX options (TXO)accurately,this study applied HistoricalVolatility model,GARCH M odel,Volatility Index (VIX)and Implied Volatility Functions (IVF) to estimate the volatility of option.M oreover,the estimated prices of volatilitywere inputtedinto BS modelto calculate the theoreticalprices,thanwe couldfind outthe mostappropriate modelto estimate the volatility through comparing inaccuracy betweentheoreticalprices andrealizedoptionprices.

The studyshows thatno single modelcanbe suitedto alldealscenarios ofTXO.The investors should choose suitable models according to theirneeds,and they can acquire the mostaccurate prices.Classified by the differentials between moneyness and maturity date, DQGDQDO\]LQJWKHLQDFFXUDF\RIWKHSULFHLW¶VWKHPRVWDFFXUDWHWRDGRptGARCH(1,1)model WRHVWLPDWHWKHYRODWLOLW\LQWKHSRUWLRQRIWKHFDOO,W¶VPRVWHIILFLHQWWRFKRRVHWKHHYDOXDWLRQ

ofIVF modelin the portion ofthe put.In addition,no matterwhatevaluated model,the theoreticalprices whatyouevaluate willdiverge from realizedprices ifonlythe days whichis awayfrom maturitydate is longer.Inotherwords,the inaccuracyofthe price is more.

KeywordΚTXO,Volatility,ImpliedVolatilityFunction(IVF),GARCH M odel

໸Εᖄᓵ

؀᨜ཚຄٌ࣐ࢬ࣍ 2001 ڣ 12 ִ 24ֲංנፕਐᙇᖗᦞ(១ጠ TXO)Δא؀᨜ᢞٌࢬ

࿇۩ၦףᦞैᏝਐᑇ੡ᑑऱᇷขΔ༼ࠎԱ෼ຄؑ໱ऱދᇷԳޓڍᑌऱᝩᙠֱऄΔࠌࠡދ ᇷᖙ܂ޓ༄ڶᐘࢤ Ζፕਐᙇᖗᦞऱٌ࣐ၦດڣᏺף Δٌ࣐ᑷ࿮ऱ࿓৫բլࠅ࣍ࠡהഏ ୮ΔދᇷԳ૞ڕ۶إᒔေᏝᙇᖗᦞऱᏝ௑Δሒࠩᝩᙠऱய࣠Δױᎅਢॺൄૹ૞ऱٌ࣐࿜

ฃΖൕመװऱኔᢞઔߒਐנ Δ່౨ᐙ᥼ေᏝᄷᒔࢤऱڂై੡ं೯৫ (Volatility)Δྥۖ

Black-Scholes Model (១ጠ BS Model)ڇैᏝऱᖲ෷։಻ؘႊ੡ኙᑇൄኪ։಻Δ׊ैᏝ໴

ሟ෷ऱ᧢ฆᑇՈਢࡐࡳլ᧢ऱൄᑇ࿛೗๻Δઃᄎທګ෻ᓵᏝ௑ऱೣᎄΔڂڼं೯৫ऱ۷ ૠױᎅਢေᏝᙇᖗᦞऱᏝ௑່੡ᣂ᝶ऱ૞ైΖ

ء֮ܓشᖵ׾ं೯ᑓী(Historical Volatility Model)ΕGARCH ᑓী۷ૠᑑऱᇷขऱं

೯৫܂੡ᙇᖗᦞऱं೯৫Δא֗ຘመኔᎾऱᙇᖗᦞհٌ࣐ᇷறזԵ BS Model ֘ංᖄנ ឆܶं೯৫৵Δ٦ലឆܶं೯৫זԵं೯෷ਐᑇ(Volatility IndexΔ១ጠ VIX)ࡉឆܶं೯ ࠤᑇ(Implied Volatility FunctionsΔ១ጠ IVF)࿛ᑓী۷ૠᙇᖗᦞऱं೯৫Δၞԫޡല۷ૠ ଖזԵ BS Model ૠጩٺᑓীՀऱᙇᖗᦞ෻ᓵᏝ௑ΔᘝၦࠡፖኔᎾᏝ௑ၴऱᎄ஁Δۖᎄ

஁Օ՛ᄎᐙ᥼ኙ TXO ऱေᏝፖቃྒྷհᄷᒔ৫Δ٦ࠉᖕլٵऱൣቼნᖞנ່ᔞٽऱं೯ ৫۷ૠᑓীΖ

၁Ε֮᣸ڃ᥽

Latane and Rendleman(1976)א॒ףୂᙇᖗᦞٌ࣐ࢬ (១ጠ CBOE)ٌ࣐ऱ 24୮ᑑऱ ֆ׹੡ࠏΔ۞ 1973 ڣ 10 ִ 5 ֲ۟ 1974ڣ 6 ִ 28 ֲַ٥ૠ 38 ၜऱᇷறΔࠉᖕ BS Model

ေᏝ၇ᦞᏝ௑ΔૠጩኔᎾ၇ᦞऱឆܶं೯৫Δ࿇෼ࡉኔᎾऱं೯৫ڶ೏৫ઌᣂࢤΔ֠ࠡ

ڇԫଡઌᅝ९ऱڶயཚၴᏝؓᙇᖗᦞਢ່ඕტऱΔ܀ਢڇԫଡឆܶᑑᄷ஁ڶৰՕऱޏ᧢

ழΔڇᏝփᙇᖗᦞ൷२ࠩཚֲழ༓׏լ࠹ᐙ᥼Ζא Vega ףᦞֱؓ݁ڤڇޢԫଡᨠኘֲ

հլٵᙇᖗᦞՀऱឆܶं೯৫࿯ղլٵऱᦞૹΔױ܂੡ᙇᖗᦞآࠐं೯৫ऱቃྒྷΖ Canina and Figlewski(1993)א 1983 ڣ 3 ִ۟ 1987 ڣ 3 ִऱ S&P 100 ਐᑇᙇᖗᦞ (OEX)੡ઔߒᑌءΔࠌشለ೏ऱࢼᑌ᙮෷(ֲ᙮෷)ࡉለ࿍ᑌءཚၴ(48 ଡִ)ऱᦤזᇷற ቃྒྷឆܶं೯৫Δ࿇෼ឆܶं೯৫ࡉآࠐ໴ሟं೯৫޲ڶઌᣂࢤΔං៬Աࢬڶᙇᖗᦞေ

Ꮭ෻ᓵऱഗء଺ঞΔຍᑌऱ࿨࣠Ո֧࿇Աޓڍऱ৵ᥛઔߒࡉ൶ಘΖ

Christensen and Prabhala(1998)א S&P100 ਐᑇᙇᖗᦞ(OEX)۞ 1983 ڣ 11 ִ۟ 1995 ڣ 5 ִ (139 ଡִࢨՕપ 11.5 ڣ)੡ᑌءཚၴΔઔߒᇷற೴։੡ഽᒌছ(1983 ڣ 11 ִ۟

1987 ڣ 9 ִ)Εഽᒌ৵(1987 ڣ 12 ִ۟ 1995 ڣ 5 ִ)ࡉࢬڶᑌءཚၴΔܓشለ܅ऱࢼᑌ

᙮෷(ޢִ)Εለ९ཚ׊ྤᦤזᣂএऱᑌءᇷறΔኙኔᎾं೯৫ࡉឆܶं೯৫ףאֺለΖ

࿨ᓵ࿇෼ΔഽᒌছኔᎾं೯৫ऱ᧢ฆᑇֺឆܶं೯৫ऱ᧢ฆᑇᝫ૞՛Δ܀ڇഽᒌ৵ኔᎾ

ं೯৫ऱ᧢ฆᑇֺឆܶं೯৫ऱ᧢ฆᑇᝫ૞ՕΔ׌૞ូڂ࣍ैؑऱഽᒌ࿇س࿨ዌࢤऱޏ

᧢Ζ׼؆ܓشࢬڶᑌءཚၴઔߒ৵࿇෼ΔኔᎾं೯৫ࡉឆܶं೯৫ऱ։಻ઃڶৰ೏ऱೣ

ኪࡉ೏௿୽Δઌኙ࣍ BS Model ኙैᏝऱᖲ෷։಻೗๻੡ኙᑇൄኪ։಻ڶࢬլٵΖ Dumas, Fleming and W haley(1998)א 1988 ڣ 6 ִ۟ 1993 ڣ 12 ִऱ S&P500 ᙇᖗᦞ

੡ᑌءΔאࡳࢤं೯৫ࠤᑇֱऄ(the deterministic volatility function approach)܂੡ᙇᖗᦞ

ေᏝֱऄΔઔߒ࿇෼ं೯৫ࡉ Time-adjusted moneyness(Ꮭփ؆࿓৫)ᙟထᐌપᏝ௑ࡉ၏

ࠩཚֲऱլٵΔं೯৫ᄎᙟհޏ᧢Δࠀנ෼´პూण´ऱቹݮΖܓشอૠᛀࡳլٵ࿨ዌՀ ऱं೯৫۷ૠᑓীΔ࿨࣠࿇෼။壄១ऱᙇᖗᦞေᏝ࿨ዌᑓী။ࠋΔૉं೯ࠤᑇآףא壄 ១ᄎࠌࡳࢤं೯৫ࠤᑇֱऄቃྒྷᎄ஁။ࠐ။ՕΔڕ࣠٦ףՂழၴ೶ᑇΔቃྒྷ࿨࣠Ոലޓ

஁Ζ

೶Εઔߒֱऄ ԫΕBlack-Scholes ᙇᖗᦞေᏝᑓী

BS Model ੡ 1973 ڣطભഏ Black ࡉ Scholes ࠟۯᆖᛎᖂृංᖄנᙇᖗᦞૡᏝᑓীΔ

ࠡֆڤڕՀΚ

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ΰԫαᖵ׾ं೯ᑓী(Historical Volatility Model)

ԫ౳ኙᑑऱᇷขऱं೯৫ױאီ੡ᑑऱᇷข໴ሟ෷ऱᑑᄷ஁Δڇ۷ૠं೯৫ழΔᄎ ࠌشࡐࡳऱழၴၴሶ܂੡ᑑऱᇷขऱᨠኘཚΔຏൄᇷற။ڍ۷ૠՂᄎ။ᄷᒔΔ܀ਢं೯ ৫ᄎڂழၴऱޏ᧢ۖ᧢೯ Δᨠኘཚץܶ֜ڍመװऱᇷறኙቃྒྷآࠐऱं೯৫ᄎڶࢬೣ

ᎄΔࢬאመװऱઔߒڍආشฝ೯࿗Ց੡ 60֚Δࠀ׊೶ەHull(2006)ലं೯৫ଊՂ ^T(T੡

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ैᏝਐᑇ ᖵ׾ं೯৫

ቹ 1 ؀᨜ףᦞैᏝਐᑇࡉᖵ׾ं೯৫հၴऱ᧢֏

ൕቹ 1 ൓व؀᨜ףᦞैᏝਐᑇऱழၴ᝟Ⴈቹנ෼Աं೯ፋႃ(volatility

clustering)ऱ෼ွΔڶՕ(՛)ऱं೯נ෼հ৵Ոᄎנ෼Օ(՛)ऱं೯ΔैᏝਐᑇऱᖵ׾ं

೯৫ՈॺࡐࡳൄᑇΖ

ΰԲαԫ౳֏۞ݺಱូฆᔆයٙ᧢ฆᑇᑓী (Generalized Autoregressive Conditional HeteroskedasticityΔ GARCHᑓী)

1982 ڣ Engle ༼נ۞ݺಱូයٙ᧢ฆᑇ(ARCH)հ৵Δᤉۖ Bollerslev ࣍ 1986 ڣ༼

נ GARCH ᑓীΔࠀᐖऑሎشڇᆖᛎംᠲՂΔ֠ࠡڇ८ᘜᏆ഑ՂࠠڶઌᅝऱრᆠΖءઔ ߒܓش GARCH(1,1)ᑓী༴૪ছԫཚࡉᅝཚऱ᧢ฆᑇࡉᎄ஁ٻऱᣂএΔࠡᑓী๻ࡳڕՀΚ

i i

i u

u Eu _1H (7)

2 2 2

0 1 1 1

i i i

V D uH _ D uV _ (8)

ࠡխΔH_i²_1੡ছԫཚऱྲྀ஁ֱؓΔV_i²_1੡ছԫཚऱं೯৫ऱֱؓΖ ΰԿαं೯෷ਐᑇ(Volatility IndexΔVIX)

ं೯෷ਐᑇ(Volatility Index, VIX)հشຜਢ੡Ա༼ࠎދᇷԳޓڍऱؑ໱ಛஒΔא֗ᘝ ၦދᇷԳኙآࠐؑ໱ं೯৫ऱቃཚ઎ऄΔආشᙇᖗᦞऱឆܶं೯৫ףᦞؓ݁৵ࢬ۷נհ ਐᑑΔঞױז।ؑ໱آࠐऱं೯৫ቃཚΖ

ء֮೶ەᔤན֮(ا93)༼נऱVIXհᒳࠫΔ۷ૠፕਐᙇᖗᦞऱឆܶं೯৫ Δࠡૠጩ

ֱڤࡉޡᨏڕ।1ࢬقΚ

।1 VIXհᒳࠫ

ᙇᖗᦞऱݮڤ ګٌၦ່ՕऱԿଡݧ٨հឆܶं೯৫ ؓ݁ឆܶं೯৫ ၇ᦞ V_c1^iv V_{c 2}^iv V_c3^iv (V +_c1^iv V +_{c 2}^iv V )/3=_c3^iv V_c^iv ᔄᦞ V^iv_p1 V^iv_{p 2} V^iv_p3 (V +^iv_p1 V^iv_{p 2}+V^iv_p3)/3=V^iv_p

VIXTXO=(V +_c^iv V )/2^iv_p (9) ॵုΚ V ।قឆܶं೯৫Δc।ق၇ᦞΔp।قᔄᦞ^iv

ᇷறࠐᄭΚᔤན֮(2004) ء֮ല 2006 ڣ 9 ִ 1 ֲ۟ 2007 ڣ 6 ִ 29 ֲၴऱ؀᨜ףᦞैᏝਐᑇࡉ VIX հၴऱ

᧢֏ᢄګڕቹ 2 ࢬقΔᅝ VIX ೏נאছऱֽᄷΔቃཚآࠐՕᒌਐᑇലנ෼Ղይऱ᝟ႨΔ

ૉ VIX ܅࣍אছऱֽᄷΔቃཚآࠐՕᒌਐᑇലנ෼Հၓऱ᝟ႨΖ

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˅˃˃ˉ˂˄˄˂˅ˋ

˅˃˃ˉ˂˄˅˂˄ˇ

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˅˃˃ˊ˂˃ˆ˂˃ˆ

˅˃˃ˊ˂˃ˆ˂˅˃

˅˃˃ˊ˂˃ˇ˂˃ˌ

˅˃˃ˊ˂˃ˇ˂˅ˇ

˅˃˃ˊ˂˃ˈ˂˄˄

˅˃˃ˊ˂˃ˈ˅ˌ

˅˃˃ˊ˂˃ˉ˄ˇ

˼́˷˸̋

˃ˁ˄

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ቹ 2 ؀᨜ףᦞैᏝਐᑇࡉ VIX հၴ᧢֏

ΰ؄αឆܶं೯ࠤᑇ(Implied volatility functionsΔIVF)

1998 ڣ Dumas et al.࣍ψImplied volatility functions: Empirical testsωԫ֮խ༼נ IVF ᑓীΔشಱូᑓী۷ૠឆܶं೯৫ Δಱូᑓীխऱಱូڂ՗ڶᐌપᏝ௑ (K)֗ᐌપᏝ௑

ֱؓႈΕڣ֏ऱࠩཚֲ(T)ΕࠩཚֱֲؓႈΕ֗ᐌપᏝ௑ፖࠩཚֲٌՐႈΔ٦ച۩່՛ؓ

ֱऄ(OLS)۷ጩנٺಱូڂ՗ऱএᑇ Δ٦ലٺএᑇזԵڼಱូڤං۷ᙇᖗᦞऱं೯৫

৵ΔޣנᙇᖗᦞᏝଖΔࠡं೯৫۷ૠऱޡᨏڕՀΚ 1.ലբवઌᣂᇷறזԵ BS Model ଙංឆܶं೯৫¹Ζ

2.๻ࡳಱូᑓীΔലឆܶं೯৫֗բवઌᣂᇷறሉԵᑓীΔച۩ OLS ۷ૠΔ۷ጩנٺএ ᑇΔࠡಱូᑓীڕՀΚ

2 2

0 1 2 3 4 5 (10)

i Ki Ki Ti Ti Ki Ti i

V D D u D u D u D u D u u H 3.۷ૠנऱٺএᑇזԵಱូᑓীխΔၞԫޡ۷ૠឆܶं೯৫Ζ 4.۷ૠנऱឆܶं೯৫٦ࡉቃ๻ऱ່՛ं೯৫ 0.001 ࠷່ՕଖΖ

2 2

0 1 2 3 4 5

max(0.001, ) (3.12)

i Ki Ki Ti Ti Ki Ti

V D D D D D D

š

 u  u  u  u  u u (11)

ԿΕᏝ௑ᎄ஁ऱֺለᄷঞ

መװऱઔߒڇᎄ஁ֺለՂຏൄආشᏝ௑ᎄ஁Εؓ݁࿪ኙᎄ஁ࡉઌኙᏝ௑ᎄ஁Δࠀ׊

ലᑌءᇷற೴։լٵऱࠩཚֲࡉᏝփ؆࿓৫ (Moneyness)ૠጩं೯৫۷ૠᑓীऱ෻ᓵᏝ

௑ࡉؑ໱Ꮭ௑ऱ஁ฆΔ։ܑᎅࣔڕՀΚ ΰԫαᏝ௑ᎄ஁(Price Error,១ጠ PE)

Ꮭ௑ᎄ஁ױאᘝၦं೯৫۷ૠᑓীՀࢬေᏝऱ෻ᓵᏝ௑ΔፖኔᎾؑ໱Ꮭ௑ֺለਢܡ ڶ๯೏۷ࢨ܅۷ऱ෼ွΔࠡᎄ஁ଖૉ੡إଖΔࠡ෻ᓵᏝ௑ڶ๯܅۷Δ֘հΔঞ๯೏۷Δ

ࠡૠጩֆڤڕՀΚ

mkt i i 1

1 (C -C ) (12)

n

i

PE n

¦

ࠡխΔC^mkt_i ΚᙇᖗᦞऱኔᎾᏝ௑Ι i

š

C Κ۷ૠᑓীՀऱᙇᖗᦞ෻ᓵᏝ௑Ι n Κᙇᖗᦞऱᑇၦ ΰԲαؓ݁࿪ኙᎄ஁(Mean Absolute Error,១ጠ MAE)

ؓ݁࿪ኙᎄ஁ᘝၦ෻ᓵᏝ௑ࡉኔᎾऱᏝ௑հၴऱ஁ฆࢤऱ༏৫Δૉᎄ஁ଖ။՛।ق ۷ૠᑓী။ړΔࠡૠጩֆڤڕՀΚ

mkt i i 1

1 |C -C )| (13)

n

i

MAE n

¦

ΰԿαઌኙᏝ௑ᎄ஁(Relative Price ErrorΔ១ጠ RPE)

Ꮭ௑ऱೣᎄૉڶەၦኔᎾᏝ௑ڂైΔױאޓࠠ᧯ܧ෼ᎄ஁ኙኔᎾᏝ௑ऱ᧢֏ࡉᐙ᥼

࿓৫Δֺࠡ෷Օ।قᎄ஁ኙኔᎾᏝ௑հ᧢֏ՕΔᐙ᥼ՈՕΔ֘հΔঞᎄ஁ኙኔᎾᏝ௑հ

᧢֏՛Δᐙ᥼Ո՛ΔઌኙᏝ௑ᎄ஁ૠጩֆڤڕՀΚ

mkt mkt

i i i

1

1 ( (C -C )/ C ) (14)

n

i

RPE n

¦

؄Εಱូ։࣫

ᛀࡳٺ۷ૠᎄ஁ኙᑓীᎄ஁࠹ࠩୌࠄڂైऱᐙ᥼Δಱូᑓীխऱ๯ᇞᤩ᧢ᑇ੡Ꮭ௑

ᎄ஁Εؓ݁࿪ኙᎄ஁ࡉઌኙᏝ௑ᎄ஁Δᇞᤩ᧢ᑇڶᙇᖗᦞᏝփ؆࿓৫Εࠩཚֲऱ֚ᑇ(T) ࡉٺᑓী۷ૠऱं೯৫ıΔࠡᓤಱូڤڕՀΚ

ု¹Κء֮এຘመ M atlabຌ᧯խऱ financetoolboxհ blsimpv.m ࠤᑇޣנឆܶं೯৫Ζ

0 1 2 3

1

0 1 2 3

0 1 2 3

0 1 2 3

: 0

: 0,j 1,2,3

PE (15)

MAE (16)

RPE

j

H H

S T

K

S T

K

S T

K D D D D

D D D D V H

D D D D V H

D D D D V

 u  u  u 

 u  u  u 

 u  u  u 

۟֟ڶԫଡ լ੡

(17) H

ᛀࡳՂ૪ಱូڤኙᎄ஁ਢܡڶᇞᤩ౨ԺΔၞԫޡᘝၦՂ૪ޢԫଡᇞᤩ᧢ᑇኙᎄ஁ਢܡࠠ

ڶᇞᤩ౨ԺΖ

ᆥΕኔᢞ։࣫

ԫΕᇷறࠐᄭ

ΰԫα؀᨜ᢞٌ࣐ࠦࢬףᦞैᏝਐᑇ

ء֮ऱᇷறএආش؀᨜ᢞٌ࣐ࠦࢬ࿇۩ၦףᦞैᏝਐᑇ (TAIEX)ޢֲگᒌᏝ௑Δᑌ ءཚၴ੡ 2006 ڣ 9 ִ 1 ֲ۟ 2007 ڣ 6 ִ 29 ֲ٥ૠ 203ଡֲٌ࣐ऱگᒌᏝ௑Ζ

ΰԲα؀᨜ཚຄٌ࣐ࢬैᏝਐᑇᙇᖗᦞ

ආش؀᨜ཚຄٌ࣐ࢬैᏝਐᑇᙇᖗᦞΔᑌءཚၴ੡ 2006 ڣ 9 ִ 1 ֲ۟ 2007 ڣ 6 ִ 29 ֲऱፕਐᙇᖗᦞΖᇷறଵೈऱයٙ੡Κ(1)ᅝֲऱگᒌᏝࡉګٌၦ੡ሿऱᙇᖗᦞΙ(2)

၏ࠩཚֲآየԫֲऱᙇᖗᦞΙ(3)ं೯৫լٽ෻ऱᙇᖗᦞ²Ζ ΰԿαྤଅᙠܓ෷

א࢓ઔߒ֮᣸խΔኔᢞᇷறऱྤଅᙠܓ෷ຏൄආشਙࢌֆ႘ࢨഏ஄ࠦऱܓ෷Δ܀ਢ ݺഏऱਙࢌֆ႘ࢨਢഏ஄ࠦઌᣂᇷறለ౒׎Δࢬאء֮ආش؀᨜Ꭼ۩ԫڣཚࡳཚژཱིܓ

෷܂੡ BS Model խऱྤଅᙠܓ෷Ζ

ΰ؄αፕਐᙇᖗᦞᏝփ؆࿓৫ࡉլٵऱࠩཚֲհ։ᣊ

א Sofiane(2005)༼נᙇᖗᦞऱᏝփ؆࿓৫(S/KΔSΚᑑऱᇷข KΚᐌપᏝ௑)։ᣊ।

ڕ। 2Δ܂੡೴։ءኔᢞᇷறऱ၇ᔄᦞᏝփ؆࿓৫ऱࠉᖕΖ

। 2 ၇ᔄᦞᏝփ؆࿓৫։փ।

၇ᦞᏝփ؆࿓

৫

ᒤ໮ ᔄᦞᏝփ؆࿓

৫

෡৫Ꮭ؆ S/K<0.94 ෡৫Ꮭփ Ꮭ؆ 0.94Љ

S/K<0.97

Ꮭփ 0.97ЉS/K<1

Ꮭؓ

1ЉS/K<1.03

Ꮭؓ

Ꮭփ 1.03Љ S/K<1.06

Ꮭ؆

෡৫Ꮭփ S/KЊ1.06 ෡৫Ꮭ؆

ᇷறࠐᄭΚSofiane(2005)

ု² Κं೯৫լٽ෻ऱᙇᖗᦞԫ౳੡ੌ೯ࢤለ஁ΔፖگᒌᏝ௑ೣᎄऱլٽ෻ᇷறΖ

ቹ 3 ឆܶं೯৫ऱᏝփ؆࿓৫(/S/K)

ൕቹ 3 ൓वΔڇ၇ᦞհᏝؓॵ२ழऱٌ࣐ၦ່ڍΔࠡឆܶं೯৫ֺᏝ؆ࡉᏝփழለ

՛Δڇ෡৫Ꮭփऱឆܶं೯৫ለՕ׊ለ࿇ཋΙլመᔄᦞঞڇᏝ؆ॵ२ழऱٌ࣐ၦ່ڍΔ

ࠡឆܶं೯৫ڇᏝؓழ່܅Δڇ෡৫Ꮭ؆ऱឆܶं೯৫ለՕ׊ለ࿇ཋΖ

ቹ 4 2006 ڣ 9 ִ 1 ֲ၇ᦞլٵऱࠩཚֲឆܶं೯৫᧢֏

ൕቹ 4 ױवΔं೯৫პూ(volatilitysmile)ऱ෼ွᄎᙟထ၏ࠩཚֲऱ֚ᑇ။९ۖڶگ ᚹऱ෼ွΔპూणऱቹݮᄎ᧢൓ለ੡ؓࡖΖ

Ղ૪ऱኔᢞ࿨࣠ߩאᢞࣔ BS Model Հऱं೯৫੡ൄᑇհ೗๻ਢլګمऱΔאՀء

֮אլٵऱं೯৫۷ૠᑓী۷ጩं೯৫ऱ۷ૠଖΔലं೯৫۷ૠଖזԵ BS Model ေᏝ

ࠡᏝ௑Δ٦ፖኔᎾᏝ௑ֺለΔޣנᎄ஁ଖၞ۩։࣫Δބנᔞٽፕਐᙇᖗᦞऱ۷ૠᑓীΖ ء֮ല 2007 ڣ 6 ִऱ TXO ီ੡ᑌء؆ᇷறΔ٥ૠ 20 ଡֲٌ࣐Δࠉլٵऱࠩཚ֚

ᑇࡉᏝփ؆࿓৫า։੡ 18 ጟᣊΔڕ। 3 ࢬقΚ

। 3 ࠉᏝփ؆࿓৫ፖࠩཚֲ։ᣊհ၇Εᔄᦞᑌء؆ଡᑇ

၇ᦞ ᔄᦞ

ٌ࣐ၦ ၏ࠩཚཚၴ ٌ࣐ၦ ၏ࠩཚཚၴ

Ꮭփ؆

/ࠩཚֲ Љ30 30~60 Њ60 total Ꮭփ؆

/ࠩཚֲ

Љ30 30~60 Њ60 total І0.94 70 58 96 224 І0.94 23 1 22 46 0.94~0.97 79 62 63 204 0.94~0.97 58 7 8 73 0.97~1.00 78 59 55 192 0.97~1.00 75 28 16 119 1.00~1.03 65 50 47 162 1.00~1.03 71 39 37 147 1.03~1.06 25 18 27 70 1.03~1.06 73 55 42 170 Њ1.06 20 5 15 40 Њ1.06 278 179 280 737 ᑌء؆ 337 252 303 892 ᑌء؆ 578 309 405 1292

ᇷறࠐᄭΚءઔߒᖞ෻

ԲΕᏝ௑ᎄ஁։࣫

੡ၞ۩ٺं೯ᑓীေᏝऱ෻ᓵᏝ௑ࡉኔᎾᏝ௑հ։࣫Δא 2007 ڣ 6 ִ 1 ֲ۟ 6 ִ 29 ֲऱ TXO ၇ᔄᦞऱᇷற੡ࠏΔຘመլٵऱं೯৫۷ૠᑓীޣנं೯৫۷ૠଖΔזԵ BS Model ૠጩ෻ᓵᏝ௑Δ٦אኔᎾऱኔᎾᏝ௑ףאֺለΔᇷறნᖞ৵ڕቹ 5 ࡉቹ 6 ࢬ قΖ

ቹ 5 լٵᑓীऱ၇ᦞ෻ᓵᏝ௑ፖኔᎾᏝ௑հၴऱ᧢֏

ቹ 6 լٵᑓীऱᔄᦞ෻ᓵᏝ௑ፖኔᎾᏝ௑հၴऱ᧢֏

ൕቹ 5 ࡉቹ 6 ᨠኘ൓वΔڇլٵᑓীऱ၇ᔄᦞ෻ᓵᏝ௑ፖኔᎾᏝ௑஁ฆࢤլՕΔא ՀࠌشᏝ௑ᎄ஁ֺለᄷঞ։࣫ٺ۷ૠᑓীऱᄷᒔ৫Ζ

ΰԫαᏝ௑ᎄ஁(Price Error,១ጠ PE)

ء֮א 2007 ڣ 6 ִऱᑌء܂੡ᑌء؆ᇷறΔࠉլٵࠩཚ֚ᑇࡉᏝփ؆࿓৫า։੡

18 ᣊΔࠌشᏝ௑ᎄ஁։࣫ٺ։ᣊլٵऱं೯৫۷ૠᑓীࢬေᏝऱ෻ᓵᏝ௑ፖኔᎾᏝ௑հ

ၴऱؓ݁ᎄ஁Δױאࠉؓ݁ଖܒܑٺं೯৫۷ૠᑓীࢬ۷ૠऱ෻ᓵᏝ௑ਢܡڶ๯೏۷ࢨ

܅۷ऱ෼ွΖ

ൕቹ 7 ױवڇ၇ᦞऱຝ։Δ՛࣍ࢨ࿛࣍ 30 ֚ࡉտ࣍ 30 ࡉ 60 ֚ऱࠩཚֲՀऱ෡৫ Ꮭ؆ΕᏝ؆ࡉᏝؓΔאࠌش GARCH(1,1)ᑓী۷ૠய່࣠ړΔᖵ׾ं೯৫ᑓীய࣠ڻհΔ լመࠟृऱ෻ᓵᏝ௑ઃڶ๯೏۷ऱ෼ွΖՕ࣍ࢨ࿛࣍ 60 ֚ऱࠩཚֲऱ෡৫Ꮭ؆ࡉᏝ؆Δ

ٍਢ GARCH(1,1)ᑓী۷ૠᎄ஁່՛Δ܀ਢڇᏝؓࡉ෡৫Ꮭփழࠌش IVFᑓী۷ૠΔࠡ

ய࣠ለࠋ׊෻ᓵᏝ௑ڶ๯೏۷ऱ෼ွΙࠌش VIX ᑓী۷ૠ၇ᦞऱं೯৫ய࣠ለ஁Δႛڶ ڇ՛࣍ࢨ࿛࣍ 30 ֚ࡉտ࣍ 30 ࡉ 60 ֚ऱࠩཚֲऱ෡৫Ꮭ؆ऱؓ݁ᎄ஁ଖ່՛Δ੡ࢬڶ ᑓীխ່ࠋऱΔࠡ෻ᓵᏝ௑༓׏ຟ๯܅۷Ζ

ڇᔄᦞऱຝ։Δڇٺᑓীࢬ۷ૠऱ෻ᓵᏝ௑ፖኔᎾᏝ௑ऱؓ݁ᎄ஁ڕቹ 8 ࢬقΔ༓

׏א IVFᑓী۷ૠؓ݁ᎄ஁່՛Δࠌش IVFᑓী۷ૠᔄᦞऱं೯৫।෼נ່ړऱய࣠Δ լመࠡ෻ᓵᏝ௑ڇլٵऱࠩཚֲڶ๯܅۷ࢨ೏۷ऱ෼ွΖ

ءઔߒٍ࿇෼ྤᓵ۶ጟ۷ૠᑓীΔ၏ࠩཚֲ֚ᑇ။९ΔᏝ௑ᎄ஁Ոᄎ။ՕΖ

ቹ 7 լٵं೯৫۷ૠᑓীऱ၇ᦞ PE ։ܑࡉᏝփ؆࿓৫(S/K)Εࠩཚֲ֚ᑇհᣂএ

ቹ 8 լٵं೯৫۷ૠᑓীऱᔄᦞ PE ։ܑࡉᏝփ؆࿓৫(S/K)Εࠩཚֲ֚ᑇհᣂএ

ΰԲαؓ݁࿪ኙᎄ஁(Mean Absolute Error,១ጠ MAE)

ؓ݁࿪ኙᎄ஁ᘝၦ෻ᓵᏝ௑ࡉኔᎾऱᏝ௑հၴऱ஁ฆࢤऱ༏৫Δૉᎄ஁ଖ။՛।ق ۷ૠᑓী။ړΖലٺं೯৫۷ૠᑓীࢬ۷ૠऱ MAE אᏝփ؆࿓৫ࡉࠩཚֲऱ֚ᑇᢄ፹ ګڕቹ 9 ࢬقΖ࿨࣠᧩قΔڇ၇ᦞऱຝ։אࠌش GARCH(1,1)ᑓী۷ૠऱய່࣠ړΙڇ ᔄᦞऱຝ։ڕቹ 10 ࢬقΔא IVF ᑓী۷ૠய່࣠ࠋΖ

ቹ 9 լٵं೯৫۷ૠᑓীऱ၇ᦞ MAE ։ܑࡉᏝփ؆࿓৫(S/K)Εࠩཚֲ֚ᑇհᣂএ

ቹ 10 լٵं೯৫۷ૠᑓীऱᔄᦞ MAE ։ܑࡉᏝփ؆࿓৫(S/K)Εࠩཚֲ֚ᑇհᣂএ ΰԿαઌኙᏝ௑ᎄ஁(Relative Price ErrorΔ១ጠ RPE)

Ꮭ௑ऱೣᎄૉףԵኔᎾᏝ௑܂੡ەၦڂైΔױאޓࠠ᧯ܧ෼ᎄ஁ኙኔᎾᏝ௑Ꮭऱ᧢

֏ࡉᐙ᥼ऱ࿓৫Ζൕቹ 11 ױवΔڇ၇ᦞऱຝ։ፖՂ૪ࠟጟᏝ௑ᎄ஁ֺለᄷঞऱ࿨࣠ઌ ۿΔઃਢא GARCH(1,1)ᑓী۷ૠऱய່࣠ړΔૉֺ෷ለՕ।قᎄ஁ኙኔᎾᏝ௑ऱ᧢֏

ՕΔᐙ᥼ՈՕΔ֘հΔঞᎄ஁ኙኔᎾᏝ௑ऱ᧢֏՛Δᐙ᥼Ո՛Ζ

ൕቹ 12 ൓वڇᔄᦞऱຝ։ΔኙᏝփ؆࿓৫ࡉ၏ࠩཚֲ֚ᑇऱլٵ։ᣊ༓׏݁א IVF ᑓীࢬ۷ૠऱᎄ஁ኙኔᎾऱᏝ௑᧢֏່՛ࡉᐙ᥼່՛Ζ

ቹ 11 լٵं೯৫۷ૠᑓীऱ၇ᦞ RPE ։ܑࡉᏝփ؆࿓৫(S/K)Εࠩཚֲ֚ᑇհᣂএ

ቹ 12 լٵं೯৫۷ૠᑓীऱᔄᦞ RPE ։ܑࡉᏝփ؆࿓৫(S/K)Εࠩཚֲ֚ᑇհᣂএ ΰ؄αጵٽေ࣫

ጵٽՂ૪ኔᢞ։࣫Δء֮࿇෼޲ڶٚ۶ԫଡ໢ԫᑓীᔞش࣍ࢬڶፕਐᙇᖗᦞऱٌ࣐

ൣቼΔؘႊࠉࠡᏁޣᙇᖗᔞشऱቃྒྷᑓীΔթ౨ᛧ൓່壄ᒔऱေᏝΔᆖნᖞូ౏אՀ࿨

ᓵΔࠀڕ। 4Ε5 ࢬقΖ

ԫΕڇ PE ։ֱ࣫૿ ΔՕ᧯ۖߢ၇ ᦞࢨᔄᦞڇլٵࠩཚֲࡉᏝփ؆࿓৫Հ Δ։ܑא GARCH(1,1)ࡉ IVF ࿛ࠟጟᑓীڶለࠋऱ۷ૠய࣠Ζ

ԲΕڇ MAE ։ֱ࣫૿Δڇ၇ᦞऱຝٝٵᑌא GARCH(1,1)ऱய່࣠ࠋΔլመ IVF ڇࠩ

ཚֲՕ࣍ࢨ࿛࣍ 60 ֚ऱᏝؓᙇᖗᦞՈ।෼լঋΙڇᔄᦞຝٝঞ༓׏א IVF ऱᜎய

່ࠋΔլመ၏ࠩཚֲ။९ΔቃྒྷԺለ஁Ζ

ԿΕڇ RPE ։ֱ࣫૿Δڇ၇ᦞऱຝٝՈਢ GARCH(1,1)।෼່ᚌΔૉࠩཚֲՕ࣍ࢨ࿛

࣍ 60 ֚ऱᙇᖗᦞਢא IVF ᑓীڶለࠋऱய࣠ΙڇᔄᦞऱຝٝΔՕીՂਢא IVF

੡່ᔞऱ۷ૠᑓীΖ

؄Εլᓵڇ PEΕMAE ࡉ RPE հ։࣫၇ᔄᦞڇլٵऱൣቼՀࢬࠌشऱ່ᔞ۷ૠᑓীΔ

࿨࣠ՕીՂຟઌٵΖ

նΕءઔߒٍ࿇෼Δլᓵڇٚ۶۷ૠᑓীՀΔ၏ࠩཚֲ֚ᑇ။९ΔᏝ௑ᎄ஁Ոᄎ။ՕΖ

। 4 ၇ᦞլٵൣቼՀ່ᔞشհ TXO ቃྒྷᑓীნᖞ

၏ࠩཚཚၴ

Ꮭփ؆࿓৫/ࠩཚֲ

Љ30 30~60 Њ60

І0.94 GARCH(1,1) GARCH(1,1) GARCH(1,1) 0.94~0.97 GARCH(1,1) GARCH(1,1) GARCH(1,1) 0.97~1.00 GARCH(1,1) GARCH(1,1) IVF

1.00~1.03 GARCH(1,1) GARCH(1,1)Ε

ᖵ׾ं೯ᑓী IVF

1.03~1.06 GARCH(1,1)ΕIVF ᖵ׾ं೯ᑓী VIXΕIVFΕᖵ׾ं೯ᑓী

Њ1.06 VIX GARCH(1,1)ΕVIX ᖵ׾ं೯ᑓীΕIVF ᇷறࠐᄭΚءઔߒᖞ෻

। 5 ᔄᦞլٵൣቼՀ່ᔞشհ TXO ቃྒྷᑓীნᖞ

၏ࠩཚཚၴ

Ꮭփ؆࿓৫/ࠩཚֲ

Љ30 30~60 Њ60

І0.94 IVFΕVIX IVF VIX

0.94~0.97 IVF IVF IVFΕVIX

0.97~1.00 IVFΕVIX IVF IVF

1.00~1.03 IVF IVF IVF

1.03~1.06 IVF IVF IVF

Њ1.06 IVF IVFΕVIX IVF

ᇷறࠐᄭΚءઔߒᖞ෻

ԿΕᛀࡳᏝ௑ᎄ஁(PE)Εؓ݁࿪ኙᎄ஁(MAE)ࡉઌኙᏝ௑ᎄ஁(RPE)ࡉᐙ᥼ᑓীᎄ஁ڂ

ైհಱូ։࣫

ᛀࡳٺ۷ૠᎄ஁ኙᑓীᎄ஁࠹ࠩୌࠄڂైऱᐙ᥼Ζಱូᑓীխऱ๯ᇞᤩ᧢ᑇ੡Ꮭ௑

ᎄ஁(PE)Εؓ݁࿪ኙᎄ஁(MAE)ࡉઌኙᏝ௑ᎄ஁(RPE)Δᇞᤩ᧢ᑇڶᙇᖗᦞᏝփ؆࿓৫ (S/KΔS ੡ᑑऱᇷขᏝ௑ΕK ੡ᐌપᏝ௑)Εࠩཚֲऱ֚ᑇ(T)ࡉٺᑓী۷ૠऱं೯৫ıΔ

ࠡᓤಱូڤڕՀΚ

0 1 2 3

1

2

0 1 2 3

2

0 1 2 3

: 0

: 0,j 1,2,3

PE ~ (0, ) (18)

MAE ~ (0, ) (19)

RPE

j

H H

S T N s

K

S T N s

K

D D D

D

D D D D V H H

D D D D V H H

D

 u  u  u 

 u  u  u 





۟֟ڶԫଡլ੡

2

0 1 S 2 3 ~ (0, ) (20)

T N s

K

D D D V H H

 u  u  u  

ᛀࡳڼಱូڤኙᎄ஁ਢܡڶᇞᤩ౨ԺΔၞԫޡᘝၦՂ૪ޢԫଡᇞᤩ᧢ᑇኙᎄ஁ਢܡ

ࠠڶᐙ᥼౨ԺΔٺं೯৫ᑓীհᎄ஁ଖᄎ࠹ࠩୌࠄڂైհᐙ᥼Δء֮։ܑא၇ᔄᦞࠐ೴

։ᎅࣔΖ

ΰԫα༉၇ᦞۖߢ

1Εڇᖵ׾ं೯ᑓীխΔᏝ௑ᎄ஁(PE)࠹ࠩཚֲፖं೯৫۷ૠଖ᧩ထऱإٻᐙ᥼Ιؓ݁

࿪ኙᎄ஁(MAE)࠹Ꮭփ؆࿓৫(S/K)Εࠩཚֲፖं೯৫۷ૠଖ᧩ထऱإٻᐙ᥼ ΙઌኙᏝ

௑ᎄ஁(RPE)࠹Ꮭփ؆࿓৫(S/K)ፖࠩཚֲ᧩ထऱ૤ٻᐙ᥼Ζ

2Εڇ VIX ᑓীխΔᏝ௑ᎄ஁(PE)࠹ࠩཚֲፖं೯৫۷ૠଖ᧩ထऱ૤ٻᐙ᥼Ιؓ݁࿪ኙ ᎄ஁(MAE)࠹Ꮭփ؆࿓৫(S/K)Εࠩཚֲፖं೯৫۷ૠଖ᧩ထऱإٻᐙ᥼ ΙઌኙᏝ௑ᎄ

஁(RPE)࠹Ꮭփ؆࿓৫ (S/K)ፖࠩཚֲ᧩ထऱإٻᐙ᥼ Δۖं೯৫۷ૠଖ᧩ထऱ૤ٻᐙ

᥼Ζ

3Εڇ GARCH(1,1)ᑓীխΔᏝ௑ᎄ஁(PE)࠹Ꮭփ؆࿓৫(S/K)Εཚֲፖं೯৫۷ૠଖ᧩

ထऱ૤ٻᐙ᥼Ιؓ݁࿪ኙᎄ஁(MAE)࠹Ꮭփ؆࿓৫(S/K)Εࠩཚֲፖं೯৫۷ૠଖ᧩ထ ऱإٻᐙ᥼ΙઌኙᏝ௑ᎄ஁(RPE)࠹Ꮭփ؆࿓৫(S/K)Εࠩཚֲፖं೯৫۷ૠଖ᧩ထऱ૤

ٻᐙ᥼Ζ

4Εڇ IVF ᑓীխΔᏝ௑ᎄ஁(PE)࠹ࠩཚֲፖं೯৫۷ૠଖ᧩ထऱ૤ٻᐙ᥼ΔۖᏝփ؆

࿓৫(S/K)ڶ᧩ထऱإٻᐙ᥼Ιؓ݁࿪ኙᎄ஁(MAE)࠹Ꮭփ؆࿓৫(S/K)Εࠩཚֲፖं೯ ৫۷ૠଖ᧩ထऱإٻᐙ᥼ΙઌኙᏝ௑ᎄ஁(RPE)࠹Ꮭփ؆࿓৫(S/K)ፖࠩཚֲ᧩ထऱإٻ ᐙ᥼Δۖं೯৫۷ૠଖ᧩ထऱ૤ٻᐙ᥼Ζ

ΰԲα༉ᔄᦞۖߢ

1Εڇᖵ׾ं೯ᑓীխΔᏝ௑ᎄ஁(PE)࠹Ꮭփ؆࿓৫(S/K)᧩ထऱ૤ٻᐙ᥼Δۖࠩཚֲ᧩

ထऱإٻᐙ᥼Ιؓ݁࿪ኙᎄ஁(MAE)࠹Ꮭփ؆࿓৫(S/K)᧩ထऱ૤ٻᐙ᥼Δۖࠩཚֲ᧩

ထऱإٻᐙ᥼ΙઌኙᏝ௑ᎄ஁(RPE)࠹Ꮭփ؆࿓৫(S/K)᧩ထऱإٻᐙ᥼Δۖं೯৫۷ૠ ଖ᧩ထऱ૤ٻᐙ᥼Ζ

2Εڇ VIX ᑓীխΔᏝ௑ᎄ஁(PE)࠹Ꮭփ؆࿓৫(S/K)ፖं೯৫۷ૠଖ᧩ထऱ૤ٻᐙ᥼ Δ

ۖࠩཚֲڶ᧩ထऱإٻᐙ᥼ Ιؓ݁࿪ኙᎄ஁(MAE)࠹ࠩᏝփ؆࿓৫(S/K)᧩ထऱ૤ٻᐙ

᥼Δۖࠩཚֲ᧩ထऱإٻᐙ᥼ΙઌኙᏝ௑ᎄ஁(RPE)࠹ࠩཚֲፖं೯৫۷ૠଖ᧩ထऱ૤

ٻᐙ᥼ΔۖᏝփ؆࿓৫(S/K)᧩ထऱإٻᐙ᥼Ζ

3Εڇ GARCH(1,1)ᑓীխΔᏝ௑ᎄ஁(PE)࠹Ꮭփ؆࿓৫(S/K)ፖं೯৫۷ૠଖ᧩ထऱ૤

ٻᐙ᥼Δۖࠩཚֲ᧩ထऱإٻᐙ᥼Ιؓ݁࿪ኙᎄ஁(MAE)࠹ࠩཚֲፖं೯৫۷ૠଖ᧩ထ ऱإٻᐙ᥼ΔۖᏝփ؆࿓৫(S/K)᧩ထऱإٻᐙ᥼ΙઌኙᏝ௑ᎄ஁(RPE)࠹ࠩཚֲፖं೯ ৫۷ૠଖ᧩ထऱ૤ٻᐙ᥼ΔۖᏝփ؆࿓৫(S/K)᧩ထऱإٻᐙ᥼Ζ

4Εڇ IVF ᑓীխΔᏝ௑ᎄ஁(PE)࠹ࠩཚֲፖं೯৫۷ૠଖ᧩ထऱ૤ٻᐙ᥼ΔۖᏝփ؆

࿓৫(S/K)᧩ထऱإٻᐙ᥼Ιؓ݁࿪ኙᎄ஁(MAE)࠹ࠩཚֲፖं೯৫۷ૠଖ᧩ထऱإٻ ᐙ᥼ΔۖᏝփ؆࿓৫(S/K)᧩ထऱ૤ٻᐙ᥼ΙઌኙᏝ௑ᎄ஁(RPE)࠹ࠩཚֲፖं೯৫۷ૠ ଖ᧩ထऱ૤ٻᐙ᥼ΔۖᏝփ؆࿓৫(S/K)᧩ထऱإٻᐙ᥼Ζ

᜔հΔ.ྤᓵ༉၇ᦞࢨᔄᦞۖߢΔIVF ᑓীࠡؓ݁᧢ᑇᇞᤩ౨Ժᚌ࣍ GARCH(1,1) ᑓীΕVIX ᑓীፖᖵ׾ं೯ᑓীΖ

۟࣍ڇٺጟᑓীխΔᔄᦞಱូڤհR ଖઃ೏࣍၇ᦞಱូڤΔ᧩قᔄᦞऱಱូڤᅝ² խհᇞᤩ᧢ᑇΔઌለ࣍၇ᦞΔለࠠڶᐙ᥼Ꮭ௑ᎄ஁հᇞᤩ౨ԺΔطڼංឰΔ၇ᦞऱಱូ

ڤᅝխೈԱᏝփ؆࿓৫Εࠩཚֲऱ֚ᑇࡉं೯৫࿛ᇞᤩ᧢ᑇ؆Δᚨࡸڶޓࠠᇞᤩ౨Ժऱ

᧢ᑇآ౏ԵಱូڤᅝխΔॣޡ೗๻ڕګٌၦࡉྤଅᙠܓ෷࿛᧢ᑇΔ൫ਢܡᒔኔࠠڶᐙ᥼

౨Ժսڶৱ৵ᥛၞԫޡ᧭ᢞΖ

ٔΕ࿨ᓵ

ދᇷԳԫ؟ၞԵ८ᘜؑ໱ٌ࣐Δܛؘႊ૿ኙଅᙠࡉ໴ሟհၴऱ᧢֏Δۖᙇᖗᦞ೸঴

ঞ༼ࠎԱދᇷԫጟᝩᙠऱጥሐΖء֮א BS Model ܂੡ᙇᖗᦞေᏝᑓীΔ։࣫ᙇᖗᦞऱ Ꮭଖਢܡ֗ڕ۶࠹ࠩᑑऱᇷขΕᐌપᏝ௑Εྤଅᙠܓ෷Εࠩཚֲऱ֚ᑇࡉं೯৫࿛ڂై

հᐙ᥼Δ࿇෼ࠡխא࠹ࠩं೯৫ऱ᧢֏ᐙ᥼່੡ᣂ᝶ΔڂڼΔڕ۶ڇլٵऱൣቼՀބנ ᔞٽհᙇᖗᦞं೯৫ቃྒྷᑓীΔᄕ੡ૹ૞Ζ

ءઔߒ࿇෼Δ޲ڶٚ۶ԫଡ໢ԫᑓীᔞش࣍ࢬڶऱፕਐᙇᖗᦞऱٌ࣐ൣቼΔދᇷԳ

ᚨࠉࠡᏁޣᙇᖗᔞشऱቃྒྷᑓীΔթ౨ᛧ൓່壄ᒔऱေᏝΖലᏝփ؆࿓৫ࡉࠩཚֲऱլ ٵףא։ᣊΔࠀאᏝ௑ᎄ஁ऱֺለᄷঞ։࣫ڇլٵऱൣቼՀऱ၇ᔄᦞ່ᔞհं೯৫۷ૠ ᑓীΔ࿨࣠᧩قΔڇ၇ᦞֱ૿ࠌش GARCH(1,1)ᑓী۷ૠं೯৫່੡ᄷᒔΔ۟࣍Օ࣍ 60

֚ऱࠩཚֲՀऱᏝؓΕᏝփࡉ෡৫Ꮭփऱ၇ᦞΔঞא IVF ᑓীቃྒྷ౨Ժ່ࠋΙڇᔄᦞ ຝ։Δ༓׏א IVF ᑓীऱ۷ૠய່࣠ړΖڼ؆Ո࿇෼Δլᓵ༉۶ጟ۷ૠᑓীΔ၏ᠦࠩ

ཚֲ֚ᑇ။९Δࢬ۷ૠנऱ෻ᓵᏝ௑ᄎ။ೣᠦኔᎾᏝ௑ΔᏝ௑ᎄ஁Ոᄎ။ՕΖጵٽۖߢΔ

ྤᓵ၇ᦞࢨᔄᦞऱं೯৫۷ૠᑓীΔࠡᔞش࣍၏ࠩཚֲऱ֚ᑇא 60 ֚հփ੡ࡵΔ၌መ 60 ֚ܛྤऄၞ۩ڶயऱቃྒྷΖ

೶ە֮᣸

1.ຫᷞڳΔ³լٵं೯ࢤ۷ૠᑓীՀ؀ਐᙇᖗᦞေᏝᜎயֺለ´ΔࣟܦՕᖂٞᄐጥ෻ߓጚ Փᓵ֮Δاഏ԰ԼԲڣքִΖ

2.႓ࢣࠋΔ³ᙇᖗᦞေᏝᑓীհኔᢞ։࣫-א؀ਐᙇᖗᦞ֗ S&P 500 ᙇᖗᦞ੡ࠏ´Δഏم

೏ႂᚨشઝݾՕᖂ८ᘜᇷಛઔߒࢬጚՓᓵ֮Δاഏ԰ԼնڣքִΖ

3.ພᤔᐝΔ³ፕਐᙇᖗᦞေᏝ֗ଅᙠଖ۷ૠ´Δഏم೏ႂᚨشઝݾՕᖂ८ᘜᇷಛઔߒࢬጚ Փᓵ֮Δاഏ԰ԼքڣքִΖ

4.ᔤན֮Δ³ं೯෷ਐᑇ(VIX)ऱᚨش´Δ৬ဎދᇷִעΔاഏ԰ԼԿڣնִΖ

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