ቓ൧ࢌၞҦࠣቓ൧അᙣં }ᅋေ~ Ч໓ഡ࠹ਔ၂ᇕࡥֆ֥ܥקБࡎࡎҵ֥ࠏྀቓ൧ࢌၞҦđѩ০Ⴈ௹ࠊൎࢌၞඔऌؓھࢌၞҦࣉྛҩ൫đࢲݔؿགྷھҦ֥൬ၭაކჿࡎ֥۬ѯหᆘaࢌၞ֥ࠃᄁӱ؇ૡ్ཌྷܱđՖطіૼቓ൧അᄝഡ࠹ቓ൧Ҧ֥ൈީđླေॉ੮֞ഈඍਆ۱ၹbѩđЧ໓֥ҩ൫ࢲݔߎࢣൕԛ၂۱ቓ൧അ֥ᙣંbᆌؓھᙣંđЧ໓ิԛਔཌྷႋ֥ࢳथϷمb }ܱՍ~ ቓ൧അaઙછࡎҵaࢌၞҦaᙣં }Abstract~ In this paper, the profitability of simple mechanic market-making strategies with fixed quoting spreads are tested. It is found that the profitability is obviously related to the volatility range and trading volume of the contracts. Therefore, it is suggested that, when designing their market-making strategies, market makers should take such two factors into account. What’s more, a market maker paradox is also revealed during the test. Solution to this paradox is also put forward. }Keywords~ Market maker, Bid-ask spread, Trading strategy, Paradox ෛሢݓᆣಊࢌၞᇕ֥ರၭپڶđᄝ൧ӆഈႄೆቓ൧അ֥сေྟ္ರૼཁbູਔᄹࣉؓቓ൧അྛູaၛࠣቓ൧Ҧ֥ಪᆩđЧ໓ഡ࠹ਔ၂ᇕࡥֆ֥ቓ൧ࢌၞҦđѩ০Ⴈ௹ࠊ1994Ē2004୍֥ൎٳгࢌၞඔऌđؓھቓ൧Ҧࣉྛਔҩ൫đؿགྷھҦ֥൬ၭაቓ൧ᇕ൧ӆࡎ֥۬ѯหᆘaࢌၞࠃᄁӱ؇ਆ۱ၹૡ్ཌྷܱđѩߎࢣൕԛ၂۱ቓ൧അ֥ᙣંb Ч໓֥ଽಸ܋ٳඹ۱҆ٳğֻ၂҆ٳ༵ࢺകЧ໓෮ഡ࠹֥ࡥֆቓ൧ࢌၞҦĠֻؽ҆ٳࢺകЧ໓෮Ⴈ֥ဢЧඔऌĠֻ҆ٳБۡЧ໓෮ؿགྷ֥ࢲݔĠֻඹ҆ٳሹࢲಆ໓b ၂aܥקБࡎࡎҵ֥ࠏྀቓ൧ࢌၞҦ ݓ࠽ഈቓ൧അ֥ቓ൧ࢌၞҦनඋႿ܄ඳ֥ނྏࠏૡđ൞ቔູФ֥ࢌၞҦđቓ൧Ҧ၂ϮЇওೂ༯۱ࠎЧቆӮ҆ٳğࠎሙࡎaБࡎࡎҵaБֆਈbࠎႿؓቓ൧അ֥Ⴕܱ࣮đЧ໓ഡ࠹ਔೂ༯ࡥֆ֥ܥקБࡎࡎҵ֥ࠏྀቓ൧ࢌၞҦğ 1aࠎሙࡎ ھቓ൧Ҧ֥БࡎၛࠎሙࡎູᇏྏđઙೆБࡎູࠎሙࡎࡨಀઙೆБࡎࡎҵđછԛБࡎູ 64
ࠎሙࡎࡆഈછԛБࡎࡎҵb္ࠧđ ھቓ൧Ҧ֥ઙછࡎҵ=છԛБࡎĒઙೆБࡎ=છԛБࡎࡎҵĐઙೆБࡎࡎҵb Ҧ֥ࠎሙࡎ֥ഡᇂބטᆜ࿖ೂ༯ࡥ߄ჰᄵğ č1Ďૄ۱ࢌၞರֻ֥၂۱ࠎሙࡎູ֒ರ֥षࡎĠ č2Ďtൈख़đೂݔ൧ӆࡎ۬ીႵӑԛҦ֥Бࡎٓຶᆭଽđቓ൧Ҧ҂ؿളӮࢌđᄵ҂טᆜࠎሙࡎĠ č3Ďtൈख़đೂݔ൧ӆࡎ۬ӑԛҦ֥БࡎٓຶđᄵοҦ֥ཌྷႋБࡎࣉྛӮࢌđӮࢌؿളᆭުđטᆜҦ֥ࠎሙࡎđྍ֥ࠎሙࡎູؿളӮࢌᆭުֻ֥၂۱Ӯࢌࡎb 2aБࡎࡎҵ Бࡎࡎҵ֥ഡᇂҐႨቋࡥֆ֥ٚൔğ ൮༵đБࡎࡎҵ౼ູଖ۱ܥק֥ᆴĠ ఃՑđචшࡎҵ౼ᆴؓӫđ္ࠧ౼ઙೆБࡎࡎҵĢછԛБࡎࡎҵb ႮႿ௹ࠊ֥ቋཬࡎ۬эࡎ໊൞10ჭđ෮ၛᄝҩ൫ᇏđֆшБࡎࡎҵ֥ऎุ౼ᆴ൞ၛ10ჭູֆ໊đ౼Ֆ10ჭ֞200ჭ܋20ᇕ౼ᆴđ္ࠧሹ֥ઙછࡎҵၛ20ჭູֆ໊đ౼Ֆ20ჭ֞400ჭ֥20ᇕ౼ᆴb 3aБֆਈ Бֆਈοೂ༯ࡥ߄ჰᄵ౼ᆴğ č1Ďᆞӈ౦ঃ༯đҦ֥ֆшБֆਈन౼ູ1൭č௹ࠊކჿ֥1൭=5ؕĎĠ č2Ďೂݔ၂ٚཟഈ֥࣪ӻҝӑݖ5൭đᄵϜҝٚཟഈ֥Бֆਈᄹࡆᇀ2൭b২ೂğቓ൧Ҧ֥࣪ӻҝູ6൭؟ֆđӑݖ5൭֥ѓሙđᄵઙೆБֆਈಯູ1൭đછԛБֆਈ౼ູ2൭bᆃ၂ቓم֥ଢ֥൞ٝᆸԛགྷҦ֥࣪ӻҝժݖնb൙ൌіૼđھܿᄵॖၛႵི॥ᇅҦ֥࣪ӻҝܿଆb 4aҝࠏᇅbԢਔഈඍ3۱ࠎЧቆӮ҆ٳᆭຓđቓ൧അᄝૄ۱ࢌၞರࢲඏൈđၹቓ൧ྙӮ֥࣪ӻҝ๙ӈնႿ0b൞၂۱ቓ൧അ๙ӈ߶ᄝૄರ൧ӆ൬൧ᆭభϜૄರቓ൧ྙӮ֥ڄགժಆ҆ҝࠇᆀࣉྛປಆؓԊbཌྷܱ֥ҩ൫္іૼđ௹ࠊࢌၞ֥ۯ၀ڄགޓնđ෮ၛđЧ໓ࡥֆࡌഡđᄝૄ۱ࢌၞರࢲඏൈđھҦᄝ֒ರྙӮ֥࣪ӻҝࡼο֒ರ௹ࠊ֥൬ࡎࣉྛҝb ቋުđЧ໓ࡌഡࢌၞٮႨູਬbᆃ࠻൞ູਔࡥ߄࠹ෘđൈ္൞ॉ੮֞ቓ൧അ҂൞௴๙֥ࢌၞᆀđമᇀᄝႵ֥൧ӆഈđቓ൧അ҂ࣇ҂࢚ବࢌၞٮႨđّط߶ؓؿള֥ૄгቓ൧ࢌၞ൬౼၂ק֥ٮႨb ഈඍࡥֆቓ൧ࢌၞҦ൞ႨFoxpro টщཿӱࣉྛҩ൫֥bႵܱ֥࠹ਈٳ༅ᄵ০ႨSAS টປӮb ؽaဢЧඔऌ Ч໓෮Ⴈ֥ဢЧඔऌ൞1994Ē2004୍ࡗ௹ࠊކჿ֥ൎٳгࢌၞඔऌđႮഈݚ௹ࠊࢌၞ෮ิ܂bऎุطđЧ໓༵ުҐႨೂ༯ਆোඔऌဢЧğ č1Ď1ᄅކჿඔऌbՖ1994Ē2004୍đૄ୍࿊౼୍֒ྍष֥1ᄅކჿ֥ٳгࢌၞඔऌb২ೂ1994୍đ࿊Cu9501ކჿđ1995୍đ࿊Cu9601ކჿđ֩֩bಖުϜૌԱ৳ఏটđ֤֞၂۱ॴ୍֥ٳгࢌၞਙbಸၞࢳđ๙ӈ၂۱௹ࠊކჿᄝܫஇԚ௹උႿჹᄅކჿđࢌၞ၂Ϯޓౢ֎đෛሢൈࡗ֥၍đࡼᇯࡶӮູ൧ӆഈ֥ᇶ৯ކჿđࢌၞਈᇯࡶᄹնđෛሢࢌ۩ᄅٺ֥ਢ࣍đࢌၞਈႻᇯࡶࡨഒbၹՎđЧކჿඔऌဢЧ֥၂۱ૼཁหᆘ൞҂؎ࣜࢌၞਈ֥ᇛ௹ྟэ߄b č2ĎٳোކჿඔऌbھোဢЧඔऌ֥࿊౼ٚم൞ğ൮༵đૄ۱ᄅؓ֒ᄅႵࢌၞਈ֥ 65
௹ࠊކჿοఃᄅ؇ࢌၞਈՖն֞ཬஆਙđٳљ࿊ԛ֒ᄅࢌၞਈቋն֥ކჿčࡥӫູਈቋնކჿĎaࢌၞਈ֩Ⴟஆਙ֥ᇏ໊ඔ֥ކჿčࡥӫູਈᇏࡗކჿĎބࢌၞਈቋཬ֥ކჿčࡥӫູਈቋཬކჿĎđಖުϜᆃུކჿ֥ٳгࢌၞඔऌٳљԱ৳ఏটđ֤֞ਈቋնކჿaਈᇏࡗކჿaਈቋཬކჿᆃ3۱ඔऌဢЧb ಸၞࢳđਈቋնކჿဢЧ္ࣼ൞1994Ē2004୍ࡗ௹ࠊ۲ᄅᇶ৯ކჿ෮ቆӮ֥ဢЧbఃૼཁหᆘ൞൧ӆࢌၞᇔٳࠃᄁđطਈቋཬކჿဢЧᄵཌྷّđఃૼཁหᆘ൞ࢌၞᇔࠞఃౢ֎bᇀႿਈᇏࡗކჿđႮႿ࿊౼֥ѓሙ൞ᇏ໊ඔđط҂൞नඔđ෮ၛఃࢌၞਈ္൞ொཬ֥bі1Бۡਔᆃਆো܋4ᇕඔऌဢЧᄝ1994Ē2004୍௹ࡗ֥ᄅ؇ࢌၞਈ֥҆ٳ࠹หᆘb і1 1994Ē2004୍ࡗ3ᇕဢЧ֥ᄅ؇ࢌၞਈ࠹หᆘ čֆ໊ğ൭Ď ٳোކჿဢЧ 1ᄅކჿဢЧਈቋնކჿਈᇏࡗކჿਈቋཬކჿ नᄅࢌၞਈ 131,377440,121 15,404 776 ѓሙҵ 338,911705,322 8,730 1,929 ቋնᆴ 2,596,6303,619,082 47,800 13,666 ቋཬᆴ 228,700 946 2 aҩ൫ࢲݔ ൮༵Бۡؓ1ᄅކჿဢЧᆳྛభඍࡥֆቓ൧ࢌၞҦ֥൬ၭሑঃb 1aࡥֆቓ൧Ҧ֥൬ၭ і2བྷ༥Бۡਔؓ1ᄅކჿဢЧđ20ᇕБࡎࡎҵ༯ࡥֆቓ൧Ҧᄝ۲ކჿഈ֥൬ၭၛࠣۄ࠹หᆘb 200ቓ൧൬150ၭຣ100ჭ500102030405060708090100110120130140150160170180190200ቓ൧ֆшБࡎࡎҵ ჭ
-50 1 ۲ᇕБࡎࡎҵ༯ࡥֆቓ൧ࢌၞҦ֥࠹൬ၭ 1૭ਔ20ᇕֆшБࡎࡎҵ༯ھࡥֆቓ൧Ҧ֥ሹ൬ၭbಸၞु֞đᄝ16ᇕБࡎࡎҵ༯đھࡥֆቓ൧Ҧሹุ൬ၭູڵđᆺႵᄝֆшБࡎࡎҵູ10a20a40a50ჭൈđھࡥֆቓ൧Ҧሹุഈॖၛ౼֤ᆞ֥൬ၭb҂ݖđᄝБࡎࡎҵ౼ູ10ჭൈđھࡥֆቓ൧Ҧᄝ 66
1994Ē2004୍ࡗ෮౼֤֥࠹൬ၭۚղຣჭbၹູЧ໓֥ҩ൫൞ࡌקھቓ൧ҦૄՑᆺࢌၞ1൭đط1ᄅކჿဢЧඔऌᇏ֥֥ቋۚӮࢌࡎ൞31450ჭ/ؕđο7%֥Ќᆣࣁ࠹ෘđࢌၞ1൭ቋ؟ᆺླေೆ3145057%Ģჭđ෮ၛđཌྷؓႿֆՑࢌၞೆ֥ሧࣁਈđຣ֥൬ၭ൞ࣙದ֥b ቋնᆴຣቋཬᆴჭ ѓሙҵ ቓ൧ֆшБࡎࡎҵ ჭ
2 ۲۲ᇕБࡎࡎҵ༯ࡥֆቓ൧ࢌၞҦ൬ၭ֥ቋնᆴaቋཬᆴބѓሙҵ 67
і2 ؓ1ᄅކჿဢЧᆳྛࡥֆቓ൧ࢌၞҦ֥൬ၭ ֆ໊ğຣჭ ֆшБࡎࡎҵ ୍ٺ102030 40 5060708090100110 120130140150160170180190 200 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 ሹ࠹ नᆴ ѓሙҵ ቋնᆴ ቋཬᆴ Range* ࠹ؿള 195823 38064 17199 10522 7469 4957 3909 3222 2682 2263 1674 1493 1313 1159 1035 891 825 758 701 643 ࢌၞՑඔ * Rangeğ=ቋնᆴĒቋཬᆴb 68
2ᄵ૭ਔ۲ᇕБࡎࡎҵ༯đھࡥֆቓ൧ࢌၞҦ֥൬ၭ֥3۱࠹หᆘbఃᇏđቋնᆴaቋཬᆴaѓሙҵٳљ൞ᆷᄝཌྷႋБࡎࡎҵ༯đھࡥֆቓ൧ࢌၞҦᄝ1994Ē2004୍௹ࡗ۲୍ቓ൧൬ၭ֥ቋնᆴaቋཬᆴބѓሙҵb၇ऌ2đޓཁಖđֆшБࡎࡎҵᄀཬđھࡥֆቓ൧Ҧ൬ၭ֥ቋնᆴᄀնđൈቋཬᆴ္ᄀཬč္ࠧᄀնĎđཌྷႋ֥൬ၭ֥ѓሙҵ္ᄀնb֝ᇁᆃ၂གྷའ֥ᆰࢤჰၹ൞đҦ֥Бࡎࡎҵᄀཬđؿള֥ࢌၞՑඔᄀ؟bೂі2෮ൕđ২ೂđᄝֆшБࡎࡎҵ౼ູ10ჭൈđھࡥֆቓ൧Ҧ࠹ؿളࢌၞ195823ՑĠطᄝֆшБࡎࡎҵ౼ູ200ჭൈđھࡥֆቓ൧Ҧ࠹ؿളࢌၞՑඔᆺႵ643Ցbᆃဢđᄝቓ൧ࡎҵࢠཬൈđೂݔ൧ӆሑঃ൞ؓቓ൧ҦႵ০đᄵႮႿࢌၞՑඔ؟đቓ൧Ҧ֥࠹႔০္նĠೂݔ൧ӆሑঃؓቓ൧Ҧ҂০đᄵႮႿࢌၞՑඔ؟đቓ൧Ҧ္֥նb 2a႕ཙቓ൧Ҧ൬ၭ֥ၹ ࣉ၂֥҄ٳ༅іૼđھࡥֆቓ൧Ҧ֥൬ၭაކჿࡎ֥۬ѯหᆘaၛࠣކჿ֥ࢌၞࠃᄁሑঃႵܱb࠺ھࡥֆቓ൧Ҧᄝૄ۱ࢌၞರ֥ቓ൧൬ၭູPLđކჿ֒ರ֥ࢌၞਈູtVolđႨކჿࡎ۬֒ರ֥ږҵč=֒ರቋۚࡎĒ֒ರቋ֮ࡎĎটіൕࡎ֥۬ѯหᆘđ࠺ູtRangeđಖުၛPLູၹэਈđၛVolaRangeູሱэਈܒᄯೂ༯݂߭ଆğ ttttPL=α+β⋅Range+β⋅Vol+ε itii1iti2ititఃᇏğiіൕֆшБࡎࡎҵđi=10đ20đllđ200b ູਔх૧ؿളເ݂߭đླေ༵ဒഈඍ3۱эਈਙ൞ڎթᄝֆ໊۴bֆ໊۴ဒҐႨADFٚمbဒࢲݔіૼđᄝ20ᇕБࡎࡎҵ༯đഈඍ3۱эਈਙन҂թᄝֆ໊۴bֆ໊۴ဒࢲݔі3bູࢫസږđі3ᆺБۡਔֆшБࡎࡎҵູ10ჭa100ჭൈ֥ֆ໊۴ဒࢲݔb і3 ֆ໊۴ADFဒ i=10i=100 ਙ Type Tau Pr<TauF Pr>F Tau Pr<Tau F Pr>F Zero Mean <.0001 <.0001 PLSingle Mean <. <.0001 197 it Trend <. <.0001 Zero Mean <.0001 VolSingle Mean <. it Trend <. Zero Mean <.0001 <.0001 RangeSingle Mean <. <.0001 it Trend <. <.0001 і4Бۡਔؓഈඍଆࣉྛ݂֥߭ࢲݔbՖі4ॖၛु֞ğ č1ĎPLაRange֥ܱ༢bؓႿֆшБࡎࡎҵ֥෮Ⴕ20ᇕ౼ᆴđRange֥݂߭༢itititඔ၂ੰཁᇷູڵbၹູRangeޙਈ֥൞֒ರ௹ࠊࡎ֥۬ᆒ֕ږ؇đ෮ၛđ݂߭ࢲݔіૼđitھࡥֆቓ൧ҦᆺൡႨႿࡎ۬ԩႿᅎږᆒ֥֕൧ӆđ၂֊൧ӆࡎ۬ؿളږ؇ࢠն֥ᆒ֕đં൞ؿളࢠնږ֥ഈᅨߎ൞ؿളࢠնږ؇֥༯יđھࡥֆቓ൧Ҧࡼؿളն֥bၹՎđᆃ၂ࢲݔౢԣֹіૼđؓቓ൧അطđсྶေٳ൧ӆ֥ѯหᆘোđٳљᆌؓ҂֥൧ӆѯหᆘҐႨ҂֥ቓ൧Ҧbطູਔିܔࠣൈ؎൧ӆ෮ԩ֥ѯሑঃđႵсေഡ࠹ཌྷႋ֥ࡓ॥ᆷѓđၛьᄝാঔնᆭభࠣൈטᆜቓ൧Ҧb 69
і4 ݂߭ࢲݔ ֆшࡎҵ ༢ඔ t P-Valueֆшࡎҵ ༢ඔ t P-ValueIntercept * J * J * * Vol Vol ititIntercept * J * J * Vol Vol ititIntercept * J * J * Vol Vol ititIntercept * J * J * Vol Vol ititIntercept * J * J * Vol Vol ititIntercept ** * J * J * Vol Vol ititIntercept * * J * J * Vol Vol ititIntercept * * J * J * Vol Vol ititIntercept * * J * J * Vol Vol ititIntercept * * J * J * Vol Vol itit* ཁᇷྟඣູ1%Ġ** ཁᇷྟඣູ5%b č2ĎPLაVolᆭࡗ֥ܱ༢ğᄝֆшБࡎࡎҵູ10ჭൈđVol֥݂߭༢ඔཁᇷູᆞđitititіૼՎൈ൧ӆ֥ࢌၞᄀࠃᄁđھࡥֆቓ൧Ҧ֥൬ၭᄀնb൞ؓႿֆшБࡎࡎҵ֥ః19ᇕ౼ᆴđVol֥݂߭༢ඔෙಖनູᆞđ҂ཁᇷb۴ऌᆃ၂ࢲݔđෙಖPLაVolitititᆭࡗ֥ܱ༢҂ೂPLაRangeᆭࡗ֥ܱ༢ପહ఼đ൞ႵႮಪູđᄝPLაVolᆭࡗ္ititititթᄝሢଖᇕ৳༢đᆺ҂ݖᆃᇕ৳༢ѩ҂൞ࡥֆ֥ཌྟܱ༢b 70
3aቓ൧Ҧ൬ၭა൧ӆ֥ࢌၞࠃᄁሑঃᆭࡗ֥ܱ༢ ູਔࣉ၂҄ฐ෬PLაVolᆭࡗ֥ܱ༢đЧ໓ႻٳљႨਈቋնކჿaਈᇏࡗކჿaਈititቋཬކჿᆃোඔऌဢЧؓభඍࡥֆቓ൧ࢌၞҦࣉྛਔҩ൫bཌྷܱ֥ҩ൫ࢲݔі5b3ᄵᆰܴ૭ਔі5ᇏ֥Ҧ࠹൬ၭაֆшБࡎࡎҵᆭࡗ֥ܱ༢b ቓ൧ਈቋնކჿ൬ਈᇏࡗކჿ ၭਈቋཬކჿຣ ჭ 102030405060708090100110120130140150160170180190200 ֆшБࡎࡎҵ ჭ
3 1994Ē2004୍3ᇕٳোဢЧ༯ࡥֆቓ൧ࢌၞҦ֥࠹൬ၭ Ֆ3ᇏॖၛु֞đᆃ3۱ဢЧᆭࡗđھࡥֆቓ൧Ҧ൬ၭაБࡎࡎҵ֥ܱ༢թᄝૼཁ֥ҵၳb൙ൌഈđؓႿᆃᇕҵၳđॖၛ০Ⴈೂ༯݂߭ଆটࣉྛဒğ PL=α+α⋅D+α⋅Dij01mid,ij2minij +β⋅Ln(spread)+β⋅D⋅Ln(spread)+β⋅D⋅Ln(spread)+ε0ij1midij2minijij,ijijఃᇏğ i іൕဢЧোđi=ਈቋնކჿဢЧđਈᇏࡗކჿဢЧđਈቋཬކჿဢЧĠ j іൕֆшБࡎࡎҵ֥োđj=1đ2đlđ20Ġ PLіൕھࡥֆቓ൧Ҧ֥࠹൬ၭĠ Dູྴэਈđೂݔቓ൧Ҧ൞ؓਈᇏࡗކჿဢЧൌീ֥đᄵ౼ᆴູ1đڎᄵ౼ᆴmidູ0Ġ Dູྴэਈđೂݔቓ൧Ҧ൞ؓਈቋཬކჿဢЧൌീ֥đᄵ౼ᆴູ1đڎᄵ౼ᆴminູ0Ġ Ln(spread)ູֆшБࡎࡎҵ֥ሱಖؓඔb ݂߭ࢲݔೂ༯ğ PL=−⋅D−⋅Dijmid,ijmin,ij () () () −⋅Ln(spreadl)+⋅D⋅Ln(spread)+⋅D⋅Ln(spread)ijmid,ijijmin,ijij () () ()2F=đAdjusted RĢ ഈൔᇏđ۲݂߭༢ඔ༯૫֥ওݼѓᇿ֥൞ཌྷႋ֥t࠹ਈđ෮Ⴕᆃུ࠹ਈᄝ1%֥ඣഈཁᇷb 71
і5 1994Ē2004୍3ᇕٳোဢЧ༯ࡥֆቓ൧ࢌၞҦ֥൬ၭࠣ࠹หᆘ ֆ໊ğຣჭ ֆшБࡎࡎҵ 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 ਈ ࠹൬ၭ ቋ नᆴ ն ѓሙҵ ކ ቋնᆴ ჿ ቋཬᆴ ဢ ࠹ࢌၞ 670398106758 44647 2576617352112728577676554534493 340828592466214719071622146513011164 1035 Ч Ցඔ Ց
࠹൬ၭ ਈ ᇏ नᆴ ࡗ ѓሙҵ ކ ቋնᆴ ჿ ቋཬᆴ ဢ ࠹ࢌၞ 37836 18024 11119 8039 6298 4420 3645 3105 2649 2292 1728 1574 1387 1263 1134 944 876 813 751 682 Ч Ցඔ Ց
࠹൬ၭ ਈ ቋ नᆴ ཬ ѓሙҵ ކ ቋնᆴ ჿ ቋཬᆴ ဢ ࠹ࢌၞ 19201297 1001 821731513471425363336 231224215205191165156147138 131 Ч Ցඔ Ց
72
ഈඍ݂߭ࢲݔႻॖၛіൕӮğ ⎧−⋅Ln(spread)đ for i=ਈቋնކჿဢЧĠij⎪ PL=−+⋅Ln(spread)đ for i=ਈᇏࡗކჿဢЧĠ⎨ijij⎪−+⋅Ln(spread)đ for i=ਈቋཬކჿဢЧbij⎩ၹՎđၛഈ݂߭ࢲݔౢԣіૼđ൧ӆࢌၞ֥ࠃᄁӱ؇ؓቓ൧ࢌၞҦ֥൬ၭ္Ⴕཁᇷ֥႕ཙğ č1ĎؓႿ൧ӆࢌၞࠃᄁ֥ਈቋնކჿဢЧđ݂֥߭ࢩएཛཁᇷູᆞđོੱཁᇷູڵđіૼؓႿਈቋնކჿဢЧđھࡥֆቓ൧ࢌၞҦ൞ॖၛ႔০֥đ൞ᄹնቓ൧Бࡎࡎҵđಏ߶ࢆ֮ቓ൧Ҧ֥႔০b္ࠧđؓႿਈቋնކჿဢЧđቓ൧അಸၞൌགྷ႔০đѩቓ൧അ֥ྟ࿊ᄴႋھ൞෪ཬБࡎࡎҵđၛᄹࡆቓ൧႔০b č2ĎؓႿਈᇏࡗކჿဢЧބਈቋཬކჿဢЧđ݂֥߭ࢩएཛཁᇷູڵđོੱཁᇷູᆞđіૼؓႿਈᇏࡗކჿဢЧބਈቋཬކჿဢЧđھࡥֆቓ൧ࢌၞҦ൞֥đ൞๙ݖᄹնቓ൧Бࡎࡎҵđॖၛࢆ֮ቓ൧Ҧ֥حb္ࠧđؓႿਈᇏࡗކჿဢЧބਈቋཬކჿဢЧđቓ൧അಸၞؿളđ֤ቓ൧അ֥ྟ࿊ᄴႋھ൞ᄹնБࡎࡎҵđၛࡨഒb ؓႿᆃ၂ࢲݔđॖၛᆰܴഈࢳğؓႿ൧ӆࢌၞࠃᄁ֥ކჿđࡎ֥۬э၂Ϯ൞৵࿃֥đ32ѩቓ൧അ֥ӻҝժ္ಸၞᇛሇđၹՎܥקཬږ؇ઙછࡎҵ֥ࢌၞҦಸၞൌགྷ႔০bཌྷّđؓႿ൧ӆࢌၞ҂ࠃᄁ֥ކჿđࡎ֥۬э၂Ϯ൞๋ᄁ֥đѩቓ൧അ֥ӻҝժޓᇛሇđၹՎಸၞؿളb ၛഈࢲݔіૼđቓ൧അᄝഡ࠹ቓ൧ࢌၞҦ֥ൈީđԢਔႋھॉ੮ࡎ֥۬ѯږ؇ᆃ၂ၹᆭຓđߎႋھॉ੮ቓ൧ކჿ֥൧ӆࢌၞࠃᄁሑঃğೂݔॖၛ࿊ᄴ֥߅đቓ൧അႋھ࿊ᄴҕაؓ൧ӆࢌၞࠃᄁ֥ކჿ֥ቓ൧đѩđቓ൧ކჿ֥൧ӆࢌၞᄀࠃᄁđቓ൧അᄀႋھ෪ཬሱ֥࠭ቓ൧Бࡎࡎҵđၹູᆃဢॖၛᄹࡆ႔০bაՎൈđቓ൧അႋھх૧ҕაؓପུ൧ӆࢌၞ҂ࠃᄁ֥ކჿ֥ቓ൧đࠧь҂֤҂ေҕაؓࢌၞ҂ࠃᄁކჿ֥ቓ൧đቓ൧അ္ႋھᄝᄍྸ֥ٓຶଽ࣐ॖିֹᄹնሱ֥࠭Бࡎࡎҵđၛࡨഒቓ൧b ൞đᆃဢ၂টࣼթᄝ၂ᇕᙣંğ ၂ٚ૫đ၂۱ࢌၞᇕᆭ෮ၛေႄೆቓ൧അđ൞ၹູЧദࢌၞ҂ࠃᄁđ༐ຬ๙ݖቓ൧അ֥ቓ൧ྛູটࠃᄁࢌၞbೂݔЧദ֥ࢌၞၘࣜޓࠃᄁđᄵࣼીсေႄೆቓ൧അĠൈđቔູ൧ӆ֥ܵᆀđ္༐ຬϜቓ൧അ֥Бࡎࡎҵཋק֤ᄀཬᄀݺđၹູቓ൧അ֥БࡎࡎҵᄀཬđᄀႵ০Ⴟ՜ࣉࢌၞ֥ࠃᄁb ൞ਸ਼၂ٚ૫đؓႿЧദࢌၞ҂ࠃᄁ֥ࢌၞᇕđೂݔ൧ӆܵᆀܿק֥Бࡎࡎҵഈཋཬđᄵቓ൧അ֥ྟ࿊ᄴႋھх૧ҕა֥ؓቓ൧đၹູಸၞؿളĠࠧ൞ᄝ࿊ᄴҕაቓ൧ᆭުđቓ൧അ္ႋھᄝᄍྸ֥ٓຶଽ࣐ॖିֹᄹնሱ֥࠭ቓ൧Бࡎࡎҵđၛࡨഒቓ൧b൞ቓ൧Бࡎࡎҵᄀնđᄀ҂ಸၞࠃᄁ൧ӆ֥ࢌၞbّط൞ؓପུЧദࢌၞၘࣜޓࠃᄁ֥ކჿđቓ൧അҌႋھ࣐ॖିֹ෪ཬሱ֥࠭ቓ൧Бࡎࡎҵb ၹՎđაᆃ۱ൗࢸഈ֥ޓ؟ః൙౦၂ဢđቓ൧അ္ဢᆺ߶ϲဆaൈ္ᆺႋھϲဆoࣆഈเpaط҂൞o࿒ᇏෂฒp֥࢘b ၹՎđ൧ӆ֥ܵᆀᄝᇅר॓࿐֥ቓ൧അܵᇅ؇֥ൈީđсྶေԉٳॉ੮֞ഈඍᙣં֥ग़ܴྟđط҂ି၂఼ᇅཋקቓ൧അ֥ቓ൧ၬༀބܿקఃБࡎࡎҵ֥ٓຶb၂۱ࢳथ֥Ϸ 32 ൙ൌഈđᄝ௹ࠊ൧ӆഈթᄝሢ҂ഒ֥ࢌၞᆀđૌૄ฿ᄝՖ൙ሢॹઙࣉછԛ֥ࢌၞđ္ࠧ෮໌֥әֆbૌᆸ႔ބᆸ֥ࡎ໊๙ӈᆺ൞1֞ࠫ۱ቋཬэࡎ໊č௹ࠊ֥ቋཬэࡎູ໊10ჭĎbႮႿ௹ࠊ֥ࢌၞٮႨޓ֮đؓႿૌটඪđ௹ࠊࡎ۬1۱ࡎ໊֥эđࣼॖၛൌགྷ႔০b۴ऌЧ໓֥ҩ൫ࢲݔčі5Ďᄝ௹ࠊᇶ৯ކჿഈၛ20ჭ֥චшБࡎࡎҵࣉྛࠏྀ֥؋ཌࢌၞđಯಖॖၛࠆ֤ࣙದ֥႔০bၹՎᆃ္ࡗࢤඪૼđәֆᆃᇕࢌၞҦ൞Ⴕളթ֥၇ऌ֥b 73
م൞đᄝཟቓ൧അٳቓ൧ᇕ֥ൈީđॖၛϜ൧ӆࢌၞࠃᄁ֥ᇕބࢌၞ҂ࠃᄁ֥ᇕࣉྛձđѩؓਆোᇕܿקཌྷ֥࣍ቓ൧ၬༀބቓ൧Бࡎࡎҵٓຶbᆃဢđ൧ӆ֥ܵᆀॖၛϜؓࢌၞ҂ࠃᄁᇕ֥ቓ൧ၬༀ֥ิۚaϜᄍྸ֥ቋնቓ൧Бࡎࡎҵٓຶ෪ཬđൈđᄝؓࢌၞࠃᄁᇕࣉྛቓ൧֥০֥་ႄ༯đቓ൧അ္ಯಖ߶჻ၩᇶӵքؓࢌၞ҂ࠃᄁᇕ֥ቓ൧b ඹaሹࢲ Ч໓֥࣮ࢲݔіૼđቓ൧ࢌၞҦ֥൬ၭაކჿࡎ֥۬ѯหᆘa൧ӆࢌၞ֥ࠃᄁӱ؇ૡ్ཌྷܱğ 1aؓႿЧ໓෮ҐႨ֥ࡥֆ֥ܥקࡎҵ֥ࠏྀቓ൧ࢌၞҦđ௹ࠊކჿࡎ֥۬ᆒ֕ږ؇ᄀնđҦᄀಸၞđᆺႵᄝކჿࡎ۬ӯᅎږᆒ֕ൈđھҦҌಸၞൌགྷ႔০đՖطіૼđቓ൧അᄝഡ࠹ቓ൧Ҧ֥ൈީđླေିࠣൈя്൧ӆࡎ֥۬ѯหᆘđѩٳљࣼ҂֥ѯหᆘഡ࠹҂֥ቓ൧Ҧb 2aؓႿЧ໓෮ҐႨ֥ࡥֆ֥ࡎҵܥק֥ࠏྀቓ൧ࢌၞҦđᄝ൧ӆࢌၞࠃᄁ֥౦ঃ༯ಸၞൌགྷ႔০đѩՎൈБࡎࡎҵᄀཬđ႔০ᄀ؟ĠّᆭđؓႿ൧ӆࢌၞ҂ࠃᄁ֥ކჿđھҦಸၞؿളđѩБࡎࡎҵᄀ༯đᄀ؟b෮ၛቓ൧അᄝ࿊ᄴေҕაቓ൧֥ᇕ֥ൈީđླေॉ੮ఃࢌၞਈ֥նཬđႋھ࿊ᄴପུЧദࢌၞࠃᄁࠇᆀࢌၞਈऎႵᄹӉమ৯֥ކჿࣉྛቓ൧bطؓႿପུ҂֤҂ҕაቓ൧֥aЧദ֥ࢌၞѩ҂ࠃᄁ֥ᇕđቓ൧അႋھ࿊ᄴᄝᄍྸ֥ٓຶଽ࣐ॖିֹঔնሱ֥࠭Бࡎࡎҵđၛࡨഒb ൞ᆃဢࣼթᄝሢቓ൧അᙣંđၹູቋླေቓ൧അaၛࠣླေቓ൧അ෪ཬБࡎࡎҵ֥ఞఞ൞ପུЧദ֥ࢌၞ҂ࠃᄁ֥ᇕbቔູ൧ӆ֥ܵᆀđᄝॉ੮ႄೆቓ൧അ֥ൈީđླေԉٳॉ੮֞ھᙣં֥ग़ܴྟb၂۱ࢳथϷم൞ᄝٳቓ൧ᇕൈđေϜࢌၞࠃᄁބࢌၞ҂ࠃᄁ֥ᇕࣉྛձđᆃဢđ࠻ିܔิۚؓࢌၞ҂ࠃᄁᇕ֥ቓ൧ၬༀđൈႻିܔቓ൧അႨؓࢌၞࠃᄁᇕ֥ቓ൧০টҀؓࢌၞ҂ࠃᄁᇕ֥ቓ൧đ֤ૌಯಖିܔႵࠒࠞྟҕაؓࢌၞ҂ࠃᄁᇕ֥ቓ൧b 74
