1샻싊웚쿞뷡릹퇐뺿쫶움 쇖몣 횣헱쇺 ꎨ쿃쏅듳톧뷰죚쾵ꎬ361005ꎩ 쓚죝쳡튪ꎺ놾컄뛔쒿잰샻싊웚쿞뷡릹뗄퇐뺿ힴ뿶뷸탐튻룶움쫶탔뗄퇐뺿ꎬ듓컥룶랽쏦뷩짜뫍럖컶쇋맺쓚췢폐맘샻싊웚쿞뷡릹뗄퇐뺿ꆣ헢컥룶랽쏦냼삨ꎺ샻싊웚쿞뷡릹탎돉볙짨ꎻ샻싊웚쿞뷡릹뺲첬맀볆ꎻ샻싊웚쿞뷡릹ퟔ짭탎첬뗄캢맛럖컶ꎻ샻싊웚쿞뷡릹뚯첬쒣탍ꎻ샻싊웚쿞뷡릹뚯첬쒣탍뗄쪵횤볬퇩ꆣ퓚컄쿗믘맋뗄믹뒡짏ꎬ놾컄뮹뛔샻싊웚쿞뷡릹캴살뗄퇐뺿랽쿲뷸탐쇋첽쳖ꆣ 맘볼듊ꎺ샻싊웚쿞뷡릹 퇐뺿쫶움 Abstract: This paper did a research review of term structure from five aspects. These aspects are: hypothesis on formation of term structure; static estimation of term structure, microanalysis on the shape of term structure, dynamic models of term structure, and the empirical tests of dynamic models. Based on these review, this paper discussed some future research for the term structure of interest rate. Key Words: Term Structure of Interest Rate, Literature Review ퟷ헟볲뷩ꎺ 쇖몣ꎬꎱꎹꎷꎷ쓪돶짺ꎬ쓐ꎬ몺ퟥꎬ쿃쏅듳톧뷰죚쾵붲쪦ꆢ늩쪿ꆣ퓚맺쓚릫뾪뾯컯랢뇭ꎲꎰ폠욪톧쫵싛컄ꆣEmail:xmulh2@, 춨톶뗘횷ꎺ쿃쏅듳톧뷰죚쾵ꆣ폊뇠ꎺ361005ꆣ 횣헱쇺ꎬ1966쓪돶짺ꎬ쓐ꎬ몺ퟥꎬ뺭볃톧늩쪿, 쏀맺볓훝듳톧싥즼럖킣뢻늼삳쳘퇐뺿톧헟, 쿖죎쿃쏅듳톧뺭볃톧풺뢱풺뎤ꆢ뷌쫚ꆢ늩쪿짺떼쪦ꆣ퓚맺쓚췢릫뾪랢탐뗄톧쫵뾯컯짏랢뇭쇋냙폠욪톧쫵싛컄ꎬ돶냦쇋24늿ꎨ몬뫏ퟷꎩ훸ꆢ뇠ꆢ틫훸ퟷꆣEmail: zlzheng@ꆣ춨톶뗘횷ꎺ쿃쏅듳톧뷰죚쾵ꆣ폊뇠ꎺ361005ꆣ 샻싊웚쿞뷡릹ꎨterm structureꎩꎬ쫇쒳룶쪱뗣늻춬웚쿞뗄샻싊쯹ퟩ돉뗄튻쳵쟺쿟ꆣ틲캪퓚쒳룶쪱뗣ꎬ쇣쾢욱햮좯뗄떽웚쫕틦싊뗈폚룃쪱웚뗄샻싊ꎬ쯹틔샻싊웚쿞뷡릹튲뿉틔뇭쪾캪쒳룶쪱뗣쇣쾢욱햮좯뗄쫕틦싊쟺쿟ꎨyield curveꎩꆣ쯼쫇닺뚨볛ꆢ뷰죚닺욷짨볆ꆢ놣횵뫍럧쿕맜샭ꆢ쳗샻틔벰춶믺뗈뗄믹ힼꆣ틲듋ꎬ뛔샻싊웚쿞뷡릹컊쳢뗄퇐뺿튻횱쫇뷰죚쇬폲뗄튻룶믹놾뿎쳢ꆣ 샻싊웚쿞뷡릹쫇튻룶럇뎣맣삫뗄퇐뺿쇬폲ꎬ늻춬뗄톧헟뚼듓늻춬뗄뷇뛈뛔룃컊쳢뷸탐쇋첽쳖ꎬ듓쒳튻랽쏦뗃돶쇋튻킩뷡싛뫍붨틩ꆣ룹뻝늻춬뗄뷇뛈뫍랽쿲ꎬ헢킩퇐뺿믹놾짏뿉틔럖캪컥샠ꎺꎨ1ꎩ샻싊웚쿞뷡릹탎돉볙짨ꎻꎨ2ꎩ샻싊웚쿞뷡릹뺲첬맀볆ꎻꎨ3ꎩ샻싊웚쿞뷡릹ퟔ짭탎첬뗄캢맛럖컶ꎻꎨ4ꎩ샻싊웚쿞뷡릹뚯첬쒣탍ꎻꎨ5ꎩ샻싊웚쿞뷡릹뚯첬쒣탍뗄쪵횤볬퇩ꆣ놾컄룹뻝헢컥룶럖샠뛔샻싊웚쿞뷡릹퇐뺿뷸탐쇋헻샭뫍쫶움ꎬ늢퓚믹뒡짏쳡돶쇋캴살뿉쓜뗄퇐뺿랽쿲ꆣ 퓚샻싊웚쿞뷡릹컄쿗믘맋랽쏦ꎬ폐뗄톧헟틑뺭퓚듳솿퇐뺿뗄믹뒡짏뷸탐쇋쿠맘뗄컄쿗믘맋퇐뺿ꎬ뇈죧Jabbour and Mansi(2002)뛔샻싊웚쿞뷡릹뺲첬맀볆뗄믘맋ꎬGibson, Lhabitant 1룐킻뷌폽늿폅탣쟠쓪뷌쪦훺볆뮮ꆰ훐맺탅폃럧쿕뛈솿뫍뿘훆쒣탍ꆱ쿮쒿ꆢ뷌폽늿죋컄짧믡뿆톧퇐뺿2003쓪뛈늩쪿뗣믹뷰퇐뺿쿮쒿ꆰ훐맺샻싊샠뷰죚닺욷뗄짨볆뫍뚨볛ꆱꎨ03JB790016ꎩꆢ뢣붨쪡짧뿆ꆰ쪮컥ꆱ맦뮮ꎨ뗚뛾웚ꎩ쿮쒿ꎨ2003B069ꎩ뗄훺ꆣ놾컄맛뗣뷶듺뇭ퟷ헟룶죋맛뗣ꆣ
and Talay(2001)ꎬYan(2001), Dai and Singleton (2003)뛔샻싊웚쿞뷡릹뚯첬쒣탍뗄맩쓉뫍헻샭ꎬ틔벰Shiller and McCulloch(1990)뫍Melino(1986)뛔샻싊웚쿞뷡릹튻냣룅쓮뗄럖컶ꆣ떫쫇헢킩믘맋뚼횻벯훐폚샻싊웚쿞뷡릹퇐뺿뗄쒳튻랽쏦ꎬ쎻폐뛔샻싊웚쿞뷡릹퇐뺿ퟷ좫쏦뗘럖컶뫍헻샭ꎬ늢뛔캴살뗄랢햹랽쿲뷸탐ퟜ뷡뫍맩쓉ꆣ놾컄뗄뒴탂횮뒦벴퓚폚듋ꎬ춨맽컥룶럖샠뛔샻싊웚쿞뷡릹퇐뺿뷸탐쿠뛔좫쏦뗘헻샭뫍쫶움ꎬ늢퓚믹뒡짏쳡돶캴살뿉쓜뗄퇐뺿랽쿲ꆣ 튻ꆢ샻싊웚쿞뷡릹탎돉볙짨 샻싊웚쿞뷡릹쫇평늻춬웚쿞뗄샻싊쯹릹돉뗄튻쳵쟺쿟ꆣ평폚늻춬웚쿞뗄샻싊횮볤듦퓚닮틬ꎬ쯹틔샻싊웚쿞뷡릹뿉쓜폐뫃벸훖탎ힴꎺ쿲짏쟣킱ꆢ쿲쿂쟣킱ꆢ쿂낼ꆢ짏춹뗈ꆣ캪쇋뷢쫍헢킩늻춬탎ힴ뗄샻싊웚쿞뷡릹ꎬ죋쏇뻍쳡돶쇋벸훖늻춬뗄샭싛볙짨ꆣ헢킩볙짨냼삨ꎺ쫐뎡풤웚볙짨ꎨexpectation hypothesisꎩꎬ쫐뎡럖룮볙짨ꎨmarket segmentation hypothesisꎩ뫍쇷뚯탔욫뫃볙짨ꎨliquidity preference hypothesisꎩꆣ캪쇋뛔헢킩볙짨뷸탐퇩횤ꎬ늻춬뗄톧헟듓늻춬뗄뷇뛈뷸탐쇋럖컶ꆣ ꎨ튻ꎩ뛔쫐뎡풤웚볙짨ퟔ짭쎬뛜뗄럖컶 퓚쫐뎡풤웚볙짨뗄뻹뫢쳵볾쿂ꎬ쿠춬웚쿞쓚늻춬춶랽쪽쯹믱뗃뗄풤웚쫕틦싊펦룃쫇쿠춬뗄ꆣ 1ꆢ퓚쒳튻룶쪱웚ꎬ돖폐뛌웚햮좯뫍뎤웚햮좯뗄웚췻쫕틦싊쫇튻퇹뗄ꆣ뛔튻룶웚쿞캪1웚뗄쇣쾢햮좯뛸퇔ꎬ웤ퟜ쫕틦싊캪1+rꎻ뛔웚쿞캪n웚뗄쇣쾢햮좯뛸퇔ꎬ웤1웚뗄ퟜ쫕틦1,tnP(1+r)n−1,t+1n,t싊캪=ꆣ웤훐ꎬr,i=1,2,...,n듺뇭쪱뿌t뗄i웚샻싊ꆣ쯹틔ꎬ룃냦i,tn−1P(1+r)ntn−1t+놾뿉틔뇭쪾캪ꎺ n(1+r)n,tn−(n−1)1+r=E)=(1+r)E(1+r) ꎨ1ꎩ 1,ttn,ttn−1,t+1n−1(1+r)n−1,t+12ꆢ뎤웚햮좯퓚n룶쪱웚훐뗄ퟜ쫕틦싊뗈폚n룶튻웚햮좯퓚n웚훐뗄뢴뫏ퟜ쫕틦싊뗄웚췻횵ꎬ튲뗈폚1웚햮좯폫n-1웚햮좯뢴뫏ퟜ쫕틦싊뗄웚췻횵ꆣ nn−1(1+r)=E((1+r)(1+r)(1+r)....(1+r))=(1+r)E((1+r))ꎬ n,tt1,t1,t+1,t+21,t+n−1,ttn−1,t+1n(1+r)n,t1+r= ꎨ2ꎩ 1,tn−1E((1+r))tn−1,t+1nn(1+r)(1+r)n,tn,t룹뻝ꎨ1ꎩꎬ1+r=E)ꎬ룹뻝ꎨ2ꎩꎬ1+r=ꆣ 1,tt1,tn−1n−1(1+r)E((1+r))n−1,t+1tn−1,t+1nn(1+r)(1+r)n,tn,t떫쫇ꎬ평햲즭늻뗈쪽뿉횪ꎬE≠ꎬꎨ1ꎩ뫍ꎨ2ꎩ뮥쿠tn−1n−1(1+r)E((1+r))n−1,t+1tn−1,t+1쎬뛜ꎨCox, Ingersoll and Ross, 1981ꎩꆣ Cochrane(2000)퓚솬탸쪱볤쳵볾쿂뛔룃컊쳢뷸탐쇋럖컶ꎬ죏캪퓚솬탸쪱볤쳵볾쿂ꎬ룃볙짨쫇튻훂뗄ꆣ떫쫇Lin(2003)춨맽퇏룱뗄췆떼횤쏷쇋ꎬ퓚솬탸쪱볤쳵볾쿂ꎬ헢룶ퟔ쿠쎬뛜춬
퇹듦퓚ꆣ쯹틔쫐뎡풤웚볙짨놾짭뻍듦퓚ퟅ좱쿝ꆣ ꎨ뛾ꎩ뛔샻싊웚쿞뷡릹탎돉볙짨볬퇩 늻춬뗄톧헟샻폃늻춬뗄랽램ꎬ쪹폃늻춬맺볒뗄쫽뻝뛔샻싊웚쿞뷡릹탎돉볙짨뷸탐쇋볬퇩ꆣ퓚죽룶볙짨훐ꎬ쫐뎡풤웚볙짨쫇ퟮ훘튪뗄볙짨ꎬ쯹틔듳뛠쫽뗄퇐뺿뚼쫇솢ퟣ폚쫐뎡풤웚볙짨ꎬ늢퓚듋믹뒡짏뾼싇쇷뚯탔틧돪ꆣ 1ꆢ펢맺쫐뎡ꆣCargill(1975)샻폃펢맺뗄쇏뛔샻싊웚쿞뷡릹뗄풤웚볙짨뷸탐쇋쪵횤럖컶늢뻜뻸쇋쫐뎡풤웚볙짨ꆣ 2ꆢ쏀맺쫐뎡ꆣLeeꎨ1989ꎩ샻폃퓚듺뇭탔춶헟킧폃ퟮ듳뮯뗄믹뒡짏ꎬ쪹폃맣틥뻘랽램뛔쫐뎡풤웚볙짨뗄럇쿟탔맘쾵뷸탐쇋럖컶ꎬ죏캪쯦쪱볤뇤뮯뗄럧쿕틧돪뫍틬랽닮뛔럖컶햽뫳쏀맺뗄햮좯쫐뎡쪮럖훘튪ꆣCulbertson(1957)뛔쇷뚯탔틧돪뗈펰쿬샻싊웚쿞뷡릹뗄틲쯘뷸탐쇋럖컶ꎬ랢쿖쫐뎡풤웚볙짨늻쓜뷢쫍쏀맺햽뫳쇏ꆣCampbell(1986a)뛔샻싊웚쿞뷡릹뷸탐쇋쿟탔맀볆ꎬ늢횤쏷늻춬탎쪽뗄쫐뎡풤웚볙짨퓚뎣쫽뗄럧쿕틧돪쳵볾쿂뿉틔춬쪱돉솢ꎬ듓뛸뻍뷢뻶쇋Cox, Ingersoll and Ross(1981)쯹쳡돶뗄늻춬탎쪽뗄쫐뎡풤웚볙짨퓚럧쿕틧돪캪0쪱뮥쿠쎬뛜뗄컊쳢ꆣCampbell and Shiller(1991)퓲럖컶쇋뎤뛌웚샻싊닮뻠ꎨYield spreadꎩ뛔붫살샻싊뇤뚯뗄풤웚쓜솦늢랢쿖쇋튻킩폫쫐뎡풤웚볙짨늻럻뗄쿖쿳ꆣMankiw and Miron(1986)춨맽붫샺쪷쇏뮮럖돉늻춬뗄쟸폲ꎨregimeꎩ뛔샻싊웚쿞뷡릹뗄쫐뎡풤웚볙짨뷸탐쇋쪵횤볬퇩ꆣBekaert, Hodrick and Marshall(1997)뛔쫐뎡풤웚볙짨믘맩쒣탍훐뗄킡퇹놾욫컳컊쳢뷸탐쇋럖컶ꎬ퇐뺿뇭쏷킡퇹놾쪱볤탲쇐뿉틔떼훂맀볆뗄욫컳ꆣ 3ꆢ좫쟲쫐뎡ꆣMcCown(2001)샻폃8룶맺볒뗄쫽뻝뛔샻싊웚쿞뷡릹탎ힴ뫍막욱쫐뎡쫕틦횮볤뗄쿠맘탔뷸탐쇋럖컶ꆣ쪵횤뷡맻뇭쏷ꎬ떱샻싊웚쿞뷡맻떹쪱ꎨinvertedꎩꎬ3룶맺볒돶쿖뢺럧쿕틧돪ꆣ뛸쟒ꎬ죧맻쏀맺뫍뗂맺뗄샻싊웚쿞뷡릹떹ꎬ웤쯻맺볒믡돶쿖뢺뗄럧쿕틧돪ꎬ듓뛸횤쪵쇋튻룶쫀뷧탔럧쿕틲ퟓ뗄듦퓚ꆣ 4ꆢ훐맺쫐뎡ꆣ뚫뎽ꎨ1996ꎩ뫍쯎뮴쯉ꎨ1997ꎩ럖뇰샻폃럇쿟탔믘맩뫍쿟탔믘맩뗄랽램뛔컒맺뗄쇣쾢욱햮좯뷸탐럖컶ꆣ쳆웫쏹뫍룟쿨ꎨ2002ꎩ샻폃춬튵닰뷨쫐뎡뗄샻싊쫽뻝뛔풤웚샭싛뷸탐쇋쪵횤ꆣ쪵횤뷡맻뇭쏷ꎺ춬튵닰뷨샻싊믹놾짏럻뫏쫐뎡풤웚샭싛ꎬ벴뎤뛌웚샻싊뗄닮뿉틔ퟷ캪캴살샻싊뇤뚯뗄솼뫃풤닢ꎬ떫쫇뛌웚샻싊튲듦퓚ퟅ튻킩맽뛈랴펦뗄쿖쿳ꆣ듋췢ꎬ뮹폐퇮듳뾬ꆢ퇮폂ꎨ1997ꎩꎬ튦뎤믔ꆢ솺풾뻼ꎨ1998ꎩ뛔맺햮쫕틦싊뗄퇐뺿ꆣ떫헢킩퇐뺿듳늿럖뚼쫇춣쇴퓚쾢욱햮좯뗄떽웚쫕틦싊짏ꎬ쎻폐퇐뺿헦헽틢틥짏뗄샻싊웚쿞뷡릹ꆣ 5ꆢ쫐뎡뗷닩쇏ꆣFroot(1989)룹뻝쫐뎡뗷닩쇏뛔쫐뎡풤웚볙짨퓚맀볆붫살샻싊뗄폐킧탔뷸탐쇋쪵횤럖컶ꆣ쪵횤럖컶뷡맻뇭쏷쫐뎡풤웚볙짨퓚뛌웚쓚컞킧ꎬ퓚뎤웚쓚뻟폐튻뚨뗄맀볆쓜솦ꆣ 뛾ꆢ샻싊웚쿞뷡릹뺲첬맀볆 떱쫐뎡짏듦퓚뗄햮좯훖샠폐쿞쪱ꎨ쳘뇰뛔햮좯쫐뎡늻랢듯맺볒뛸퇔ꎩꎬ죧뫎룹뻝폐킧뗄햮좯볛룱쇏뛔헻룶샻싊웚쿞뷡릹뷸탐맀볆ꎬ쫇뷸탐햮좯퇐뺿뗄튻룶훘튪쓚죝ꆣ늻춬뗄톧헟쳡돶쇋늻춬뗄맀볆랽램ꎬ웤뫋탄뻍쫇뛔쳹쿖몯쫽δ(m)뗄맀볆ꆣ m0볙짨P=100δ(m)+cδ(m)dmꎬP듺뇭햮좯볛룱ꎬδ(m)쫇웚쿞캪m뗄떥캻쇣쾢햮0∫0좯뗄쳹쿖횵ꎬm쫇햮좯뗄떽웚죕ꎬc쫇샻쾢뛮ꆣ 0죧맻볙짨ꎺ kδ(m)=a+af(m)ꎬa=1,f(0)=0ꎬ퓲 0∑jj0jj=1
knkP=100(1+af(m))+c(1+af(m)) ∑jj0∑∑jjij=1i=0j=1km0=100+cm+a(100f(m)+cf(m)dm) 0∑jj0j∫0j=1틲듋ꎬ죧맻컒쏇쇮ꎺ m0y=P−100−cmꎬx=100f(m)+cf(m)dmꎬ뻍뿉틔뗃떽ꎺ 0jj0j∫0ky=ax ∑jjj=1k퓚믘맩쒣탍훐ꎬ y=ax+ε ∑jjtj=1쯹틔퓚쒳룶쪱뗣t,컒쏇뻍뿉틔춨맽뛔f(m)틔벰k뗄볙짨쟳돶aꎬ춨맽a뻍뿉틔쟳돶jjj죎뫎쪱웚뗄헛쿖횵ꆣ틲듋ꎬ퇐뺿뗄훘뗣퓚폚뛔몯쫽탎쪽틔벰럖룮쟸볤k뗄톡좡ꆣ쿠맘뗄퇐뺿폐McCulloch(1971)ꎬLin and Yeh(2001)ꎬCarleton and Cooper(1976)ꎬShea(1984)ꎬFisher, Nychka and Zervos(1995)뗈ꆣJeffrey, Linton and Nguyen(2000)퓲뛔늻춬뗄몯쫽맀볆뷡맻뷸탐쇋뇈뷏ꆣ횣헱쇺뫍쇖몣ꎨ2003aꎩ샻폃McCulloch(1971)퇹쳵몯쫽뫍쾢욱냾샫램뛔컒맺쫐뎡샻싊웚쿞뷡릹뷸탐쇋뺲첬맀볆ꎬ릹퓬돶훐맺헦헽뗄쫐뎡샻싊웚쿞뷡릹ꆣ횣헱쇺뫍쇖몣ꎨ2003bꎩ맀볆돶훐맺햮좯쫐뎡뗄캥풼럧쿕틧돪늢뷸탐쇋럖컶ꆣ쇖몣뫍횣헱쇺ꎨ2004ꎩ퓲뛔훐맺쫐뎡샻싊뗄쇷뚯탔틧돪뷸탐쇋맀볆뫍럖컶ꆣ 죽ꆢ샻싊웚쿞뷡릹ퟔ짭탎첬캢맛럖컶 샻싊웚쿞뷡릹뗄뇤뚯튲폐욽탐틆뚯뫍럇욽탐틆뚯ꆣ평폚샻싊횱뷓뫍햮좯뗄쫕틦싊쿠맘ꎬ헢킩늻춬랽쪽뗄틆뚯뛔햮좯ퟩ뫏뗄쫕틦믡닺짺뫜듳뗄펰쿬ꎬ늢뷸뛸펰쿬햮좯ퟩ뫏맜샭뗄벼쫵ꆣ캪쇋뫢솿샻싊웚쿞뷡릹뗄탎ힴ뇤뚯뛔햮좯춶ퟩ뫏뗄펰쿬늢퓚듋믹뒡짏뷸탐폐킧뗄맜샭ꎬ듯떽ꆰ쏢틟ꆱ뗄쒿뗄ꎬ훚뛠뗄톧헟뛔샻싊웚쿞뷡릹놾짭뗄탎첬ퟷ쇋듳솿뗄럖컶ꎬ늢뛔샻싊웚쿞뷡릹뗄욽탐틆뚯뫍럇욽탐틆뚯쳵볾쿂뗄햮좯ퟩ뫏쳗웚놣횵뗄컊쳢뷸탐쇋짮죫뗘퇐뺿ꆣ ꎨ튻ꎩ샻싊웚쿞뷡릹틲ퟓ쒣탍폫훷돉럖럖컶 샻싊웚쿞뷡릹틲ퟓ쒣탍쯹쓜ퟶ뗄뻍쫇뷒쪾쇋쫽뻝쯹낵쪾뗄샻싊뇤뚯잱퓚틲쯘뗄춳볆탎쪽ꆣ웤뺭뗤컄쿗쫇Litterman and Scheinkman(1991)ꆣ쯻쏇돆헢킩틲쯘캪쮮욽ꎨlevelꎩꆢ쟣킱돌뛈ꎨsteepnessꎩ뫍쟺뛈ꎨcurvatureꎩꆣ쯻쏇퓚뛔쏀맺샻싊웚쿞뷡릹뗄퇐뺿훐ꎬ뷨본쇋뛠틲쯘쳗샻뚨볛샭싛ꎬ춨맽붨솢쿟탔뛠틲ퟓ쒣탍ꎬ뾼달쇋햮좯쫕틦폫쾵춳럧쿕틲쯘뫍럇쾵춳럧쿕틲쯘횮볤뗄맘쾵ꆣ쯻쏇퇐뺿쇋쮮욽틲쯘ꆢ쟣킱틲쯘틔벰쟺뛈틲쯘퓚샻싊웚쿞뷡릹뇤뮯훐뗄ퟷ폃ꆣDai and Singleton(2000)폃뗄틲쯘캪ꎺ쮮욽ꎨlevelꎩꆢ킱뛈ꎨslopeꎩ뫍뫻뗻쪽ꎨbutterflyꎩꆣChen and Scott(1993)ꎬ퓲돆헢킩틲쯘캪ꎺ돖탸탔ꎨpersistentꎩꆢ뷏짙돖탸탔ꎨless persistentꎩ뫍잿뻹횵믖뢴 ꎨstrong mean-revertingꎩꆣ헢킩뚼쫇폃살쏨쫶잱퓚틲쯘쫇죧뫎펰쿬샻싊웚쿞뷡릹뗄ꆣ 쯦뫳퇐뺿죋풱닉좡샠쯆뗄랽램ꎬ헫뛔늻춬맺볒뗄햮좯쫐뎡햹뾪듳솿뗄퇐뺿ꎬ죧Buhler and Zimmermann(1996), DꆯEcclesia and Zenios(1994), Sherris(1994), Martellini and Priaulet(2000), Maitland(1999), Schere and Avellaneda(2000) 럖뇰뛔뗂맺ꆢ죰쪿ꆢ틢
듳샻ꆢ냄듳샻퇇ꆢ램맺ꆢ쓏럇ꆢ삭쏀뗈맺볒뫍뗘쟸뗄샻싊웚쿞뷡릹뷸탐쇋훷돉럖뫍틲ퟓ럖컶ꆣ훬럥ꎨ2002ꎩ뫍쇖몣ꎨ2004ꎩ뛔훐맺뗄쫐뎡샻싊웚쿞뷡릹뷸탐쇋훷돉럖럖컶ꎬ늢퓚듋믹뒡짏뛔훐맺햮좯ퟩ뫏뗄쳗웚놣횵쳡돶쇋죴룉붨틩ꆣ ꎨ뛾ꎩ 샻싊웚쿞뷡릹뗄뇤뚯틔벰닺쏢틟 샻싊웚쿞뷡릹뇤뚯쫇횸늻춬웚쿞뗄샻싊뗄쿠뛔뇤뚯ꎬ쟺쿟뗄욽탐틆뚯쫇횸쯹폐웚쿞뗄샻싊뇤뚯쫇쿠춬뗄ꎬ뛸샻싊웚쿞뷡릹뗄럇욽탐틆뚯헢틢캶ퟅ룷훖웚쿞샻싊뇤뚯뗄믹뗣쫇늻춬뗄ꆣ 1ꆢ샻싊웚쿞뷡릹뗄욽탐틆뚯 뛔폚샻싊웚쿞뷡릹뗄욽탐틆뚯ꎬ뺭뗤뗄뛔닟쫇틀뻝뻃웚뛔쿠펦뗄햮좯ퟩ뫏뷸탐쏢틟ꆣ쏢틟뗄몬틥쫇컞싛샻싊죧뫎뇤뚯ꎬ닺폫뢺햮뗄뻃웚욥엤뻍뿉틔좷놣닺ퟩ뫏폐뎥뮹릫쮾햮컱뗄쓜솦ꆣ쯼쫗쿈평Readingtonꎨ1952ꎩ쳡돶뗄ꆣ뻃웚펳쇋닺볛룱뛔폚샻싊뇤뚯뗄쏴룐탔ꆣ틲듋ꎬ뻃웚퓚샻싊뇤뚯뫍햮좯쫕틦싊뇤뚯횮볤붨솢쇋솪쾵ꆣFisher and Weil (1971)ꎬBierwag뗈(1981),Bierwag뗈(1983), Brennan and Schwartz(1983)뗈뚼햹쪾쇋헢훖랽램죧뫎쓜릻복짙쫐뎡럧쿕ꆣ쇭췢ꎬBierwag and Khang(1979)죏캪떱횻듦퓚튻훖늻좷뚨탔살풴펰쿬샻싊웚쿞뷡릹쪱ꎬ샻폃뻃웚뿉틔뛔쾢욱햮좯뗄닺ퟩ뫏뷸탐쏢틟ꆣIngersoll(1983) ꎬNelson and Schaefer(1983) 뫍Brennan and Schwartz(1983)뚼쿔쪾돶뻃웚뇈웤쯻룼캪뢴퓓뗄랽램뇭쿖뗃룼뫃ꆣ 2ꆢ샻싊웚쿞뷡릹뗄럇욽탐틆뚯 럇욽탐틆뚯횸샻싊웚쿞뷡릹탎ힴ뗄뇤뮯ꆣ샺쪷뗘뾴ꎬ뿉틔맛달떽솽훖샠탍뗄샻싊웚쿞뷡릹럇욽탐틆뚯ꎺꎨ1ꎩ킱뛈뗄뇤뮯ꆣ샻싊웚쿞뷡릹킱뛈뗄뇤뮯쫇횸샻싊웚쿞뷡릹뇤뗃욽뮺믲헟뚸쟍ꆣꎨ2ꎩ쟺싊뗄뇤뮯ꆣ샻싊웚쿞뷡릹솽뛋뫍샻싊웚쿞뷡릹뗄훐볤늿럖랢짺쿠쯆떫쫇랽쿲쿠랴뗄뇤뮯ꆣ튲놻돆캪뫻뗻쪽뮻(butterfly shift)ꆣ뿉틔럖캪헽뫻뗻쪽뫍랴뫻뗻쪽솽훖ꆣ 평폚럇욽탐틆뚯쪱뒫춳틢틥짏뗄뻃웚늻퓙쓜릻뿌뮭돶듳늿럖뗄볛룱뇤뚯ꎬ틲듋튪볌탸샻폃뻃웚ꎬ뻍뇘탫뛔헢룶룅쓮뫍벼쫵뷸탐췘햹ꆣGarbade(1985)쳖싛쇋샻싊웚쿞뷡릹뗄킱싊랢짺뇤뮯쪱ꎬ죧뫎쏢틟ꆣGultekin and Rogalski(1984),Elton뗈(1988)뫍Elton 뗈(1990)퓚뛠틲ퟓ쒣탍뗄믹뒡짏랢햹늢볬퇩쇋쪵횤훷틥뗄뻃웚램퓲ꆣKlaffky뗈(1992)퓲쳡돶쮫뻃웚ꎨ훘탂릹붨뻃웚reshaping durationꎩ살랴펳샻싊웚쿞뷡릹퓚벫뗣뗄뇤뮯ꆣ Chambers and Carleton(1988)쳡돶뛠캬뻃웚(multiple duration)뗄붨틩ꎬ쯻쏇돆횮캪뻃웚쪸솿ꎨduration vectorsꎩꆣReitano (1992,1996)퇐뺿쇋럇욽탐틆뚯ꎬ쳡돶쇋쿠쯆뗄랽램ꎬ짨볆돶뻃웚쪸솿ꎨ랽쿲탔뻃웚ꎩ살랴펳뇤뮯뗄랽쿲ꎬ늢돆캪늿럖뻃웚(partial duration)ꆣ헢튻랽램평Hoꎨ1992ꎩ폨틔쇋랢햹ꆣ Ho(1992)쳡돶쇋믹폚쿠펦떽웚죕샻싊뇤뮯뗄ꆰ뫋탄샻싊뻃웚ꆱ(key rate duration)ꆣMoreno(1997)쳡돶ꆰ튻냣탔뻃웚ꆱ뗄랽램ꎬ죏캪뿉춨맽붫뒫춳뻃웚뫍춹탔튻냣뮯ꎬ틔믱뗃튻냣뮯뗄뻃웚뫍춹탔ꆣ튻냣뮯뻃웚뗄랽램뿉폃살볆쯣쳗웚놣 쯤좻훚뛠톧헟솦춼춨맽뛔뻃웚뗄룄퓬살뺡뿉쓜뗘쪹횮쓜릻뫢솿햮좯뗄샻싊럧쿕ꎬ떫퓚쪵볹훐튲듦퓚ퟅ쏢틟닺늻쓜췪싺뗘랢믓ퟷ폃뗄뿉쓜탔ꎬ뛸쟒뻃웚튲컞램뺫좷뗘뛈솿햮좯뗄샻싊럧쿕ꆣ웤훷튪풭틲폐ꎺ ꎨ1ꎩ췆동뫍쳡잰쫪믘럧쿕ꆣ쏢틟닺ꎨ틔벰뻃웚ꎩ쫇믹폚헢퇹뗄탅쓮ꎬ벴햮좯쯹풼뚨뗄쿖뷰쇷믡내쪱ퟣ뛮횧뢶ꆣ헢틢캶ퟅ쏢틟닺쫇틔쯹폐햮좯뚼늻믡놻췆동뫍쳡잰쫪믘캪볙짨잰쳡뗄ꆣ헢벴쫇쮵볙짨햮좯늻듦퓚췆동횧뢶럧쿕뫍쳡잰쫪믘럧쿕ꆣ쯹틔ꎬ죧맻햮좯ퟩ뫏훐뗄쒳훖햮좯놻췏잷믲쳡잰쫪믘ꎬ헻룶ퟩ뫏뻍쪧좥쇋쏢틟ퟷ폃ꆣ ꎨ2ꎩ퓚럇쮮욽샻싊웚쿞뷡릹짏뗄뛠훘럇욽탐틆뚯ꆣ쏢틟닺ꎨ틔벰뻃웚ꎩ뮹믹폚헢퇹뗄볙짨ꎺ샻싊웚쿞뷡릹쫇쮮욽뗄ꎬ쟺쿟뗄틆뚯쫇욽탐뗄ꎬ늢쟒틆뚯횻랢짺퓚믱뗃쯹릺싲뗄햮좯맦뚨뗄죎뫎횧뢶횮잰ꆣ떫쫇퓚쿖쪵훐ꎬ샻싊웚쿞뷡릹퓚뾪쪼늻쫇쮮욽뗄ꎬ뛸쟒샻싊웚쿞뷡릹뗄틆뚯볈늻뿉쓜쫇욽탐뗄ꎬ튲늻뿉쓜퓚쪱볤짏폐죎뫎뗄쿞훆ꆣ
ꎨ3ꎩ훘탂욽뫢ꆣ쪹폃쏢틟닺듦퓚뗄쇭튻룶컊쳢쫇쪱볤뗄쇷쫅뛔쯹돖폐햮좯뗄뻃웚뫍풼뚨쿖뷰쇷돶뗄뻃웚뗄펰쿬ꆣ쯦ퟅ쪱볤쇷쫅뫍샻싊웚쿞뷡릹뇤뮯ꎬ뻃웚뿉쓜믡내늻춬뗄쯙뛈룄뇤ꎬ햮좯ퟩ뫏뻍늻퓙뻟폐쏢틟쓜솦ꆣ헢틢캶ퟅ햮좯ퟩ뫏탨튪뺭뎣퓙욽뫢ꆣ 헢샯뗄훘탂욽뫢쫇횸돶쫛떱잰돖폐뗄쒳킩햮좯ꎬ붫쯻쏇쳦뮻돉쇭튻훖햮좯ꎬ틔뇣쪹탂뗄햮좯ퟩ뫏뗄뻃웚폫풼뚨뗄쿖뷰쇷돶뗄뻃웚놣돖튻훂ꆣ늻맽ꎬ평폚햮좯뗄쳦뮻믡듸살돉놾ꎬ뛸헢훖쳦뮻뗄돉놾뿉쓜믡뎬맽퓙욽뫢쯹듸살뗄쫕틦ꆣ ꎨ4ꎩ훚뛠뗄뫲톡닺ꆣ춨뎣듦퓚뛠훖뻟폐맦뚨뻃웚뗄햮좯ퟩ뫏ꎬ춶헟쏦쇙늻춬뗄톡퓱랽낸ꆣ튻훖랽램쫇쳴톡뻟폐ퟮ룟떽웚쫕틦싊뗄ퟩ뫏ꎨ벴쫇돉놾ퟮ뗍뗄ꎩꆣ쇭튻훖랽램쫇톡퓱폫쒿뇪ퟩ뫏ퟮ쿠쯆뗄ퟩ뫏ꎬ헢훖ퟩ뫏뇈웤쯻죎뫎ퟩ뫏뚼폐룼ퟮ킡뗄쯦믺맽돌럧쿕ꎨ벴춶ퟩ뫏뗄늨뚯싊ퟮ킡ꎩꆣ퓚헢훖ퟩ뫏훐ꎬ쯹폐햮좯뗄뻃웚뚼ퟮ뷓뷼풼뚨뗄쿖뷰쇷돶뗄뻃웚ꆣ떫쫇뛾헟쯹뻟폐뗄샻싊럧쿕좴췪좫늻튻퇹ꆣ 쯄ꆢ샻싊웚쿞뷡릹뚯첬쒣탍 ꎨ튻ꎩ믹놾샻싊웚쿞뷡릹뚯첬쒣탍 룹뻝샻싊웚쿞뷡릹쒣탍뗄췆떼맽돌ꎬ뿉틔럖캪솽훖샠탍ꎺ뗚튻훖샠탍뻍쫇뻹뫢쒣탍(Equilibrium Model)ꎬ룹뻝쫐뎡뗄뻹뫢쳵볾쟳돶샻싊쯹뇘탫ퟱ톭뗄튻룶맽돌ꎬ퓚헢킩쒣탍훐ꎬ쿠맘뗄뺭볃뇤솿쫇쫤죫뇤솿ꎬ샻싊쮮욽쫇쫤돶뇤솿ꎻ쇭튻훖샠탍쫇컞쳗샻쒣탍ꎨNo arbitrage Modelꎩꎬ춨맽쿠맘햮좯뗈닺횮볤뇘탫싺ퟣ뗄컞쳗샻쳵볾뷸탐럖컶ꎬ듋쪱샻싊쮮욽쫇튻룶쫤죫뇤솿ꎬ쿠맘뷰죚릤뻟뗄볛룱쫇쫤돶뇤솿ꆣ뇘탫쳘뇰횸돶뗄쫇ꎬ헢킩쒣탍뚼쫇붨솢퓚럧쿕훐탔쫀뷧훐ꎬ쯹쏨쫶뗄뻹쫇럧쿕훐탔쫀뷧훐뗄샻싊뇤뚯탐캪ꆣ 1ꆢ뻹뫢쒣탍ꆣ훷튪냼삨Vasicek(1977) 쒣탍뫍CIR(1985)쒣탍ꎬ듋췢뮹폐Rendleman and Barter(1980),Brennan and Schwartz(1982)뗈ꆣ ꎨ1ꎩ Vasicek(1977) 쒣탍ꆣVasicekꎨ1977ꎩ쳡돶ꎺ퓚럧쿕훐탔쫀뷧훐ꎬ샻싊뗄뇤뮯맽돌ퟱ듓ꎺ dr=k(θ−r)dt+σdzꎬa,b,σ뚼쫇뎣쫽ꆣ 웤훐ꎬr뇭쪾뛌웚쮲쪱샻싊ꎬk뇭쪾샻싊뻹횵믘맩쯙뛈ꎬθ뇭쪾뎤웚뻹횵ꎬσ뇭쪾늨뚯싊ꆣ Vasicek쒣탍쫇훚뛠샻싊웚쿞뷡릹쒣탍훐ퟮ볲떥뗄튻룶ꆣ쯼볙짨쯹폐뗄닎쫽뚼쫇뎣쫽ꎬ늻쯦쪱볤뇤뮯ꎬ뛸쟒늨뚯싊튲쫇튻룶뎣쫽ꎬ쎻폐뾼싇떽샻싊쮮욽뛔늨뚯싊룟뗍뗄펰쿬틔벰늨뚯싊놾짭뗄GARCH킧펦뗈ꆣ떫쫇쯼좴쓜릻뇈뷏뫃뗘쓢뫏쿖쪵쫽뻝ꆣ좱쿝쫇맽폚볲떥ꎬ쎻폐뾼싇떽샻싊뇘탫쫇튻룶듳폚0뗄헽쫽ꎬ틲듋퓚쒣쓢맽돌훐뻍뿉쓜돶쿖샻싊캪뢺뗄쟩뿶ꎬ헢늻럻뫏쿖쪵쟩뿶ꆣ ꎨ2ꎩCIR쒣탍ꆣCox, Ingersoll and Ross(1985a,b)퓚튻룶뿧웚뗄닺쫐뎡뻹뫢쒣탍훐뛔샻싊뗄웚쿞뷡릹쒣탍뷸탐쇋퇐뺿ꎬ늢쳡돶쇋CIR쒣탍ꆣ뻟쳥쓚죝캪ꎺ dr=k(θ−r)dt+σrdZꆣ CIR쒣탍뗄폅뗣쫇쯼닺짺폚뺭볃훐뗄쓚퓚뺭볃뇤솿뫍ퟜ쳥뻹뫢ꆣ틲듋ꎬ쯼냼몬쇋럧쿕믘뇜ꆢ쪱볤쿻럑욫뫃ꆢ닆뢻쿞훆ꆢ떼훂럧쿕늹뎥뗄틲쯘뫍훚뛠뗄춶톡퓱ꆣ뺡맜룃릫쪽뻟폐훚뛠폅뗣ꎬ떫쫇쯼첫뢴퓓ꎬ퓚맀쯣뺭볃닎쫽ꆢ럧쿕닎쫽뫍뷸탐쿖쪵풤닢랽쏦닺짺삧쓑ꆣ뛸쟒쯻쏇뗃돶뗄뷡싛쫇샻싊웚쿞뷡릹캪욽탐틆뚯ꎬ헢쫇늻럻뫏쿔쪾쟩뿶뗄ꆣ 2ꆢ컞쳗샻쒣탍ꆣ훷튪냼삨HJM(1992)쒣탍ꎬHo-Lee(1986)틔벰Hull and White(1990)쒣탍ꆣ듋췢ꎬ뮹폐Black, Derman and Toy(1990)뗈ꆣ ꎨ1ꎩHJM쒣탍ꆣHeath, Jarrow and Morton(1992)쳡돶ꎬ T쪱뿌쮲쪱풶웚샻싊f(t,T)
뗄뇤뮯럾듓ꎺ Tdf(t,T)=σ(t,T)σ(t,u)dudt+σ(t,T)dz(t)ꎬ ∫t틲듋헻룶쒣탍맀볆뗄닎쫽횻폐튻룶ꎬ벴늨뚯탔ꎬ뛸쟒헢룶늨뚯탔늻믡쯦ퟅ닢뛈뗄뇤뮯뛸뇤뮯ꆣ HJM쒣탍뗄훷튪랽램쫇컞쳗샻럖컶램ꎬ벴퓚n룶틲ퟓ럧쿕쒣탍쿂ꎬ뿉틔춨맽튻룶컞럧쿕닺뫍n룶럧쿕닺뗄ퟩ뫏릹퓬닺쫐뎡짏뗄쯹폐닺ꆣ룸뚨햮좯늨뚯싊뗄웚쿞뷡릹ꎬ뻍뿉틔뗃떽햮좯뚨볛뗄좫늿탅쾢ꎬ쯼쫇컞쳗샻쒣탍뗄믹ힼ쒣탍ꆣ떫쫇쒣탍놾짭퓚펦폃뗄맽돌훐튲믡닺짺컊쳢ꆣ퓚릹퓬샻싊뇤뚯뗄뛾닦쫽믲헟죽닦쫽쒣탍쪱ꎬ샻싊춨뎣퓚짏짽뫍쿂붵뫳뻍늻믡퓙훘탂뻛뫏ꆣ튲뻍쫇쮵ꎬ샻싊쿈짏짽뫳쿂붵폫쿈쿂붵뫳짏짽횮뫳쯹듯떽뗄늻쫇춬튻룶뷚뗣ꎬ샻싊뇤뚯늻쫇십뛻뿉럲솴ꆣ헢뻍믡떼훂뛾닦쫷쒣탍뗄ퟮ훕뷚뗣뗄벸뫎삩듳ꎬ벫듳뗘퓶볓볆쯣뫍쒣쓢뗄쓑뛈ꆣ ꎨ2ꎩHo-Lee쒣탍ꆣ Ho and Leeꎨ1986ꎩ쳡돶쇋튻룶믹폚컞쳗샻볙짨뗄샻싊웚쿞뷡릹뇤뚯쒣탍ꎬ죋쏇돆횮캪Ho-Lee쒣탍ꆣ뻟쳥뇭듯쪽캪ꎺ dr=θ(t)dt+σdzꎬ 2웤훐θ(t)=F(0,t)+σtꆣF(0,t)뇭쪾쪱뿌t뗄풶웚샻싊ꎬ쿂뇪t뇭쪾뛔t뗄욫떼쫽ꆣ tHo-Lee쒣탍폃튻훖뇈뷏볲떥뗄랽쪽살쒣쓢샻싊웚쿞뷡릹쯦쪱볤뗄뿉뇤탔ꎬ평ퟮ돵뗄샻싊웚쿞뷡릹뻶뚨뗄ꎬ틲듋쯼쫇튻룶쿠뛔뚨볛쒣탍ꎬ춬쪱평ퟮ돵웚쿞뷡릹뗄췢짺탔뻶뚨샻싊웚쿞뷡릹뗄뇤뮯튲쫇췢짺뗄ꆣ ꎨ3ꎩHull and White쒣탍ꆣHull and White(1990)쳡돶ꎬVasicek쒣탍뗄튻룶삩햹쫇ꎺ dr=(θ(t)−kr)dt+σdzꆣ ꎨ뛾ꎩ튻냣뮯삩햹쒣탍 돽쇋짏쏦럖컶뗄훚뛠샻싊웚쿞믺릹뗄뚯첬쒣탍횮췢ꎬ탭뛠톧헟퓚헢믹뒡짏뷸탐쇋룼뷸튻늽뗄퇐뺿ꎬ뗃돶쇋탭뛠룼폐틢틥ꆢ룼럻뫏쪵볊뗄뷡싛ꆣ 1ꆢ믹놾샻싊웚쿞뷡릹쒣탍뗄삩햹 ꎨ1ꎩ뾼싇늨뚯싊훍뫳킧펦ꎨGARCHꎩ뗄샻싊웚쿞뷡릹쒣탍 Brenner, Harjes and Kroner(1996)쳡돶쇋튻룶튻냣뮯뗄샻싊웚쿞뷡릹쒣탍ꆣ퓚헢룶쒣탍훐ꎬ늨뚯싊늻뷶폫샻싊쮮욽쿠맘ꎬ뮹뫍탅쾢ꎨinformation shockꎩ쿠맘ꆣ ꎨ2ꎩ뛠틲ퟓ쒣탍 Longstaff and Schwartz(1992)퓚CIR쒣탍믹뒡횮짏뾼싇쇋튻룶솽틲ퟓ(폃X뫍Y뇭쪾)뻹뫢쒣탍ꆣ헢룶쒣탍뿉틔뷢쫍늻춬탎ힴ뗄쫕틦싊쟺쿟ꆣ쯹쪹폃뗄볆솿럖컶랽램캪맣틥뻘랽램ꆣ ꎨ3ꎩ럇쿟탔쒣탍 Constantinides(1992)퓲퓚CIR믹뒡횮짏쳡돶쇋튻룶튻냣뮯뗄쒣탍ꆣ쒣탍쯹쪹폃뗄랽램쫇뚨볛뫋랽램ꎬ맀볆닉폃럇쿟탔랽램ꆣ퓚듋쒣탍훐ꎬ햮좯뗄볛룱뿉틔춨맽뷢컶뗄랽램쟳돶ꎬ뿉틔춨맽쫽뻝뷸탐킣ힼꆣ ꎨ4ꎩ럂짤쒣탍(affine model) Dai and Singleton(2003)춨맽튻룶럂짤쒣탍붫튻쾵쇐뗄샻싊웚쿞뷡릹쒣탍냼몬퓚룃샭싛뿲볜훐ꎬ쳡돶쇋튻룶튻냣뮯뗄샻싊웚쿞뷡릹쒣탍ꆣ쯻쏇횱뷓볙짨ꎺ dMt=−rdt−Λ'dW(t), ttMt
웤훐ꎬr캪쮲쪱샻싊ꆣW(t)쫇N룶뛀솢뗄늼샊퓋뚯뇤솿ꆣΛ듺뇭럧쿕뗄쫐뎡볛룱ꆣ뛸tt쟒ꎬ r=r(Y(t),t),Λ=Λ(Y(t),t),tt PPdY(t)=u(Y,t)dt+σ(Y,t)dW(t)YY헢뻍쫇튻룶ퟮ튻냣뮯뗄쒣탍ꎬ뿉틔냼삨N룶늻좷뚨풴뛔샻싊뗄펰쿬ꆣ 뺭맽뷸튻늽뗄볲뮯ꎬ dMPt=−rdt−σ(r,t)dW(t) trttMt럂짤쒣탍뿉틔붫탭뛠뗄쒣탍ꎬ죧Vasicek쒣탍ꎬCIR쒣탍ꎬHull-White쒣탍ꎬHo-Lee쒣탍뗈쓉죫떽헢룶샭싛뿲볜훐ꎬ뻟폐맣랺뗄펦폃잰뺰ꆣ 2듋췢ꎬ럅뿭럂짤몯쫽뗄볙짨ꎬ듋쒣탍뮹뿉틔뇤캪뛾듎ꆪꆪ룟쮹쒣탍ꆢ럇쿟탔쯦믺늨뚯3싊쒣탍ꆢ믺훆뮯쒣탍틔벰뾼싇쳸풾탐캪뗄샻싊웚쿞뷡릹쒣탍뗈ꆣ틲듋ꎬ헢쫇튻룶튻냣뮯뗄춨폃쒣탍ꆣ 2ꆢ믺훆뮻쒣탍 Bansal and Zhou(2001)뛔듦퓚믺훆뮻쟩뿶쿂뗄샻싊웚쿞뷡릹컊쳢뷸탐쇋퇐뺿뫍럖컶ꆣ쯹쪹폃뗄볆솿럖컶랽램쫇냫닎쫽(SNP)틔벰폐킧뻘(EMM)랽램ꆣ볬퇩뷡맻뇭쏷솽틲ퟓ믺훆뮻쒣탍뿉틔뫜뫃뗘쓢뫏샺쪷쇏ꆣ. Sanders and Unal(1988)뛔Vasicek쒣탍뗄믺훆뮻컊쳢뷸탐쇋럖컶ꎬ늢쟒랢쿖늻춬뗄믺훆뿉틔뇭쿖돶늻춬뗄뻹횵믘맩쳘헷ꆣ튻킩뻹횵믘맩쿖쿳쫇쿔훸뗄ꎬ뛸튻킩퓲쫇늻쿔훸뗄ꆣ쯹틔퓚퇐뺿샻싊뗄탐캪쪱ꎬ쪱볤뒰뿚뗄톡퓱쪮럖맘볼ꆣ듋췢ꎬ뮹폐Dai, Singleton and Yang(2003)뗈ꆣ 3ꆢ쳸풾쒣탍 Baz and Das(1996)뛔쳸풾ꆪꆪ욯틆샻싊웚쿞뷡릹뚯첬쒣탍ꎨjump-diffusion modelꎩ뗄쟳뷢랽램뷸탐쇋퇐뺿ꆣ볙짨ꎬ샻싊뗄뇤뚯럾듓삩햹뗄Vasicek쳸풾ꆪꆪ욯틆맽돌ꎺ dr(t)=α(β−r(t)dt+σdW(t)+JdN(t)ꎬ N(t)럾듓튻룶잿뛈캪λ뗄늴쯉맽돌ꆣ튲뻍쫇쮵ꎬ퓚쪱볤[t,t+dt]쓚랢짺1듎쳸풾뗄룅싊캪λdtꎬ죧맻랢짺쇋쳸풾ꎬdN(t)=1ꎻ죧맻쎻폐랢짺쳸풾ꎬ퓲dN(t)=0ꆣJ듺뇭쳸풾2뗄럹뛈ꎬ럾듓튻룶뻹횵캪θꆢ랽닮캪δ뗄헽첬럖늼ꆣdW(t)뫍dN(t)뮥쿠뛀솢ꆣ퓚헢킩쳵볾쿂ꎬ N(t)ttαT−αt−αuαujr(t)=e(r(0)+eαβdu+eσdW(u))+eT ∑j∫∫00j=1T듺뇭뗚j듎쳸풾뗄쪱볤ꎬ0≺T≺T≺...≺T≺tꎬN(t)뇭쪾쳸풾뗄듎쫽ꆣ춨맽j12N(t) 2 뇈죧Ahh, Dittmar and Gallant(2002)ꆣConstantinides(1992)튲뿉틔쫓캪쯼뗄튻룶쳘샽ꆣ 3 뇈죧Anderson and Lund(1997,1998)ꎬAhn and Gao(1999)ꆣ
튻뚨뗄랽램뻍뿉틔볆쯣돶쯆좻몯쫽늢뷸탐ퟮ듳쯆좻맀볆ꆣ 4ꆢ웤쯻쒣탍 Glodstein(2000)퓲붫풶웚샻싊ퟷ캪튻룶쯦믺폲뷸탐럖컶ꎬ늢뾼싇떽늻춬뗄떽웚죕뗄뒴탂횮볤뗄쿠맘맘쾵ꆣ퓚헢룶쒣탍훐ꎬ헻룶쫕틦싊쟺쿟쫇튻룶쫤죫뇤솿ꎬ뛸늻뷶뷶쫇뛌웚샻싊ꆣ Black(1995)춨맽붫샻싊쫓캪튻룶웚좨뛔샻싊뗄럖늼뷸탐쇋럖컶ꆣ틲캪샻싊놾짭늻쓜캪뢺쫽ꎬ틲듋쯼쫇튻룶웚좨ꆣ틲듋ꎬ컒쏇뿉틔붨솢퓊탭쏻틥샻싊캪뢺쫽뗄샻싊럖늼ꎬ좻뫳붫쓇킩뢺쫽뗄샻싊쮮욽폃0쳦듺ꎬ뻍뿉틔뗃떽쿖쪵훐뗄샻싊쮮욽럖늼ꆣ 샮훙량뗈ꎨ2002ꎩ뛔듦퓚쫐뎡쒦닁쳵볾쿂뗄샻싊웚쿞뷡릹뷸탐쇋퇐뺿ꆣ헢킩쫐뎡쒦닁냼삨싲싴볛닮ꆢ붻틗럑틔벰쮰뢳뗈ꆣ퓚헢킩쒦닁쳵볾쿂ꎬ샮훙량뗈죋퇐뺿쇋쫐뎡싺ퟣ컞쳗샻럖컶쪱샻싊웚쿞뷡릹쯹펦룃싺ퟣ뗄쳵볾ꆣ 컥ꆢ샻싊웚쿞뷡릹뚯첬쒣탍뗄쪵횤볬퇩 퓚뛔샻싊웚쿞뷡릹쒣탍뗄샭싛퇐뺿믹뒡횮짏ꎬ훚뛠뗄톧헟뚼뛔늻춬뗄웚쿞뷡릹쒣탍뷸탐쇋쪵횤볬퇩ꎬ틔뛔늻춬뗄쒣탍뷸탐에뇰뫍뇈뷏ꆣ쪵횤럖컶뿉틔럖돉벸룶샠뇰ꎺꎨ1ꎩ뛔샻싊떥캻룹컊쳢뗄볬퇩ꎻꎨ2ꎩ뛔늻춬웚쿞뷡릹쒣탍뗄뇈뷏퇐뺿ꎻꎨ3ꎩ뛔쒳룶쳘뚨웚쿞뷡릹쒣탍뗄럖컶ꎻꎨ4ꎩ뛔쒣탍뿉뾿탔뗄럖컶ꆣ ꎨ튻ꎩ뛔샻싊떥캻룹뗄볬퇩 틲캪튻냣뗄샻싊웚쿞뷡릹뚯첬쒣탍뚼볙짨샻싊럾듓튻룶뻹횵믘맩맽돌ꎬ늢퓚듋믹뒡짏햹뾪럖컶ꆣ틲듋캪쇋퇩횤헢킩쒣탍뗄뿉탐탔ꎬ쫗쿈뻍뇘탫뛔샻싊쫇럱헦헽럾듓튻룶뻹횵믘맩맽돌뷸탐퇩횤ꆣ Wang and Zhang(1997)뛔샻싊뗄떥캻룹컊쳢뷸탐쇋쪵횤럖컶ꎬ틔뛔샻싊쫐뎡뗄폐킧탔뷸탐퇩횤ꆣ룹뻝쯻쏇뗄볬퇩랽램틔벰볬퇩뷡맻ꎬ떥캻룹맽돌뿉틔놻쿔훸뗘뻜뻸ꎬ뇭쏷샻싊쫐뎡듦퓚ퟅ뻹횵믘맩맽돌ꆣ Lai(1997)뛔떥캻룹컊쳢뷸탐쇋튻룶럇뎣뫃뗄샭싛럖컶뫍쪵횤볬퇩ꆣ틲캪떥캻룹횻쫇볬퇩I(1) 믲헟 I(0)맽돌, 쯼쎻폐볬퇩I(d) d<1ꎬ틲듋퓚쪵횤훐볙짨쳵볾첫잿ꆣ쯹틔탨튪튻룶탂뗄랽램살퇩횤I(d), 0<d<1ꆣ죧맻쪵횤뷡맻횧돖쯼ꎬ퓲쪱볤탲쇐럾듓튻룶뻹횵믘맩맽돌ꎬ뻟쳥쪹폃뗄럖컶랽램쫇뢵솢튶뇤뮯ꆣ Pesando(1979)뛔폐킧쫐뎡짏뗄뛌웚샻싊뫍풶웚샻싊뗄쯦믺폎ퟟ컊쳢뷸탐쇋럖컶ꆣ퓚쿖쪵짺믮훐ꎬ평폚ꎺꎨ1ꎩ풶웚샻싊뗄맀볆탔훊ꎻꎨ2ꎩ샻싊뗄럇쯦믺폎ퟟ탔ꎻ뎤웚샻싊뿉틔뇭쿖돶쏷쿔뗄탲쇐쿠맘탔ꆣ룃컄캪샻싊뗄럇떥캻룹탔헒떽쇋쟐쪵뗄횤뻝ꆣ ꎨ뛾ꎩ 뛔늻춬웚쿞뷡릹쒣탍뗄뇈뷏퇐뺿 Durham(2002)샻폃Durham and Gallant(2002)뗄볆솿럖컶랽램뛔늻춬뗄웚쿞뷡릹쒣탍뷸탐쇋쪵횤볬퇩ꆣ볬퇩뷡맻뇭쏷욯틆쿮뛔쒣탍뇭쿖뫃뮵늻믡닺짺펰쿬ꆣ뛔욯틆싊뗄뇤뮯퓶볓튻킩뇤뮯쯹쓜듸살뗄킧맻늻믡뫃폚뎣쫽욯틆싊ꆣ쯦믺늨뚯싊쓜릻쳡룟쒣탍뗄쓢뫏돌뛈ꎬ떫쫇뛔햮좯뚨볛쎻폐듸살뛠듳뗄뫃뒦ꆣ Bali(1999)뛔늻춬뗄샻싊웚쿞뷡릹쒣탍뷸탐쇋쪵횤럖컶ꎬ뷡맻뇭쏷욯틆싊뫍늨뚯싊캪뎣쫽뗄쒣탍틔벰늨뚯싊캪샻싊쮮욽몯쫽뗄쒣탍맽뛈잿뗷쇋샻싊쮮욽뛔늨뚯싊뗄펰쿬ꆣퟮ뫃뗄쒣탍쫇늨뚯싊캪샻싊쮮욽뫍탅쾢솽룶틲쯘뗄몯쫽ꆣ Chan뗈(1992)샻폃맣틥뻘ꎨGMMꎩ맀볆랽램뛔늻춬뗄샻싊웚쿞뷡릹쒣탍뷸탐쇋쪵횤뇈뷏ꎬ뷡맻뇭쏷늨뚯싊쫜럧쿕쮮욽펰쿬뗄쒣탍뇭쿖ퟮ뫃ꆣ뷡맻춬퇹뇭쏷뛔욯틆싊뷸탐룄뷸늻믡뛔쒣탍닺짺첫듳뗄펰쿬ꆣ뛸쟒ꎬ뷡맻뮹뇭쏷튻킩뺭뎣퓋폃뗄쒣탍ꎬ죧Vasicek 쒣탍뗈ꎬ뇭쿖뫜닮ꆣ Schlogl and Sommerꎨ1997ꎩ춨맽뫡뷘쏦럖컶ꎨcross sectional analysisꎩ뛔늻춬샻싊웚쿞뷡릹쒣탍뷸탐쇋볬퇩뫍뇈뷏ꆣ쪵횤뷡맻랢쿖ꎬ퓚샻싊웚쿞뷡릹뗄럖컶훐ꎬ뻹횵믘맩랽
돌뫍틲ퟓ쫽솿뗄톡퓱튪뇈뛔샻싊럖늼뗄톡퓱룼캪훘튪ꆣ Johannesꎨ2003ꎩ뛔튻냣뗄샻싊웚쿞뷡릹욯틆쒣탍뷸탐쇋럖컶ꎬ랢쿖헢킩쒣탍컞램닺짺돶춬샺쪷쫽뻝쿠럻뫏뗄럖늼늢퓚듋믹뒡짏쳡돶쇋쳸풾틲쯘ꆣ헢킩쳸풾틲쯘뫍훐퇫틸탐뗄믵뇒헾닟탐캪듦퓚뫜듳뗄쿠맘탔ꆣ뾼싇쳸풾탐캪믡펰쿬떽웚좨뗄뚨볛ꎬ떫쫇뛔햮좯뗄쫕틦싊풤닢좴늻믡닺짺펰쿬ꆣ ꎨ죽ꎩ뛔쳘뚨샻싊웚쿞뷡릹쒣탍뗄럖컶 Fernandez(2001)샻폃훇샻뗄쫽뻝닉폃럇닎쫽볬퇩뗄랽램뛔샻싊웚쿞뷡릹뷸탐쇋쪵횤럖컶ꆣ쯹맀볆뗄쒣탍쫇떥틲ퟓ쒣탍ꎬ욯틆싊뫍늨뚯싊뚼쫇샻싊쮮욽뗄몯쫽ꆣ뷡맻횤쪵쇋훇샻웚쿞뷡릹쿲쿂뗄쟷쫆ꎬ헢뿉틔폃훐퇫틸탐뗄믵뇒헾닟믲헟쫐뎡럖룮샭싛뷸탐뷢쫍ꆣ Karoui, German and Lacoste(2000)뛔HJM쒣탍훐쯹쪹폃뗄ힴ첬뇤솿톡퓱컊쳢뷸탐쇋럖컶뫍퇐뺿ꆣ퇐뺿뷡맻뇭쏷솽룶뇤솿뿉틔뷢쫍95%틔짏뗄샻싊뇤뚯ꎬ떫쫇뛔늨뚯싊퓲탨튪룼뛠뗄뇤솿ꆣ Brown and Dybvig(1986)샻폃뫡뷖쏦쏀맺맺뿢좯뗄쫽뻝뛔떥틲ퟓCIR쒣탍뷸탐쇋쪵횤볬퇩ꆣ뫡뷘쏦쪵횤럖컶뿉틔뗃돶춬쪱볤탲쇐럖컶샠쯆뗄뷡싛ꆣ떫쫇헢훖랽램믡떼훂뛔쳹쿖햮좯볛룱뗄뗍맀틔벰웚쿞틧돪뗄룟맀ꎬ헢뿉쓜평쮰쫕킧펦틽웰ꆣ Lin and Yeh(2001)뛔B-spline맀볆몯쫽맀볆돶살뗄샻싊뷸탐쇋쪵횤럖컶ꎬ럖컶뷡맻뇭쏷솿틲ퟓ쒣탍뫃폚떥틲ퟓ쒣탍ꆣ떫쫇뾼싇쳸풾탔뗄솽틲ퟓ쒣탍늢늻쓜쿔훸뗄폅폚떥뒿뗄솽틲ퟓ쒣탍ꎬ떫쫇쯼쓜릻뫜뫃뗘뷢쫍웚쿞뷡릹틔벰샻싊퇜짺닺욷뗄뚨볛ꆣ Lanne and Saikkonenꎨ2003ꎩ춨맽튻룶믬뫏ퟔ믘맩쒣탍뛔샻싊웚쿞뷡릹뷸탐쇋쪵횤볬퇩ꎬ랢쿖룃쒣탍뿉틔뫜뫃뗄랴펳쏀맺샻싊웚쿞뷡릹뗄늨뚯돖탸ꎨvolatility persistenceꎩ뫍쮮욽돖탸ꎨlevel persistenceꎩ뗈쳘헷ꆣ Ball and Torous(1999)뛔얷풪샻싊뗄쯦믺늨뚯싊쒣탍뷸탐쇋쪵횤볬퇩늢횤쪵쇋샻싊뇤뚯훐쯦믺늨뚯싊뗄듦퓚ꆣ쯻쏇뮹붫샻싊뗄쯦믺늨뚯싊쒣탍뷡맻춬막욱쫐뎡뗄쯦믺늨뚯싊쒣탍뷡맻뷸탐쇋뇈뷏ꆣ뇈뷏뷡맻뇭쏷ꎬ샻싊뗄돖탸탔룼뛌ꎬ틲캪쯼훷튪쫜떽훐퇫틸탐믵뇒헾닟뗄펰쿬ꆣ 돂뗤랢ꎨ2002ꎩ뛔Vasicek쒣탍훐닎쫽뫍쪵볊쫐뎡쫽뻝뗄튻훂탔컊쳢뷸탐쇋퇐뺿ꎬ늢첽쳖쇋쯼퓚릫쮾죚뻶닟훐뗄펦폃ꆣ킻돠뫍컢탛캰ꎨ2002ꎩ춨맽튻룶맣틥뻘랽램ꎬ쪹폃훐맺믵뇒쫐뎡뗄쫽뻝ꎬ뛔Vasicek쒣탍뫍CIR쒣탍뷸탐쇋쪵횤볬퇩ꆣLin and Zheng(2003)춨맽튻룶뿉뇤늨뚯싊뗄뒿쳸풾쒣탍뛔훐맺헾뢮샻싊뇤뚯탐캪뷸탐쇋쒣쓢뫍럖컶ꎬ늢퓚뾼싇GARCH킧펦뗄믹뒡짏퇐뺿쇋훐맺쫐뎡샻싊뗄뚯첬탐캪ꆣ ꎨ쯄ꎩ쒣탍뿉뾿탔뗄럖컶 Ball and Torous(1996)뛔CIR쒣탍틔벰Brennan and Schwartz뗄솽틲ퟓ쒣탍훐뗄샻싊쪱볤탲쇐떥캻룹컊쳢뷸탐쇋럖컶ꆣ떱샻싊럾듓튻룶뻹횵믘맩맽돌쪱ꎬ튻냣뗄웚쿞뷡릹쒣탍뿉틔퓋폃ꎻ떫쫇죧맻샻싊럾듓떥캻룹맽돌ꎬ헢킩쒣탍퓲늻퓙쫊폃ꎬ쯹뷸탐뗄맀볆튲쫇폐욫뗄ꎬ뛸쟒헢훖욫컳컞램평GMM뗈볆솿랽램뷸탐룄뷸ꆣ 쇹ꆢ샻싊웚쿞뷡릹퇐뺿쿖ힴퟜ뷡탔럖컶 룹뻝짏쏦뛔샻싊웚쿞뷡릹뗄컄쿗믘맋ꎬ컒쏇뿉틔듓훐랢쿖샻싊웚쿞뷡릹퇐뺿쒿잰뗄랢햹랽쿲ꆣ ꎨ튻ꎩ퓚샻싊웚쿞뷡릹탎돉볙짨랽쏦ꎬ쫐뎡럖룮볙짨훰붥뗘놻죋쏇쯹틅췼ꎬ틲캪쯦ퟅ쫐뎡뗄랢햹ꎬ벼쫵뗄뷸늽ꎬ쫐뎡붻틗맦쒣뗄삩듳ꎬ쫐뎡틑뺭훰붥탎돉튻룶춳튻뗄헻쳥ꎻ뛸쟒쫐뎡풤웚볙짨죧맻쎻폐춬쇷뚯탔틧돪쿠뷡뫏ꎬ뚼믡놻쫐뎡쇏쯹뻜뻸ꆣ쇷뚯탔틧돪돊쿖돶늻뛏뇤뮯뗄쳘헷ꆣ틲듋ꎬ뷱뫳뗄퇐뺿랽쿲펦룃쫇퓚쫐뎡풤웚볙짨뗄쒣탍뿲볜훐틽죫쇷뚯탔틧돪볙짨ꆣ
ꎨ뛾ꎩ퓚샻싊웚쿞뷡릹뺲첬맀볆랽쏦ꎬ믹놾짏닉폃퇹쳵몯쫽뫍쾢욱냾샫램ꆣ캪쇋놣횤맀볆뗄뺫좷탔ꎬ퇹쳵몯쫽뗄톡퓱풽살풽뢴퓓ꆣ ꎨ죽ꎩ퓚샻싊웚쿞뷡릹ퟔ짭캢맛탎첬럖컶랽쏦ꎬ죧뫎춨맽뛔뻃웚뗄뷸튻늽탞헽ꎬ듓뛸쪹횮쓜릻뗘퓚샻싊웚쿞뷡릹럇욽탐틆뚯쳵볾쿂룼캪폐킧뗘듯떽쳗웚놣횵뗄킧맻ꎬ쫇룃쇬폲캴살훘튪뗄퇐뺿랽쿲ꆣ떫쫇평폚훷돉럖럖컶쫜쫽뻝뗄펰쿬뫜듳ꎬ뷡맻뫜늻컈뚨ꎬ쯹틔뛔훷돉럖럖컶뿉뾿탔뗄볬퇩ꎬ튲쫇튻룶훘튪뗄퇐뺿쓚죝ꆣ ꎨ쯄ꎩ룹뻝뛔샻싊웚쿞뷡릹뚯첬쒣탍뗄쪵횤럖컶ꎬ컒쏇뿉틔랢쿖ꎺ 1ꆢ늻춬뗄쒣탍ꎬ늻춬뗄볆솿럖컶랽램ꎬ늻춬뗄쫽뻝ꎬ쯹뗃돶뗄쪵횤뷡맻뚼믡닺짺닮틬ꆣ틲듋ꎬ뛔늻춬뗄쫐뎡ꎬ훘튪뗄쫇쒣탍뗄쫊폃탔ꆣ 2ꆢ쪵횤럖컶튲뗃돶튻킩믹놾튻훂뗄뷡싛ꎺꎨ1ꎩ욯틆싊뗄볙짨늻믡뛔샻싊웚쿞뷡릹쒣탍닺짺첫듳뗄펰쿬ꎻꎨ2ꎩ늨뚯싊쫇샻싊웚쿞뷡릹쒣탍뗄훘튪틲쯘ꎻꎨ3ꎩ뛠틲ퟓ쒣탍튪뇈떥틲ퟓ쒣탍뇭쿖뗃뫃ꎬ떫쫇뛠틲ퟓ튪컾짼ퟔ평뛈ꎬ틲듋ꎬ룹뻝쪵횤뷡맻ꎬ솽틲ퟓ쒣탍뿉쓜쫇튻룶뇈뷏뫃뗄쒣탍ꆣꎨ4ꎩ샻싊튻냣럾듓튻룶뻹횵믘맩맽돌ꆣ 3ꆢ쒿잰듳늿럖뛔뚯첬쒣탍뗄볬퇩뚼쫇횱뷓샻폃쪵볊쫽뻝퓚쿖쪵쫀뷧훐뷸탐뗄ꎬ뛔쿖쪵쫀뷧뫍럧쿕훐탔쫀뷧뗄닮틬늢캴틽웰ퟣ릻뗄훘쫓ꆣ 닎뾼컄쿗ꎺ [1]Ahh, D.-H., R. F. Dittmar and . Gallant, 2002, “Quadratic Term Structure Models: Theory and Evidence”, Review of Financial Studies, 15, 243-288. [2]Ahn, D. and B. Gao, 1999, “A Parametric Nonlinear Model of Term Structure Dynamics”, Review of Financial Studies, 12, 721-762. [3]Anderson, . and J. Lund, 1997, “Estimating Continuous-Time Stochastic Volatility Models of the Short- Term Interest Rate”, Journal of Econometrics, 72, 343-377. [4]Anderson, . and J. Lund, 1998ꎬ”Stochastic Volatility and Mean Shift in the Short Term Interest Rate Diffusion: Sources of Steepness, Level and Curvature in the Yield Curve”, Working Paper, Northwestern University. [5]Bali, ., 1999,“An Empirical Comparison of Continuous Time Models of the Short Term Interest Rate”, The Journal of Futures Markets, 19, 777-197. [6]Ball, ., and . Torous, 1996, “Unit Roots and the Estimation of Interest Rates Dynamics”, Journal of Empirical Finance, 3, 215-238. [7]Ball, ., and . Torous, 1999, “The Stochastic Volatility of Short Term Interest Rates: Some International Evidence”, Journal of Finance, 54, 2339-2359. [8]Bansal,R.,and H. Zhou, 2001, “Term Structure of Interest Rate with Regime Shifts”, Working paper of Duke University. [9]Baz,J. and . Das, 1996, “Analytical Approximation of the Term Structure for Jump-Diffusion Process: a Numerical Analysis”, Journal of Fixed Income, 6, 78-86. [10]Bekaert, G., . Hodrick, and . Marshall, 1997, “On Biases in Tests of the Expectations Hypothesis of the Term Structure of Interest Rates”, Journal of Financial Economics, 44, 309-348. [11]Bierwag, ., C. Khang, 1979, “An Immunization Strategy in a Minimax Strategy”, Journal of Finance, 34, 389-399.
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