{"id":30401,"date":"2023-12-07T09:15:51","date_gmt":"2023-12-07T09:15:51","guid":{"rendered":"https:\/\/masterskills.org\/blog\/mo-hinh-hjm-heath-jarrow-morton-model-la-gi-dac-diem.html"},"modified":"2023-12-23T06:12:58","modified_gmt":"2023-12-22T23:12:58","slug":"mo-hinh-hjm-heath-jarrow-morton-model-la-gi-dac-diem","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/mo-hinh-hjm-heath-jarrow-morton-model-la-gi-dac-diem.html","title":{"rendered":"M\u00f4 h\u00ecnh HJM (Heath-Jarrow-Morton Model) l\u00e0 g\u00ec? \u0110\u1eb7c \u0111i\u1ec3m"},"content":{"rendered":"
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\u1ea2nh minh h\u1ecda. Ngu\u1ed3n: Sparrho.<\/p>\n<\/div>\n<\/div>\n

M\u00f4 h\u00ecnh Heath-Jarrow-Morton<\/font><\/b><\/h2>\n

Kh\u00e1i ni\u1ec7m<\/b><\/p>\n

M\u00f4 h\u00ecnh Heath-Jarrow-Morton<\/b> trong ti\u1ebfng Anh l\u00e0\u00a0Heath-Jarrow-Morton Model, <\/b>g\u1ecdi t\u1eaft l\u00e0\u00a0M\u00f4 h\u00ecnh HJM.<\/b><\/p>\n

M\u00f4 h\u00ecnh Heath-Jarrow-Morton (M\u00f4 h\u00ecnh HJM)<\/b> \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh l\u00e3i su\u1ea5t k\u00ec h\u1ea1n. L\u00e3i su\u1ea5t n\u00e0y sau \u0111\u00f3 \u0111\u01b0\u1ee3c m\u00f4 h\u00ecnh h\u00f3a theo c\u1ea5u tr\u00fac k\u00ec h\u1ea1n hi\u1ec7n t\u1ea1i c\u1ee7a l\u00e3i su\u1ea5t \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh m\u1ee9c gi\u00e1 ph\u00f9 h\u1ee3p cho nh\u1eefng ch\u1ee9ng kho\u00e1n nh\u1ea1y c\u1ea3m v\u1edbi l\u00e3i su\u1ea5t. <\/p>\n

C\u00f4ng th\u1ee9c M\u00f4 h\u00ecnh HJM<\/font><\/b><\/h3>\n

N\u00f3i chung, m\u00f4 h\u00ecnh HJM v\u00e0 c\u00e1c m\u00f4 h\u00ecnh \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng tr\u00ean c\u01a1 s\u1edf c\u1ee7a n\u00f3 tu\u00e2n theo c\u00f4ng th\u1ee9c:<\/p>\n

Df(t,T) = \u03b1(t,T)dt + \u03c3(t,T)dW(t)<\/p>\n

Trong \u0111\u00f3: <\/p>\n

df (t, T) = L\u00e3i su\u1ea5t k\u00ec h\u1ea1n t\u1ee9c th\u1eddi c\u1ee7a tr\u00e1i phi\u1ebfu kh\u00f4ng l\u00e3i su\u1ea5t v\u1edbi k\u00ec h\u1ea1n T, \u0111\u01b0\u1ee3c gi\u1ea3 \u0111\u1ecbnh l\u00e0 th\u1ecfa m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh vi ph\u00e2n ng\u1eabu nhi\u00ean b\u00ean tr\u00ean.<\/p>\n

\u03b1, \u03c3 = H\u1ec7 s\u1ed1 th\u00edch nghi<\/p>\n

W = Chuy\u1ec3n \u0111\u1ed9ng Brown (b\u01b0\u1edbc \u0111i\u00a0ng\u1eabu nhi\u00ean\u00a0– random walk) d\u01b0\u1edbi gi\u1ea3 \u0111\u1ecbnh trung l\u1eadp r\u1ee7i ro<\/p>\n

\u00dd ngh\u0129a m\u00f4 h\u00ecnh Heath-Jarrow-Morton<\/font><\/b><\/h3>\n

M\u00f4 h\u00ecnh Heath-Jarrow-Morton mang t\u00ednh l\u00ed thuy\u1ebft v\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u1edf c\u00e1c c\u1ea5p \u0111\u1ed9 ph\u00e2n t\u00edch t\u00e0i ch\u00ednh ti\u00ean ti\u1ebfn nh\u1ea5t. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng ch\u1ee7 y\u1ebfu b\u1edfi nh\u1eefng nh\u00e0 \u0111\u1ea7u t\u01b0 \u0111ang t\u00ecm ki\u1ebfm c\u01a1 h\u1ed9i ch\u00eanh l\u1ec7ch gi\u00e1, c\u0169ng nh\u01b0 c\u00e1c nh\u00e0 ph\u00e2n t\u00edch \u0111\u1ecbnh gi\u00e1 c\u00e1c c\u00f4ng c\u1ee5 ph\u00e1i sinh.\u00a0<\/p>\n

M\u00f4 h\u00ecnh HJM d\u1ef1 \u0111o\u00e1n l\u00e3i su\u1ea5t k\u00ec h\u1ea1n, v\u1edbi \u0111i\u1ec3m b\u1eaft \u0111\u1ea7u l\u00e0 t\u1ed5ng h\u1ee3p c\u1ee7a t\u1ea5t c\u1ea3 nh\u1eefng y\u1ebfu t\u1ed1 ng\u1eabu nhi\u00ean. S\u1ef1 ng\u1eabu nhi\u00ean v\u1ec1 m\u1eb7t t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i c\u1ee7a l\u00e3i su\u1ea5t \u0111\u01b0\u1ee3c \u0111i\u1ec1u khi\u1ec3n b\u1edfi s\u1ef1 bi\u1ebfn \u0111\u1ed9ng, \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111i\u1ec1u ki\u1ec7n tr\u00f4i HJM. Theo ngh\u0129a c\u01a1 b\u1ea3n, m\u00f4 h\u00ecnh HJM l\u00e0 b\u1ea5t k\u00ec m\u00f4 h\u00ecnh l\u00e3i su\u1ea5t n\u00e0o \u0111\u01b0\u1ee3c \u0111i\u1ec1u khi\u1ec3n b\u1edfi m\u1ed9t s\u1ed1 l\u01b0\u1ee3ng h\u1eefu h\u1ea1n c\u00e1c chuy\u1ec3n \u0111\u1ed9ng Brown.<\/p>\n

M\u00f4 h\u00ecnh HJM d\u1ef1a tr\u00ean c\u00f4ng tr\u00ecnh c\u1ee7a c\u00e1c nh\u00e0 kinh t\u1ebf David Heath, Robert Jarrow v\u00e0 Andrew Morton t\u1eeb nh\u1eefng n\u0103m 1980. Ba nh\u00e0 kinh t\u1ebf \u0111\u00e3 vi\u1ebft hai b\u00e0i b\u00e1o \u0111\u00e1ng ch\u00fa \u00fd v\u00e0o cu\u1ed1i nh\u1eefng n\u0103m 1980, \u0111\u1eb7t n\u1ec1n m\u00f3ng cho m\u00f4 h\u00ecnh n\u00e0y, trong \u0111\u00f3 c\u00f3 b\u00e0i b\u00e1o “Gi\u00e1 tr\u00e1i phi\u1ebfu v\u00e0 c\u01a1 c\u1ea5u k\u00ec h\u1ea1n c\u1ee7a l\u00e3i su\u1ea5t: M\u1ed9t ph\u01b0\u01a1ng ph\u00e1p m\u1edbi.”<\/p>\n

C\u00f3 nhi\u1ec1u m\u00f4 h\u00ecnh b\u1ed5 sung kh\u00e1c nhau \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng tr\u00ean Khung HJM. T\u1ea5t c\u1ea3 nh\u00ecn chung \u0111\u1ec1u dung \u0111\u1ec3 d\u1ef1 \u0111o\u00e1n to\u00e0n b\u1ed9 \u0111\u01b0\u1eddng cong l\u00e3i su\u1ea5t chuy\u1ec3n ti\u1ebfp, kh\u00f4ng ch\u1ec9 l\u00e3i su\u1ea5t ng\u1eafn h\u1ea1n ho\u1eb7c m\u1ed9t \u0111i\u1ec3m nh\u1ea5t \u0111\u1ecbnh tr\u00ean \u0111\u01b0\u1eddng cong. V\u1ea5n \u0111\u1ec1 l\u1edbn nh\u1ea5t v\u1edbi M\u00f4 h\u00ecnh HJM l\u00e0 ch\u00fang c\u00f3 xu h\u01b0\u1edbng c\u00f3 k\u00edch th\u01b0\u1edbc v\u00f4 h\u1ea1n, khi\u1ebfn cho vi\u1ec7c t\u00ednh to\u00e1n l\u00e0 g\u1ea7n nh\u01b0 kh\u00f4ng th\u1ec3. C\u00f3 nhi\u1ec1u m\u00f4 h\u00ecnh kh\u00e1c nhau \u0111\u01b0\u1ee3c ch\u1ec9nh s\u1eeda nh\u1eb1m th\u1ec3 hi\u1ec7n M\u00f4 h\u00ecnh HJM \u1edf tr\u1ea1ng th\u00e1i h\u1eefu h\u1ea1n. <\/p>\n

M\u00f4 h\u00ecnh HJM v\u00e0 \u0111\u1ecbnh gi\u00e1 quy\u1ec1n ch\u1ecdn<\/font><\/b><\/h3>\n

M\u00f4 h\u00ecnh HJM c\u0169ng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong \u0111\u1ecbnh gi\u00e1 quy\u1ec1n ch\u1ecdn, trong \u0111\u00f3 \u0111\u1ec1 c\u1eadp \u0111\u1ebfn vi\u1ec7c t\u00ecm gi\u00e1 tr\u1ecb h\u1ee3p l\u00ed c\u1ee7a h\u1ee3p \u0111\u1ed3ng ph\u00e1i sinh. C\u00e1c t\u1ed5 ch\u1ee9c giao d\u1ecbch c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng m\u00f4 h\u00ecnh \u0111\u1ec3 l\u1ef1a ch\u1ecdn gi\u00e1 nh\u01b0 m\u1ed9t chi\u1ebfn l\u01b0\u1ee3c nh\u1eb1m t\u00ecm c\u00e1c quy\u1ec1n ch\u1ecdn b\u1ecb \u0111\u00e1nh gi\u00e1 th\u1ea5p ho\u1eb7c b\u1ecb \u0111\u1ecbnh gi\u00e1 qu\u00e1 cao.<\/p>\n

C\u00e1c m\u00f4 h\u00ecnh \u0111\u1ecbnh gi\u00e1 quy\u1ec1n ch\u1ecdn l\u00e0 c\u00e1c m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc s\u1eed d\u1ee5ng c\u00e1c y\u1ebfu t\u1ed1 \u0111\u1ea7u v\u00e0o \u0111\u00e3 bi\u1ebft v\u00e0 c\u00e1c gi\u00e1 tr\u1ecb d\u1ef1 \u0111o\u00e1n, ch\u1eb3ng h\u1ea1n nh\u01b0 s\u1ef1 bi\u1ebfn \u0111\u1ed9ng, \u0111\u1ec3 t\u00ecm gi\u00e1 tr\u1ecb l\u00ed thuy\u1ebft c\u1ee7a c\u00e1c quy\u1ec1n ch\u1ecdn. Nh\u1eefng nh\u00e0 giao d\u1ecbch s\u1ebd s\u1eed d\u1ee5ng c\u00e1c m\u00f4 h\u00ecnh nh\u1ea5t \u0111\u1ecbnh \u0111\u1ec3 t\u00ecm ra gi\u00e1 t\u1ea1i m\u1ed9t th\u1eddi \u0111i\u1ec3m nh\u1ea5t \u0111\u1ecbnh, c\u1eadp nh\u1eadt t\u00ednh to\u00e1n gi\u00e1 tr\u1ecb d\u1ef1a tr\u00ean r\u1ee7i ro thay \u0111\u1ed5i.<\/p>\n

(Theo\u00a0Investopedia<\/i>)<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n M\u00f4 h\u00ecnh HJM (Heath-Jarrow-Morton Model) \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh l\u00e3i su\u1ea5t k\u00ec h\u1ea1n.\n <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[417],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/30401"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=30401"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/30401\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=30401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=30401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=30401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}