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¥I1m|I¯´ˆ˙˜u.O Abstract 'ıŒP~.£Multiple Exponential Decay Interpolation ModelØ ¥I1m|I¯´ˆ˙?1[ " ıŒP~.McCullochng ^.Nelson-Siegel-Svensson.?1 " ¢y(JL²§ıŒP~.U A¥I1m|I¯´ˆ˙/A:§[p§o. {! OK: " ˇLØˇm[d\ £wRMSEıŒP~.3´ˆ˙[¡kاok5! 5{5§§L[ " d§ıŒP~.UA¯˜5 4|dŒ§3£O¯d¡k" JEL classification : C52; E43; G12 Keywords: |˙ˇ(, ´ˆ˙[, , 1m|, I¯, ' 1. I¯´ˆ˙Nˇˆx´ˆ˙mX§ª·3ˇ ! ´ˆ˙pI²¡£ª^ " øp/´ˆ˙0=ˇ´ ˆ˙£spot yield / zero-coupon yield/ ! ²d´ˆ˙£par yield/ˇ|˙£forward rate/ " §dbyŒ§*dmp= " byŒOK˜u¯ |d/d " du?¯|6ˇ·¯3ˇ·l, ˆbyŒ·ªn«´ˆ˙Œˆ{ˇL|d*§7Ll* ¯d¥OºY|˙ˇ( " /§ˆx´ˆ˙·7 K|]d˜O " ˇd§I¯´ˆ˙[ˆØ˘·7Kl <5 " XI|˙|zU\§1¯tØ|˙+§|z |˙¯// " l3n¥ru5¥¥u¡zUeZK ß6 §¥˜gJ/\?|˙|z§LN|lƒXI¯´ˆ˙ 0#ƒ " 3de§¯?|dO|˙ˇ(15 ¢^5¯Or " I¯|˙ˇ(N]˜:d|]7lƒ GI¯´ˆ˙/Cz?D47K|&E! *²Lˇ¯˜ " ˜X[¥II¯´ˆ˙ˇdky¢¿´ " |˙ˇ(.'.˜. ".^ £interpolation/ [{§|^,¯|£~XI¯|AAAL¯|/* Preprint submitted to /²˘-CAFD#l0˘)'m September 29, 2019

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Page 1: Abstractcafd.cufe.edu.cn/docs/20200717150635694295.pdf · 2020-07-17 · ¥IÕ1m‰|I¯´ˆ˙›‡µ˜u• −˝.˙ O Abstract ˛'šâı“ŒP~ −˝.£Multiple Exponential Decay

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Abstract

�©�âõ�êP~���.£Multiple Exponential Decay Interpolation Model¤§é

¥IÕ1m½|IÅÂÃÇ­�?1[Ü"Ó�òõ�êP~�.�McCullochng

�^�.ÚNelson-Siegel-Svensson�.?1'�"¢y(JL²§õ�êP~�.U

�зA¥IÕ1m½|IÅÂÃÇ­��/�A:§[Ü`Ý�p§�oä�.

{�!O�KÖþ��`:"ÏLé'��Ïm[Üd�í���\�þ��Ø�

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���4à½|d�êâ§3£OÅ d�É��¡k�½`³"

JEL classification: C52; E43; G12

Keywords: |ÇÏ�(�, ÂÃÇ­�[Ü, ��, Õ1m½|, IÅ, í�©Û

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Page 2: Abstractcafd.cufe.edu.cn/docs/20200717150635694295.pdf · 2020-07-17 · ¥IÕ1m‰|I¯´ˆ˙›‡µ˜u• −˝.˙ O Abstract ˛'šâı“ŒP~ −˝.£Multiple Exponential Decay

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14

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0302009

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15

Page 16: Abstractcafd.cufe.edu.cn/docs/20200717150635694295.pdf · 2020-07-17 · ¥IÕ1m‰|I¯´ˆ˙›‡µ˜u• −˝.˙ O Abstract ˛'šâı“ŒP~ −˝.£Multiple Exponential Decay

Table 1: í�©ÛÚ�.�½�£ã5ÚO®o

MED SNC NSS

A|||))))))wRMSE (bps), ������SSS

Median 98.70 98.06 106.01

88.61 108.51 106.01

Max 283.19 255.06 309.49

187.57 382.59 309.49

Min 32.38 32.66 31.47

29.01 31.10 31.47

std. 41.63 42.10 50.20

33.37 55.77 50.20

B|||))))))wRMSE (bps), ������

Median 150.48 146.87 158.68

136.14 158.04 158.68

Max 10,263.07 10,265.05 14,175.49

7,697.31 10,265.05 14,175.49

Min 59.36 54.72 59.63

47.70 47.58 59.63

std. 926.42 924.96 1,574.89

694.87 924.33 1,574.89

C|||))))))k���������

Mean 3.71 4.42 4

Median 4 4 4

Max 7 8 4

Min 2 3 4

AÚB|¥��w�©O´��SÚ����.�\�þ��Ø�£wRMSEt¤�£ã5ÚO§±

Ä:£bps¤�ü L«"

C|®o��ÏS����.�Ýk���ÚO©Ù"

��Ï�2009c01��2018c12�§�À�¥IÕ1mIŽ|120����"�dêâ"

zaÚO�éAü1êâµ111�Ñ�©wRMSEt�ÚO�¶121�ÑIOz�wRMSEt�ÚO

�"

k'êâý?n9��©|�¹§��N¹A"

16

Page 17: Abstractcafd.cufe.edu.cn/docs/20200717150635694295.pdf · 2020-07-17 · ¥IÕ1m‰|I¯´ˆ˙›‡µ˜u• −˝.˙ O Abstract ˛'šâı“ŒP~ −˝.£Multiple Exponential Decay

d§n��.¥k���.´ëê�.§Ù{ü��.´�ë."du�.

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wRMSEγ

t = wRMSEγt ·

kγtkNSSt

, γ = {MED, SNC, NSS} . (17)

úª(17)¥§wRMSEγ

t´²LIOz��\�þ��Ø�§kNSSt = 4, ∀t¶Ù{kγt���

�tCz§��ÏS�ÚO©ÙXL1-C|¤«"dd��§é?¿�mt§wRMSENSS

t =

wRMSENSSt § wRMSE

MED

t ÚwRMSESNC

t ´±kNSSt �ëìXIOz�(J"

òYBliss (1996)ÚGuo (2019)§·�òFriedman�ëêu�A^uÚOþ�\

�þ��Ø�\ÈoÚ§u�n��.�)�∑wRMSEγ

t´Ä�3ÚOwÍ5�

É"L2 �Ñ��Ï�«m�FriedmanÚO�9ÙwÍ5Y²"z�Friedmanu

��Ñ�ü¶©ê£Rank score, Sγt¤�3∑wRMSEγ

téA����)Ò¥�ѧ�

�∑wRMSEγ

t��«O�ÚOþ§Ó�^u'�n��.\O[Üí���é��"

XJL2 ¥,�1�FriedmanÚO�£��310%Y²¤wͧ@�1¥����ò�

oNL«"

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γ

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L¥§z�ÚOþ½Ï�«mþéAü1ÚO(Jµ1�1�Ñ�wRMSEγt�'�

ÚO�§1�1�ÑIOz�wRMSEγ

t�éAÚOþ"ùkÏu�äA½�.3Â

ÃÇ­�[Ü¥�éuÙ¦�.�`³´ÄÏLV\���.õ�ª¼�"XJ,

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4.2. ¥IIŽ|�[Ü(J

Äk©Û��S[Ü�(J"�âL2-A|z�Ï�«m1�1¤«§MED�.

3A�¤kÏ�«m�)���∑wRMSEt±9St§ù`²MED��Ù¦ü«�.é

��Sêâ�[Ü`Ý�p"~�´10-30cÏ�f«m§∑wRMSEt�St��$�

Ø��µMED�.�Ñ�$�∑

wRMSEt§�SNC�.�)�$�ü¶©êSt"T�

É�)uü¶©êO��ª�AÏ5§3ý�õê�¹e§ü¶©ê�Ø�(J�

��"�u1-5 cÏ�f«m§SNC �.�,�)���∑wRMSEt§�TÏ�«m

�FriedmanÚO�¿ØwͧÏd�@�n��.éTÏ�«m��Sêâ�[ÜØ

�3ÚOwX5�É"Ó�§��.330-50c«m�ÉØwͧë�¿ÂØ�"XJ

*L2-A |z�Ï�«m�1�1§·�uyIOz��éA�Ä��´��"n

þ§MED�.3²þ�$�k���¹e£kMED

t = 3.71§�L1-C|¤U�Ð/[Ü�

�Sêâ§�T`³�3uA�¤kÏ�«m"�u�e�ü��.§SNC�.3�

õêÏ�«m�LyÐuNSS�.§�)IOz��(J�ÊH�Ð"�'�eNSS

�.3��S�[ÜLy��"

17

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Table 2: �\�RMSE\OoÚ, 2009/01-2018/12

FriedmanÚO�

111:∑

wRMSEγt , [Sγ ]; 121:∑

wRMSEγ

t , [Sγ]

MED SNC NSS

A|||))))))������SSS

�NÏ� 57.95∗∗∗ 1.22,[203] 1.22,[209] 1.36,[308]

39.02∗∗∗ 1.10,[185] 1.37,[259] 1.36,[276]

0-1c 18.32∗∗∗ 0.72,[217] 0.73,[225] 0.85,[278]

26.25∗∗∗ 0.65,[195] 0.82,[255] 0.85,[270]

1-5c 0.32 2.07,[237] 2.03,[245] 2.10,[238]

29.60∗∗∗ 1.92,[200] 2.28,[284] 2.10,[236]

5-10c 65.07∗∗∗ 1.68,[200] 1.69,[208] 1.92,[312]

53.22∗∗∗ 1.54,[176] 1.87,[261] 1.92,[283]

10-30c 13.36∗∗∗ 1.29,[231] 1.33,[225] 2.12,[264]

10.39∗∗∗ 1.18,[221] 1.53,[241] 2.12,[258]

30-50c 1.83 1.00,[239] 1.04,[236] 1.30,[245]

1.13 1.05,[237] 1.18,[239] 1.30,[244]

B|||))))))������

�NÏ� 18.12∗∗∗ 2.92,[219] 2.75,[223] 4.40,[278]

25.52∗∗∗ 2.52,[195] 2.92,[266] 4.40,[259]

0-1c 9.59∗∗∗ 0.62,[223] 0.61,[232] 0.71,[265]

14.37∗∗∗ 0.58,[209] 0.70,[259] 0.71,[252]

1-5c 5.40∗ 3.35,[222] 3.33,[240] 3.39,[258]

41.27∗∗∗ 2.93,[186] 3.59,[284] 3.39,[250]

5-10c 42.07∗∗∗ 1.99,[212] 1.99,[210] 2.15,[298]

35.22∗∗∗ 1.86,[187] 2.25,[269] 2.15,[264]

10-30c 5.07∗ 1.86,[242] 1.61,[227] 2.07,[251]

5.07∗ 1.78,[226] 1.78,[247] 2.07,[247]

30-50c 7.18∗∗ 4.86,[244] 1.55,[231] 20.06,[245]

2.24 4.77,[242] 1.74,[235] 20.06,[243]

***, **, * L²FriedmanÚO�©O31%!5% Ú10%Y²wͶ

n����.36�Ï�«m�ÚO(J©OЫ3A!Bü�©|¥¶

�)Ò¥�êi�ÑFriedmanu�¥���.�ü¶©êSγ¶

z�Ï�«méAü1êâµ111�Ñ∑wRMSEγt ÚS

γ¶121�ÑIOz��éA�§∑wRMSE

γ

tÚSγ"Ó�1¥����^oNL«§XJT1�FriedmanÚO�£��310%Y

²¤wͶ

��Ï�2009c01��2018c12�§�À�¥IÕ1mIŽ|120����"�dêâ"

k'êâý?n9��©|�¹§��N¹A"18

Page 19: Abstractcafd.cufe.edu.cn/docs/20200717150635694295.pdf · 2020-07-17 · ¥IÕ1m‰|I¯´ˆ˙›‡µ˜u• −˝.˙ O Abstract ˛'šâı“ŒP~ −˝.£Multiple Exponential Decay

?�Ú©Û§MED�.3��S�`³�L1-A|¤«�£ã5ÚO(JÄ

��p<y"²IOz�§MED�.�)���wRMSEt¥ ê£Median¤Ú��

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Oz�TÚOþ����Ä�8¥uMED�."L1-C|w«§SNC�.310c�

�ÏSk���þ�£4.42¤puMED�.�þ�£3.71¤§�puNSS �.�IO

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wRMSESNCt ¤"MED�.��¹�dfÐ��

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�.3��S£A|¤LyÑ�[Ü`³3��£B|¤¿���"ù«`³=

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19

Page 20: Abstractcafd.cufe.edu.cn/docs/20200717150635694295.pdf · 2020-07-17 · ¥IÕ1m‰|I¯´ˆ˙›‡µ˜u• −˝.˙ O Abstract ˛'šâı“ŒP~ −˝.£Multiple Exponential Decay

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�©µï­è5ÚO��ÇþØZ���5�`z�O{§= æ^McCulloch and

Kochin (2000) JÑ�S��5���¦{?1��Xê�O"��§UìGuo (2019)

JÑ�ëêÀJ�`z�{é�ë�.?1�`N�§=ÏLDWu�½Ù¦S��'

u�(�[Üí���xDÑS�§¿(ÜBIC�(½�.�N[Ü`Ý"nÜü�u

��(J§Ó��Ä�.k�5!�`5Ú{�5§ÅÏÀJ�Ü·�ëê�êÚ�

.äN�½"

¢yïÄÜ©�©À�2009c01��2018c12��O10c�Õ1m½|IÅ�Ý

êâ����§ÄgÓ�¦^MED§SNCÚNSSn«�.[Ü¥IIÅÂÃÇ­�§

¿$^í�©Ûé'n«�.�`�"3ù|­�[Ü�/mê0¢�¥§·�ÀJ�

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ØÚ�§"y'�Ä:§�©ÄgJÑò�ëê�.�wRMSEtIOz£=wRMSEt¤"

��SÚ��ü�©|�í�©Ûw«§MED�.3z���|Úý�Ü©Ï�

«m�)���∑wRMSEt§±9wRMSEt4��ÚIO�"ùL²§MED�.3n

«�.¥[ÜÂÃÇ­��då��§LÝ[ܯK%¿ØâÑ"�'�e§�61

�NSS�.3¥I½|�[Ü`Ý�$§­è5��¶SNC�.K0u�ö�m§é¥

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u�MED�.éÙ¦¥IÅ ½|§~XImÅ!/�ÅÚØÓµ?�è�Å�ÂÃ

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^�Å d��\�V>ïñþdÀdO�Ñ��A�d£dirty/full price¤"�Ä�¥

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lÑE|�ÏÂÃÇA=��ëYE|�ÏÂÃÇRµ

R =

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A

2

), �A��cE|ÂÃÇ�,

log (1+A) , �A�cE|ÂÃÇ�;

20

Page 21: Abstractcafd.cufe.edu.cn/docs/20200717150635694295.pdf · 2020-07-17 · ¥IÕ1m‰|I¯´ˆ˙›‡µ˜u• −˝.˙ O Abstract ˛'šâı“ŒP~ −˝.£Multiple Exponential Decay

�e5éêâ?1çÀ§ïá��³"Äk§éuu1Ï�3�c±e£Ø�)

�c¤�byÅ §�Ü�¹3��³¥"Ùg§éuu1Ï�3�c9�c±þ

£Ø�)�c¤�NEÅ §I?1çÀ"XJkü�½ü�±þ�Å äk�Ó��

ÏF§K=]Àäk��ïñd��@�Å ?\��³"2g§Gؤku1Ï�

�u�c��{Ï��u�c�NEÅ "��§�ÌBliss (1996)§Gع�ÚAÏ

6Ä5¯K�� 13"

��§ò²LçÀ��Ýî�¡��©�ü�f��8))��Sf8Ú��

f8§z�î�¡���Ó���8�50%"éu©¥½Â�z�Ï�«m§·�(Ü

ïñd�Ú¤�þ?1©|µk¤�þêâ¿�ïñd����Å äk�p�6Ä

5§�´��¹�§`kÀ\��Sf8"Ïd§¤k¹� £�)on-the-runÅ ¤

þ�©\��Sf8^u�O"

Table 3: ��Å ©|ÚO

��S �� ��oN

�N� 3,093 3,420 6,513

0-1c 568 391 959

1-5c 1,150 1,609 2,759

5-10c 1,149 1,148 2,297

10-30c 189 258 447

30-50c 25 26 51

5µ��Ï�2009c01��2018c12�§�À�¥IÕ1mIŽ|120����"êâ"

L3Ы��Ϥk�� 3ØÓ��f8±9ØÓÏ�f«m�©Ù�¹"�

õêÏ�f«mÄ�UìÙ¤�þ�¹©|µk¤�þêâ�Å ©\��Sf8§

ä�þêâ�Å �A?\��f8§Ïdü�f��|m�U�3�½�É"

Ï�3�c±e�Å äk�p�6Ä5§Ïd�õ/�©�3��S"3©|�§

u1Ï���c�NEÅ �byÅ äk�½�O�'X§ÏdÙ©��¹�by

Å ��§�õ���3��êâ|"dL¥êâ�±wÑÏ�330-50c�6Ï

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�"

±fx, �w, ï, 2008. ¥IIÅ|ÇÏ�(��.ïÄ�¢y©Û. 7KïÄ,

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