abstractcafd.cufe.edu.cn/docs/20200717150635694295.pdf · 2020-07-17 ·...
TRANSCRIPT
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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�
£wRMSE¤§õ�êP~�.3ÂÃÇ�[Ü�¡äk�é`³§o�k�5!�`
5Ú{�5§Ó���§Ý�ÑLÝ[Ü"d§õ�êP~�.U·AÅÄ5
���4à½|d�êâ§3£OÅ d�É��¡k�½`³"
JEL classification: C52; E43; G12
Keywords: |ÇÏ�(�, ÂÃÇ�[Ü, ��, Õ1m½|, IÅ, í�©Û
1. Úó
IÅÂÃÇ��NØÓÏ�Ã��ºxÂÃÇ�m�'X§Ùã�´3±Ï
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ÃÇ£spot yield / zero-coupon yield¤!²dÂÃÇ£par yield¤Ú�Ï|Ç£forward
rate¤"§�þdby¼ê�ѧ*d�m�±�p=�"by¼ê��OKÄuÅ
½|� �d½¤�d�"du?ÛÅ ½|�6Ï��´Å 3Ï�þþ´lÑ�,
ÃØby¼ê�´þãn«ÂÃǼêþÃ{ÏL½|d���*ÿ§7Ll�*
���Å�d¥�OÑÛ¹�ëY|ÇÏ�(�"¯¤±�§ÃºxÂÃÇ�´7
K½|]�½d�ÄO"Ïd§IÅÂÃÇ��[ÜÃØé�ïÆö�´7Kl�
<5`�'�"
�X·I|ǽ|zU�Øä�\§1ÅÚ�té��±|Ç�+�§½|z
|Ç��ÅÚ/¤"�l3n¥�¬ru5¥�¥'u�¡�zU�eZ�¯K
�û½6§Ù¥ÄgJÑ/\¯í?|ǽ|z§è��N½|ø¦'X�IÅÂÃÇ
�0�#�¦"3d��µe§�âÅ �?½|d��O|ÇÏ�(���15
Ú¢^5ÅÚOr"IÅ|ÇÏ�(�����N]��Ä:d�Ú½|]7�ø¦
G¹¶IÅÂÃÇ�/��Cz��±?�ÚD47K½|&E!ýÿ÷*²L±
ÏÅÄ"ïÄXÛ�Ð[Ü¥IIÅÂÃÇ�Ïdäk��y¢¿Â"
|ÇÏ�(��.��©�·��.ÚÄ��."·��.�æ^��£interpolation¤
��[Ü�{§|^,�Å ½|£~XIŽ|½AAAè�Ž|¤�*ÿ�
Preprint submitted to /²ÀÆþ-CAFD#Ñ�l�0Æ)Ø©�m September 29, 2019
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15
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
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mkγt�3z��tÏØÚ�§"y'��Ä:§Ïd·�7Lòí�©Û�ÚOþ?1
IOz§¦Ù��p'�"äNIOz��{Xeµ
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«"
·�?�ÚO���ÏSIOz���\�þ��Ø��\ÈoÚ§∑wRMSE
γ
t§
¿2g?1Friedmanu�"(J�L2¥z�Ï�«m�1�1"Ïd§3L1Ú2ü�
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,
�.LyÑ�A�´1�1ÚO�$uÙ¦�.§�1�1ÚO�puÙ¦�.§@
où��.�3LÝ[Ü�v¦é�"��§XJT�.�Ù¦�.�'§1�1Ú
1�1ÚOêâ��ÑwÍ�$§@o�±�½d�.äk[Ü`³"
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
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�©|¥¶
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z�Ï�«méAü1êâµ111�Ñ∑wRMSEγt ÚS
γ¶121�ÑIOz��éA�§∑wRMSE
γ
tÚSγ"Ó�1¥����^oNL«§XJT1�FriedmanÚO�£��310%Y
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��Ï�2009c01��2018c12�§�À�¥IÕ1mIŽ|120����"�dêâ"
k'êâý?n9��©|�¹§��N¹A"18
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�wRMSEt4��£Max¤"ùL²§MEDØ��N[Ü`Ý�p§éAÏ�Ͻ|�
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5��£std.¤§��Ù[ܽ5�ép"¥IIÅ�?½|6Ä5�¤Ù½|$é
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Ô��"3ù«�¹e§MED�.Ø=U�Ð[Ü�~�¹e�½|êâ§é4
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Oz�TÚOþ����Ä�8¥uMED�."L1-C|w«§SNC�.310c�
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k§�©ÄgòMED�.Ú\¥I½|§}Á^Ù[Ü¥IúxÂÃÇ�"Ùg§
�©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
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ØÚ�§"y'�Ä:§�©ÄgJÑò�ëê�.�wRMSEtIOz£=wRMSEt¤"
��SÚ��ü�©|�í�©Ûw«§MED�.3z���|Úý�Ü©Ï�
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I�êâk�½[ÜUå§�ØXMED�.n�"nþ¤ã§MED �.3[Ü¥I
Õ1m½|IÅÂÃÇ��¡äk�é`³§���Æâ.91�.í�"?�Ú
u�MED�.éÙ¦¥IÅ ½|§~XImÅ!/�ÅÚØÓµ?�è�Å�ÂÃ
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A. N¹µêâý?n9��©|
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^�Å d��\�V>ïñþdÀdO�Ñ��A�d£dirty/full price¤"�Ä�¥
IIÅ�3�cGE�g��cGE�gü«y76/ª§·�©OòO�Ñ�ØÓ
lÑE|�ÏÂÃÇA=��ëYE|�ÏÂÃÇRµ
R =
2 log
(1+
A
2
), �A��cE|ÂÃÇ�,
log (1+A) , �A�cE|ÂÃÇ�;
20
�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
êþ��§�þïü�f��|�êâ©�§d«mS��Ä�Uì50%�'~?1©
�"
±fx, �w, ï, 2008. ¥IIÅ|ÇÏ�(��.ïÄ�¢y©Û. 7KïÄ,
131–150.
133�ïÄ��Ïm§Õ1m½|6Ï�IÅ¥vk¹�Å "
21
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23