pca for yield curve modelling

26

Upload: zhopan77

Post on 22-Dec-2015

42 views

Category:

Documents


5 download

DESCRIPTION

PCA analysis for yield curve modelling.

TRANSCRIPT

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

Term (Y)0 10 20 30 40 50

0

0.05

0.1

0.15

Term (Y)

0 10 20 30 40 50-0.4

-0.2

0

0.2

0.4

Term (Y)

(1):0.91

(2):0.083(3):0.0031

0 10 20 30 40 50-8

-6

-4

-2

0

2x 10

-4

Term (Y)

(1):0.91

(2):0.083(3):0.0031

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

𝐹 𝜇 ∑𝛼𝑖𝑣𝑖

𝑛

𝑖

𝐹 𝜇 ∑𝛼𝑖𝑣𝑖

𝑘

𝑖

𝑘

𝐹𝛼𝑖𝐹 𝜇 ∑ 𝛼𝑖𝑣𝑖

𝑘

𝑖

𝜇 𝑘 𝑣𝑖

[ ]

∑ √

( ∑

)

( )

( )

( )

( )

0 10 20 30 40 50-3

-2

-1

0

1

2

3

Term (Y)

0 10 20 30 40

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Term (Y)

(1):0.71

(2):0.29

(3):0.00017

∑ √

-6

-4

-2

0

2

4

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

PC #

PC

ma

gn

itu

de

-6 -4 -2 0 2 40

100

200

300

400

500

600

700

PC magnitudeC

ou

nt

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): actual

(1): fit

(4): actual

(4): fit

0 10 20 30 40 500

0.02

0.04

0.06

0.08

Term (Y)

(685): actual

(685): fit

(988): actual

(988): fit

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): original

(1): actual

(1): fit

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): original

(1): actual

(1): fit

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): original

(1): actual

(1): fit

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): original

(1): actual

(1): fit

0 5 10 15

-0.5

0

0.5

1

1.5

PC #

PC

ma

gn

itu

de

-4

-2

0

2

4

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

PC #

PC

ma

gn

itu

de

( )

0 10 20 30 40 50

-0.4

-0.2

0

0.2

0.4

0.6

Term (Y)

0 10 20 30 40-1.5

-1

-0.5

0

0.5

Term (Y)

(1):0.76

(2):0.19

(3):0.042

(4):0.00084

(5):0.00011

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): actual

(1): fit

(4): actual

(4): fit

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): actual

(1): fit

(4): actual

(4): fit

0 10 20 30 40 50

0

0.02

0.04

0.06

0.08

Term (Y)

(685): actual

(685): fit

(988): actual

(988): fit

0 10 20 30 40 50

0

0.02

0.04

0.06

0.08

Term (Y)

(685): actual

(685): fit

(988): actual

(988): fit

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): original

(1): stressed

(1): fit

0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

Term (Y)

(1): original

(1): stressed

(1): fit

-5

0

5

1 2 3 4 5 6 7 8

PC #

PC

ma

gn

itu

de

[

]

[

] [

]