http://www.craft.titech.ac.jp/~nakagawa/dir2/lecture.html#tit2005_1
Agenda Value at Risk 2
3 TOPIX 10 95%
4 TOPIX or Value at Risk
5 TOPIX = log TOPIX N
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7 N TOPIX x, x, 1 2, L x N
8 x = N 1 EXCEL AVERAGE N i= 1 x i
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10 σˆ 2 = 1 N ( x x) i 2 EXCEL VAR N 1 i= 1 STDEV σˆ EXCEL
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EXCEL MEDIAN 25% 75% EXCEL QUARTILE, PERCENTILE 12
13 EXCEL AVEDEV N 1 x i x N 1 i=
TOPIX 14
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X 16
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19 p 400 28 p 28 pˆ = = 0.07 = 400 7%
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21 s x 1.96 < µ < x + 1. 96 n s n µ, n : x :, s : 1.96 = NORMSINV(0.975)
22 0.07(1 0.07) 0.07(1 0.07) 0.07 1.96 < p < 0.07 + 1.96 400 400 0.045 < p < 0.095
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28 50 20 1 50 20 0 50 20 : : 50 :, 20 : p p H p p H p p > = + = 50 20 50 20 1 1 ) (1 n n p p p p t 50 : 20 : 50 20 : 50 20 n n p
29 ) ( 1 NORMSDIST p = 0.05 0.064 (1.521) 1 1.521 400 1 400 1 0.085) 0.085(1 0.07 0.10 > = = = + = NORMSDIST p t
30
31 2 0 2 1 0 0 1 ˆ) ( 1 ˆ 0 1,, ˆ,,, µ σ µ = + = = + = > > = = N i i t i i i N i i N i i t i N t t t x w N N w w w w x x x x t L 1) (0 ) 1 ( < < = λ λ λ i w i
32 Box-Car N Moving-Window N t N N
33 t 250 252 σ = σ annual daily 250 Box-Car Moving-Window
34 TOPIX TOPIX = β + β 1 0 + β 1 2 L + β K 2 K
35 ARCH GARCH = = = + + = + = + = q i i t i p i i t i t p i i t i t t t t t t t b a a p,q a a p N x 1 2 1 2 2 1 2 2 2, ) (0,, :, σ ε σ ε σ σ ε µ ε µ ) GARCH( ) ARCH( ARCH: AutoRegressive Conditional Heteroskedasticity GARCH:Generalized ARCH
Value at Risk(VaR) Value at Risk 36
37 Value at Risk Value at Risk(VaR) -N VaR N 95 99 BIS BIS 99, N = 10
Value at Risk Value at Risk(VaR) X + Y ( X + Y ) Conditional VaR(CVaR)... VaR VaR CVaR 38
39
40 VaR
41 VaR
42 vs TOPIX 10 VaR t