商品流動性リスクの計量化に関する一考察（その2）―内生的流動性リスクを考慮したストレス・テスト―

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2 Bangia et al. G Bangia et al. exogenous liquidity risk endogenous liquidity risk et al

6 LTCMLong Term Capital Management Fed G G T RTSI LTCM i.i.d.independently and identically distributed T

8 t =1 t =5 iid T VaR tt i.i.d.

9 n λ (= np) t =7 f (x ; n, p)= n C x p x q n x n p 0np λ f f (x ; λ)= λ x e λ /x!

11 Bangia et al.finger Bangia et al. λ Bangia et al. λ (κ) LadjVaR (99%)= P t (1 e 2.33λσ t). LadjVaR (99%)VaR P t σ t κ λ =1+ φ 1 ln + φ 2 l, 3 1 > 0.5 l = κ φ 1, φ 2

12 2.33λσ

13 Q k P k Q k ( c k ) C t C = S Σ S t Σ = A V A, S ij, 1/ = Σ i = j ij 0, A 1 θ k + θ k/( p k + q k) 1 z( i) z( j) ( 1) θk /( pk + qk) 0 ij = + 1 z ( i) = 0 i Q k. i = j, i P i = j, i P i j, i P, k k k Q k Qk Q, j P k k Q k P k Q k P k Q k

14 n p k P k q k Q k θ 0 0 θ 0 1 θ k kθ k θ 0 θ k = c k θ 0 c k 0 < c k 1 V n n Σ n n C n n Cosandey Cosandey N A P N A NP=Α/N P = Α/(N+ N) A θ 0 c k

15 A P = N A A P = N + N Cosandey N N N P P 0, P 1, P 2,, P n N 0, N 1, N 2,, N n P t t 0 Nt 1 P 1 P' 1 P t /P t VaR P t 0 P0 N 0 P P t 1 1 t 2 2 N 1 P P N N 2 P N 1 2 VaR t n P P n N n n P t VaR

16 P = P + P = P N = P ( N P ) Pmarket ( N0P0 ) ( N P )( N + N ) N + N P N market N., P market N N P 0 0 A N m ( N) m CRTXBUXWIG20IBOV MEXBOLSTIKOSPI2HISG7225 TOPIXS&P500DAXSMI NVaRVaRm ( N)

17 m ( N) = Nλ λ =m( N) λ. λ VaR( N) m ( N) VaR VaR T ABCD VaR A AB

18 VaR VaR VaR

19 VaR 10 iid T B Basel Committee on Banking Supervision BIS Committee on the Global Financial System BIS

20 VaR

21 VaR VaRVaR

22 VaRVaR

23 iid T Bangia et al. Finger Cosandey JGB

25 n p=0.5q=0.5 n.i.d.normally and independently distributed i.i.d.independently and identically distributed WNwhite noise {Y n, n = 0,1, }{Z n, n = 0,1, } E[ Y n ] < E [ Y n+1 Z 0,,Z n ]=Y n, n{y n, n = 0,1, }{Z n, n = 0,1, } Z n n n +1 E [Y n+1 Z 0,,Z n ]n Y n E (ε t )=0var (ε t )=σ 2 cov(ε t, ε s )=E (ε t ε s )=0, t s

26 ε t ~NID (0,σ 2 ), ε t ~iid (0,σ 2 ), ε t ~WN (0,σ 2 ), E (ε t )=0, E (ε t )=0, cov (ε t,ε s )=0, t s, cov (ε t2, ε s2 ) 0, s t.

27 H 0 H< < H 1 StepN =5 t =1RS R = Max(X t,n ) Min(X t,n ), X t,n = Σ t (e u M N ). u=1 X t,n N e u u M N Nu= 1t StepR / S StepStepStepN=5, 6, 7, StepN log (N ) log (R / S) H H=0.647 VaR Finger

28 R AVGt 1 R AVGt = R it. p i P i=1, 2,,n t =1, 2,,T R it ti P p : P R it R AVGt θ R it (1 θ ) Rit+ θr = Rit AVGt i P. θ0 θ 1

29 R i, i Pθ = 0 θθ = 1 θp R i, i P 0 <θ < 1VaR t R t ={R 1t,R 2t, R 3t, R nt } tra R t A R = A R, t 1 θ + θ / p 1 A ij = θ / p 0 t i = j, i P i = j, i P i j, i P, j P. R i R i ΣC V t C = S Σ S t Σ = A V A, S ij, 1/ = Σ i = j ij 0. θ R 2 R 1 R 2 R 2 R 1 R 2 R 2 R 2

30 ' ' α α' α' π α α' ' ' π α ' λ R AVGt 1 = ( R ), 2 1t R 2t R 1t = ( 1 λ ) R +, 1t λ RAVGt R 2t = ( 1 λ ) R. 2t λ RAVGt λ0 λ 1 λ =0 λ λ=1 P k Q k c k

31 N VaRVaRm ( N) = N

33 Bangia, Anil, Francis X. Diebold, Til Schuermann and John D.Stroughair, Modeling Liquidity Risk: With Implications for Traditional Market Risk Measurement and Management, working paper, Wharton Financial Institutions Center, Bank for International Settlements, Stress Testing by Large Financial Institutions: Current Practice and Aggregation Issues, Basel Committee on Banking Supervision, Performance of Models-Based Capital Charges for Market Risk : 1 July-31 December 1998, September, Cosandey, David, Adjusting value-at-risk for market liquidity, Risk, October, 2001, pp Finger, Christopher C., A Methodology to Stress Correlation, Risk Metrics Monitor, Fourth Quarter,1997, pp Kahneman, D., and Riepe, M., Aspects of Investment Psychology, Journal of Portfolio Management, 24, 1998, pp

34 Tversky, Amos, The Psychology of Risk - in Quantifying the Market Risk Premium Phenomena for Investment Decision Making -, Institute of Chartered Financial Analysts, 1990.

() ( ) ( ) (1996) (1997) (1997) EaR (Earning at Risk) VaR ( ) ( ) Memmel (214) () 2 (214) 2

1 (Basel Committee on Banking Supervision, BCBS) (BCBS(24), BCBS(215) ) *1 ( ) ( (1997) (213a,b) ) 2 *1 (214) 1 () ( ) ( ) (1996) (1997) (1997) EaR (Earning at Risk) VaR 2 1 1 ( ) ( ) Memmel (214) () 2