E-mail: shigeru_yoshifuji@btm.co.jp E-mail: fuminobu_otake@btm.co.jp
Bangia et al. G Bangia et al. exogenous liquidity risk endogenous liquidity risk et al
LTCMLong Term Capital Management Fed G G T RTSI LTCM i.i.d.independently and identically distributed T
t =1 t =5 iid T VaR tt i.i.d.
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!
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 = 0 0.5. κ φ 1, φ 2
2.33λσ
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
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
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
P = P + P = 1 0 0 P N = P ( N P ) Pmarket ( N0P0 ) ( N P )( N + N ) 2 0 0 0 0 0 N + N P 0 0 0 + N market N., P market N N P 0 0 A N m ( N) m CRTXBUXWIG20IBOV MEXBOLSTIKOSPI2HISG7225 TOPIXS&P500DAXSMI NVaRVaRm ( N)
m ( N) = Nλ λ =m( N) λ. λ VaR( N) m ( N) VaR VaR T ABCD VaR A AB
VaR VaR VaR
VaR 10 iid T B Basel Committee on Banking Supervision BIS Committee on the Global Financial System BIS
VaR
VaR VaRVaR
VaRVaR
iid T Bangia et al. Finger Cosandey JGB
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
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.
H 0 H< 0.5 0.5 < 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
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
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
' ' 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
N VaRVaRm ( N) = N
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, 1998. Bank for International Settlements, Stress Testing by Large Financial Institutions: Current Practice and Aggregation Issues, 2000. Basel Committee on Banking Supervision, Performance of Models-Based Capital Charges for Market Risk : 1 July-31 December 1998, September, 1999. Cosandey, David, Adjusting value-at-risk for market liquidity, Risk, October, 2001, pp.115-118. Finger, Christopher C., A Methodology to Stress Correlation, Risk Metrics Monitor, Fourth Quarter,1997, pp. 3-11. Kahneman, D., and Riepe, M., Aspects of Investment Psychology, Journal of Portfolio Management, 24, 1998, pp. 52-65.
Tversky, Amos, The Psychology of Risk - in Quantifying the Market Risk Premium Phenomena for Investment Decision Making -, Institute of Chartered Financial Analysts, 1990.