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220 8. Tests de copule gaussienne 1−p 95% 1−p 95% 1 0.8 0.6 0.4 0.2 d 1 d 2 d 3 d 4 ρ =0.1 − 0.3 0 0 0.1 0.2 1/ν 0.3 0.4 1 0.8 0.6 0.4 0.2 d 1 d 2 d 3 d 4 ρ =0.7 0 0 0.1 0.2 1/ν 0.3 0.4 1−p 95% 1−p 95% 1 0.8 0.6 0.4 0.2 d 1 d 2 d 3 d 4 ρ =0.5 0 0 0.1 0.2 1/ν 0.3 0.4 1 0.8 0.6 0.4 0.2 d 1 d 2 d 3 d 4 ρ =0.9 0 0 0.1 0.2 1/ν 0.3 0.4 Figure 6: Same as figure 5 but comparing different distances for the same correlation coefficient ρ. 28
ˆρ d1 d2 d3 d4 CHF DEM 0.92 1.01e-02 6.70e-03 0.00e+00 7.20e-03 CHF JPY 0.53 3.44e-01 2.71e-01 2.32e-02 2.83e-01 CHF MYR 0.23 7.27e-01 8.71e-01 5.77e-01 9.26e-01 CHF THA 0.21 3.08e-02 9.47e-02 3.31e-02 9.52e-02 CHF UKP 0.69 2.80e-03 1.80e-03 6.00e-04 1.30e-03 DEM JPY 0.54 2.26e-02 1.33e-01 1.00e-01 1.51e-01 DEM MYR 0.26 4.25e-01 6.77e-01 6.22e-01 7.35e-01 DEM THA 0.24 6.53e-02 1.35e-01 3.26e-02 1.32e-01 DEM UKP 0.72 1.70e-03 4.00e-04 0.00e+00 4.00e-04 JPY MYR 0.31 2.45e-02 6.34e-02 2.26e-01 6.86e-02 JPY THA 0.34 0.00e+00 0.00e+00 3.24e-02 0.00e+00 JPY UKP 0.41 2.85e-02 3.72e-02 5.22e-02 3.09e-02 MYR THA 0.40 0.00e+00 0.00e+00 2.22e-02 0.00e+00 MYR UKP 0.21 6.94e-01 7.94e-01 6.23e-01 8.31e-01 THA UKP 0.15 5.22e-01 6.23e-01 3.21e-02 7.05e-01 Table 2: Each row gives the statistics of our test for each of the 15 pairs of currencies over a 10 years time interval from January 25, 1989 to December 31, 1998. The column ˆρ gives the empirical correlation coefficient for each pair determined as in section 3.1 and defined in (31). The columns d1, d2, d3 and d4 gives the probability to obtain, from the Gaussian hypothesis, a deviation between the distribution of the z 2 and the χ 2 -distribution with two degrees of freedom larger than the observed one for the currency pair according to the distances d1-d4 defined by (33)-(36). 29 221
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UNIVERSITE DE NICE-SOPHIA ANTIPOLIS
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4 Table des matières 2.2.2 Bulles
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6 Table des matières 7.3.2 Tests n
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8 Table des matières 12.1.1 Distri
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10 Table des matières Références
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12 m’ont souvent été d’un gra
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14 Introduction pour espérer se co
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16 Introduction les distributions e
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18 Introduction
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Chapitre 1 Faits stylisés des rent
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1.1. Rappel des faits stylisés 23
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1.1. Rappel des faits stylisés 25
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1.2. De la difficulté de représen
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1.3. Modélisation des propriétés
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Chapitre 2 Modèles phénoménologi
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2.1. Bulles rationnelles multi-dime
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2.2. Des bulles rationnelles aux kr
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Chapitre 3 Distributions exponentie
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Empirical Distributions of Log-Retu
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concerning tail fatness can be form
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To fit our two data sets, section 4
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properties, stressing the problems
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Another problem lies in the determi
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In order to obtain a process with S
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and Sornette (1999) for instance. W
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1. The Pareto distribution: 79 Fu(x
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empirical analog FN(x), estimated f
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have been chosen to converge to 1 a
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5 Comparison of the descriptive pow
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ased on the fact that the quantity
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tail (positive or negative) of the
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Equation (46) depends on c only and
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B Minimum Anderson-Darling Estimato
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C Local exponent In this Appendix,
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D Testing non-nested hypotheses wit
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where α = (c ∗ ,d ∗ ). It can
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where E0[·] denotes the expectatio
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References Andersen, J.V. and D. So
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Gouriéroux C. and A. Monfort, 1994
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Rubinstein, M., 1973, The fundament
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(a) Independent Data Stretched-Expo
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(a) Dow Jones Positive Tail Negativ
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Nasdaq Dow Jones Pos. Tail Neg. Tai
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Dow Jones positive tail Dow Jones n
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Variation coefficient Variation coe
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Mean excess function Mean excess fu
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Hill‘s estimate b u Hill‘s esti
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Wilks statistic (doubled log−like
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Tail 1−F(x) and parameter b Tail
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1.4 1.2 1 0.8 0.6 0.4 0.2 0 1 2 3 4
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Chapitre 4 Relaxation de la volatil
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Volatility Fingerprints of Large Sh
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2 Long-range memory and distinction
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Figure 2: Measuring the conditional
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the system to the accumulation of m
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Appendix C: “Conditional response
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Baillie, R.T., 1996, Long memory pr
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Chapitre 5 Approche comportementale
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5.1. Prix d’un actif et excès de
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5.2. Modèles d’opinion contre mo
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5.4. Conséquences des phénomènes
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5.5. Conclusion 157 ce qui induit u
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Chapitre 6 Comportements mimétique
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RESEARCH PAPER Q UANTITATIVE F INAN
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A Corcos et al Q UANTITATIVE F INAN
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Page 169 and 170: A Corcos et al Q UANTITATIVE F INAN
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270 9. Mesure de la dépendance ext
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Chapitre 10 La mesure du risque Dan
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10.1. La théorie de l’utilité 3
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10.2. Les mesures de risque cohére
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10.3. Les mesures de fluctuations 3
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10.4. Conclusion 361 et de manière
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Chapitre 11 Portefeuilles optimaux
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11.2. Prise en compte des grands ri
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11.3. Equilibre de marché 367 s’
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11.5. Annexe 369 Collective Origin
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11.5. Annexe 371 point λ = 1. Thus
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Chapitre 12 Gestion des risques gra
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12.1. Comprendre et gérer les risq
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12.2. Minimiser l’impact des gran
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Chapitre 13 Gestion de portefeuille
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VaR-Efficient Portfolios for a Clas
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dependence: from independence to co
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given a series of return {rt}t foll
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eads cV (u1, · · · , un) = 1
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THEOREM 4 (TAIL EQUIVALENCE FOR A S
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Independent Assets Comonotonic Asse
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3.2 Typical recurrence time of larg
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and finally w ∗ i = χ−1 i j
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where the ˆwi’s are solution of
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Choosing x > y > Aɛ, and applying
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Expanding fi(xi) around x ∗ i yie
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for all h ∈ AC. Thus, integrating
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B Asymptotic distribution of the su
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This yields × h+ Sc−2 − 2 dh
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References Acerbi, A. and D. Tasche
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Malevergne, Y. and D. Sornette, 200
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ln(T/T 0 ) T Figure 2: Logarithm
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Chapitre 14 Gestion de Portefeuille
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Multi-Moments Method for Portfolio
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choosen risk measure. Section 5 pre
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The variance of the return X of an
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This property is verified for all c
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µn=α of order n = 2, 4, 6 and 8.
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these two assets or portfolios. The
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Due to the homogeneity property of
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invested in the risky fund depends
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C. Then, if g1(X1), · · · , gn(X
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Differentiating with respect to x1,
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7.2 Transformation of the modified
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In the sequel, we will first evalua
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8.3 Non-symmetric assets In the cas
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y the variance will then increase).
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A Description of the data set We ha
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thus and finally 1 λ1 n−1 = w
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C Composition of the market portfol
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D Generalized capital asset princin
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This brings us back to the problem
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F.2 General case We now consider a
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Harvey, C.R. and A. Siddique, 2000,
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µ µ2 1/2 µ4 1/4 µ6 1/6 µ8 1/8
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Mean (10 −3 ) Variance (10 −3 )
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μ (daily return) x 10−3 2.5 2 1.
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w i w i 0.2 0.15 0.1 0.05 Mean−μ
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Figure 6: Schematic representation
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Empirical Cumulative Distribution 1
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Z 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
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Z 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
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10 0 10 −1 10 0 10 −1 10 −1 1
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10 0 10 −1 10 0 10 −1 10 −1 1
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κ 22 20 18 16 14 12 10 8 6 4 2 Exc
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Return μ 0.12 0.11 0.1 0.09 0.08 0
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Conclusions et Perspectives L’obj
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Conclusion 493 en univers gaussien
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Annexe A Evaluation de la conduite
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A.2. Eléments de contexte 497 bora
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A.4. Compétences acquises et ensei
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A.5. Conclusion 501 de la recherche
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Bibliographie ACERBI, C. (2002) :
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Bibliographie 505 BOUCHAUD, J. P. E
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Bibliographie 507 DE FINETTI, B. (1
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Bibliographie 509 GRANGER, C. W. ET
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Bibliographie 511 LILLO, F. ET R. N
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Bibliographie 513 PATTON, A. (2001)
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Bibliographie 515 SUSMEL, R. (1996)
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