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130 3. Distributions exponentielles étirées contre distributions régulièrement variables Wilks statistic (doubled log−likelihood ratio) Wilks statistic (doubled log−likelihood ratio) 80 70 60 50 40 30 20 10 SE Wilks statistics for CD vs 4 parametric families, DJpos, n=14949 IG PD 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Lower threshold, u 80 70 60 50 40 30 20 10 SE IG ED 2 χ (.95) 2 Wilks statistics for CD vs 4 parametric families, DJneg, n=13464 PD ED 2 χ (.95) 2 2 χ (.95) 1 2 χ (.95) 1 0 0 0.01 0.02 0.03 Lower threshold, u 0.04 0.05 0.06 Figure 9: Wilks statistic for the comprehensive distribution versus the four parametric distributions : Pareto (PD), Weibull (SE), Exponential (ED) and Incomplete Gamma (IG) for the Dow Jones daily returns. The upper panel refers to the positive returns and the lower panel to the negative ones. 66
Tail 1−F(x) and parameter b Tail 1−F(x) and parameter b 1.4 1.2 1 0.8 0.6 0.4 0.2 0 1.4 1.2 1 0.8 0.6 0.4 0.2 0 Sample tail 1−F(x)(thick) and "local" Pareto−b(thin), simulated Pareto−1.2,n=15000 10 20 30 40 50 x 60 70 80 90 100 Sample tail 1−F(x)(thick) and "local" Pareto−b(thin), simulated SE−0.3,n=15000 100 200 300 400 500 x 600 700 800 900 1000 Figure 10: Local index β(x) estimated for a Pareto distribution with tail index = 1.2 (upper panel) and a Stretched exponential with exponent c = 0.3 (lower panel). 67 131
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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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Page 81 and 82: empirical analog FN(x), estimated f
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Page 85 and 86: 5 Comparison of the descriptive pow
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Page 89 and 90: tail (positive or negative) of the
Page 91 and 92: Equation (46) depends on c only and
Page 93 and 94: B Minimum Anderson-Darling Estimato
Page 95 and 96: C Local exponent In this Appendix,
Page 97 and 98: D Testing non-nested hypotheses wit
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Page 101 and 102: where E0[·] denotes the expectatio
Page 103 and 104: References Andersen, J.V. and D. So
Page 105 and 106: Gouriéroux C. and A. Monfort, 1994
Page 107 and 108: Rubinstein, M., 1973, The fundament
Page 109 and 110: (a) Independent Data Stretched-Expo
Page 111 and 112: (a) Dow Jones Positive Tail Negativ
Page 113 and 114: Nasdaq Dow Jones Pos. Tail Neg. Tai
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Page 123 and 124: Variation coefficient Variation coe
Page 125 and 126: Mean excess function Mean excess fu
Page 127 and 128: Hill‘s estimate b u Hill‘s esti
Page 129: Wilks statistic (doubled log−like
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Page 135 and 136: Chapitre 4 Relaxation de la volatil
Page 137 and 138: Volatility Fingerprints of Large Sh
Page 139 and 140: 2 Long-range memory and distinction
Page 141 and 142: Figure 2: Measuring the conditional
Page 143 and 144: the system to the accumulation of m
Page 145 and 146: Appendix C: “Conditional response
Page 147 and 148: Baillie, R.T., 1996, Long memory pr
Page 149 and 150: Chapitre 5 Approche comportementale
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Page 153 and 154: 5.2. Modèles d’opinion contre mo
Page 155 and 156: 5.4. Conséquences des phénomènes
Page 157 and 158: 5.5. Conclusion 157 ce qui induit u
Page 159 and 160: Chapitre 6 Comportements mimétique
Page 161 and 162: RESEARCH PAPER Q UANTITATIVE F INAN
Page 163 and 164: A Corcos et al Q UANTITATIVE F INAN
Page 179: Deuxième partie Etude des proprié
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182 7. Etude de la dépendance à l
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192 8. Tests de copule gaussienne
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194 8. Tests de copule gaussienne 1
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200 8. Tests de copule gaussienne t
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202 8. Tests de copule gaussienne T
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204 8. Tests de copule gaussienne a
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206 8. Tests de copule gaussienne c
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208 8. Tests de copule gaussienne t
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210 8. Tests de copule gaussienne (
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212 8. Tests de copule gaussienne R
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228 8. Tests de copule gaussienne f
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236 8. Tests de copule gaussienne T
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238 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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