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336 9. Mesure de la dépendance extrême entre deux actifs financiers Negative Tail Positive Tail α = 3 α = 3.5 α = 4 α = 3 α = 3.5 α = 4 Abbott Labs 0.20 0.17 0.14 0.16 0.13 0.10 American Home Products Corp. 0.12 0.09 0.06 0.10 0.08 0.05 Boeing Co. 0.14 0.11 0.08 0.10 0.07 0.05 Bristol-Myers Squibb Co. 0.32 0.29 0.26 0.25 0.21 0.19 Chevron Corp. 0.18 0.14 0.11 0.13 0.09 0.07 Du Pont (E.I.) de Nemours & Co. 0.23 0.20 0.17 0.16 0.13 0.10 Disney (Walt) Co. 0.16 0.13 0.10 0.15 0.12 0.09 General Motors Corp. 0.26 0.22 0.19 0.20 0.16 0.13 Hewlett-Packard Co. 0.19 0.15 0.13 0.21 0.18 0.15 Coca-Cola Co. 0.24 0.20 0.18 0.20 0.17 0.14 Minnesota Mining & MFG Co. 0.26 0.23 0.20 0.20 0.17 0.14 Philip Morris Cos Inc. 0.11 0.08 0.06 0.11 0.08 0.06 Pepsico Inc. 0.17 0.14 0.11 0.14 0.11 0.09 Procter & Gamble Co. 0.24 0.21 0.18 0.20 0.16 0.13 Pharmacia Corp. 0.10 0.08 0.05 0.10 0.07 0.05 Schering-Plough Corp. 0.23 0.20 0.17 0.16 0.13 0.10 Texaco Inc. 0.02 0.01 0.01 0.02 0.01 0.01 Texas Instruments Inc. 0.43 0.42 0.41 0.31 0.28 0.26 United Technologies Corp 0.20 0.16 0.14 0.18 0.14 0.11 Walgreen Co. 0.15 0.12 0.09 0.09 0.07 0.05 Table 8: This table summarizes the mean values over the first centile of the distribution of the coefficients of (upper or lower) tail dependence for the positive and negative tails during the time interval from January 1980 to December 2000, for three values of the tail index α = 3, 3.5, 4. 37
9.2. Estimation du coefficient de dépendance de queue 337 Negative Tail Positive Tail α = 3 α = 3.5 α = 4 α = 3 α = 3.5 α = 4 Abbott Labs 0.17 0.13 0.11 0.15 0.12 0.09 American Home Products Corp. 0.14 0.11 0.08 0.15 0.11 0.09 Boeing Co. 0.14 0.10 0.08 0.10 0.07 0.05 Bristol-Myers Squibb Co. 0.27 0.24 0.21 0.27 0.24 0.21 Chevron Corp. 0.19 0.15 0.12 0.17 0.13 0.10 Du Pont (E.I.) de Nemours & Co. 0.25 0.22 0.19 0.23 0.19 0.16 Disney (Walt) Co. 0.18 0.14 0.11 0.17 0.13 0.11 General Motors Corp. 0.26 0.23 0.20 0.24 0.21 0.18 Hewlett-Packard Co. 0.17 0.14 0.11 0.23 0.19 0.16 Coca-Cola Co. 0.23 0.20 0.17 0.23 0.20 0.17 Minnesota Mining & MFG Co. 0.28 0.25 0.23 0.25 0.22 0.19 Philip Morris Cos Inc. 0.14 0.10 0.08 0.14 0.11 0.08 Pepsico Inc. 0.16 0.13 0.10 0.16 0.12 0.10 Procter & Gamble Co. 0.23 0.20 0.17 0.22 0.18 0.15 Pharmacia Corp. 0.13 0.10 0.07 0.14 0.10 0.08 Schering-Plough Corp. 0.22 0.19 0.16 0.19 0.15 0.12 Texaco Inc. 0.03 0.02 0.01 0.03 0.02 0.01 Texas Instruments Inc. 0.44 0.42 0.41 0.37 0.35 0.33 United Technologies Corp 0.16 0.12 0.10 0.15 0.12 0.09 Walgreen Co. 0.09 0.07 0.05 0.06 0.04 0.03 Table 9: This table summarizes the mean values over the first centile of the distribution of the coefficients of (upper or lower) tail dependence for the positive and negative tails during the time interval from July 1962 to December 2000, for three values of the tail index α = 3, 3.5, 4. 38
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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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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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Page 371 and 372: 11.5. Annexe 371 point λ = 1. Thus
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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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