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330 9. Mesure de la dépendance extrême entre deux actifs financiers July 1962 - December 1979 January 1979 - December 2000 July 1962 - December 2000 β ρY 2 ,ε2 β ρY 2 ,ε2 β ρY 2 ,ε2 Abbott Labs 0.8994 0.0879 0.9122 0.1879 0.9081 0.1597 American Home Products Corp. 0.9855 0.1253 0.8102 0.0587 0.8652 0.0736 Boeing Co. 1.4416 0.1196 0.9036 0.0928 1.0715 0.1279 Bristol-Myers Squibb Co. 1.0832 0.1056 1.0435 0.0457 1.0559 0.0481 Chevron Corp. 1.0062 0.1191 0.8333 0.0776 0.8873 0.0906 Du Pont (E.I.) de Nemours & Co. 1.0818 0.0960 0.9451 0.0433 0.9880 0.0595 Disney (Walt) Co. 1.5530 0.0960 1.0016 0.1304 1.1736 0.0641 General Motors Corp. 1.0945 0.1531 1.0112 0.0400 1.0371 0.0563 Hewlett-Packard Co. 1.3910 0.1023 1.3074 0.0739 1.3332 0.0832 Coca-Cola Co. 1.0347 0.2146 0.9833 0.1254 0.9995 0.1238 Minnesota Mining & MFG Co. 1.1339 0.1203 0.8756 0.2605 0.9564 0.1706 Philip Morris Cos Inc. 1.0894 0.0723 0.8598 0.0340 0.9314 0.0545 Pepsico Inc. 0.9587 0.1233 0.9004 0.3294 0.9187 0.3169 Procter & Gamble Co. 0.8293 0.1873 0.8938 0.1188 0.8738 0.1287 Pharmacia Corp. 1.0750 0.0783 0.8824 0.0373 0.9429 0.0357 Schering-Plough Corp. 1.1244 0.1284 1.0480 0.0494 1.0720 0.0540 Texaco Inc. 1.4578 0.1410 1.3811 0.0674 1.4049 0.0766 Texas Instruments Inc. 0.9414 0.1354 0.6600 0.0823 0.7481 0.1053 United Technologies Corp 1.1336 0.1243 0.9049 0.1175 0.9763 0.1098 Walgreen Co. 0.6354 0.1052 0.8554 0.1087 0.7869 0.0798 31 Table 2: This table presents the estimated coefficient β for the factor model (6) and the correlation coefficient ρY 2 ,ε2 between the square of factor and the square of the estimated idiosyncratic noise, for the different time intervals we have considered. A Fisher’s test shows that these correlation coefficients are all significantly different from zero.
9.2. Estimation du coefficient de dépendance de queue 331 Negative Tail Positive Tail q = 1% q = 2.5% q = 5% q = 1% q = 2.5% q = 5% Asset ε Asset ε Asset ε Asset ε Asset ε Asset ε Abbott Labs 5.54 5.31 3.94 4.02 3.27 3.31 5.10 4.50 4.09 3.71 3.53∗ 3.14 American Home Products Corp. 4.58 5.11 3.89 3.81 3.02∗ 3.21∗ 3.64 4.66 3.60 3.81 3.11 3.15 Boeing Co. 6.07 4.90 4.57 3.74 3.32 3.49 4.04 4.27 3.95 4.19 3.35∗ 2.93 Bristol-Myers Squibb Co. 4.32 4.27 3.31 3.95 2.99∗ 3.16∗ 5.96∗ 5.19 3.94 4.82∗ 3.62∗ 4.03∗ Chevron Corp. 5.24 4.78 3.75 3.29 2.91 3.12∗ 5.21 5.15 3.90 4.26 3.25∗ 3.07 Du Pont (E.I.) de Nemours & Co. 5.26 4.36 3.69 3.76 3.17∗ 3.23∗ 5.35 5.15 4.00 3.37 3.13 3.04 Disney (Walt) Co. 3.59 4.23 3.59 3.84 3.08∗ 3.22∗ 4.90 4.34 4.26 3.73 3.33∗ 3.29∗ General Motors Corp. 4.82 3.50 3.72 3.66 2.94∗ 3.36 3.91 4.78 3.64 3.86 2.94 3.07 Hewlett-Packard Co. 3.76 3.89 3.12∗ 3.05∗ 2.81∗ 3.00∗ 4.64 5.08 4.08 4.20 3.41∗ 3.42∗ Coca-Cola Co. 3.45 3.45 3.05∗ 3.71 2.75∗ 3.17∗ 3.91 4.26 3.16 3.61 2.81 3.16 Minnesota Mining & MFG Co. 5.16 4.86 4.06 4.35 3.43 3.71 4.35 4.47 3.96 3.31 3.14 3.06 Philip Morris Cos Inc. 4.63 3.79 3.82 3.90 3.38 3.48 4.10 4.64 3.59 3.85 3.03 3.06 Pepsico Inc. 4.89 5.35 3.93 4.49 3.02∗ 3.27 4.07 4.67 3.49 3.86 3.15 3.21∗ Procter & Gamble Co. 4.42 3.77 3.77 3.74 3.13∗ 3.42 4.14 5.39 3.59 3.73 2.97 3.40∗ Pharmacia Corp. 4.73 4.24 4.05 3.45 2.88∗ 3.34 4.46 3.72 3.95 3.90 3.14 2.99 Schering-Plough Corp. 4.59 4.70 4.20 3.87 3.37 3.33 4.60 5.88∗ 3.50 3.91 3.07 3.22∗ Texaco Inc. 5.34 4.59 3.99 3.84 3.07∗ 3.19∗ 3.83 4.10 3.94 3.67 3.14 2.98 Texas Instruments Inc. 4.08 4.54 3.36 3.13∗ 3.22∗ 2.87∗ 4.52 4.20 3.67 3.79 3.16 3.07 United Technologies Corp 4.00 4.49 3.52 3.92 3.27 3.46 4.78 4.97 3.73 3.98 3.26∗ 3.49∗ Walgreen Co. 4.63 6.50 3.85 4.26 2.94∗ 3.18∗ 5.16 4.56 3.47 3.30 3.15 2.82 32 Standart & Poor’s 500 5.17 - 4.16 - 3.91 - 3.74 - 3.34 - 2.64 - Table 3: This table gives the estimated value of the tail index for the twenty considered assets, the Standard & Poor’s 500 index and the residues ε obtained by regressing each asset on the Standard & Poor’s 500 index, for both the negative and the positive tails, during the time interval from July 1962 to December 1979. The tail indexes are estimed by Hill’s estimator at the quantile 1%, 2.5% and 5% which are the optimal quantiles given by the Hall (1990) and Danielsson and de Vries (1997)’s algorithms. The values decorrated with stars represent the tail indexes which cannot be considered equal to the Standard & Poor’s 500 index’s tail index at the 95% confidence level.
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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 280 and 281: 280 9. Mesure de la dépendance ext
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Page 369 and 370: 11.5. Annexe 369 Collective Origin
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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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