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222 8. Tests <strong>de</strong> copule gaussienne ˆρ d1 d2 d3 d4 CHF DEM 0.92 1.73e-02 1.33e-02 0.00e+00 1.31e-02 CHF JPY 0.55 1.34e-01 1.49e-01 3.83e-01 1.41e-01 CHF MYR 0.32 8.47e-01 7.00e-01 3.56e-01 7.40e-01 CHF THA 0.17 4.40e-01 7.10e-01 3.53e-02 7.11e-01 CHF UKP 0.79 3.10e-03 1.00e-03 0.00e+00 5.00e-04 DEM JPY 0.56 2.46e-02 9.43e-02 1.63e-01 9.26e-02 DEM MYR 0.35 9.32e-01 7.95e-01 3.51e-01 7.95e-01 DEM THA 0.21 4.36e-01 8.77e-01 3.47e-02 8.74e-01 DEM UKP 0.82 0.00e+00 0.00e+00 0.00e+00 0.00e+00 JPY MYR 0.34 4.90e-01 5.49e-01 3.66e-01 5.94e-01 JPY THA 0.27 3.89e-01 3.06e-01 3.37e-02 3.59e-01 JPY UKP 0.53 9.00e-04 1.66e-02 6.72e-02 1.67e-02 MYR THA 0.29 1.08e-01 8.71e-02 3.42e-02 9.30e-02 MYR UKP 0.33 1.12e-01 2.86e-01 3.54e-01 3.45e-01 THA UKP 0.21 4.34e-01 8.62e-01 3.13e-02 8.67e-01 Table 3: Same as table 2 for currencies over a 5 years time interval from January 25, 1989 to Januay 11, 1994. 30
ˆρ d1 d2 d3 d4 CHF DEM 0.92 3.15e-01 3.11e-01 5.00e-04 3.41e-01 CHF JPY 0.52 5.84e-01 6.44e-01 1.98e-02 6.74e-01 CHF MYR 0.16 7.11e-01 9.15e-01 8.83e-01 9.22e-01 CHF THA 0.25 1.10e-02 3.87e-02 1.05e-01 3.34e-02 CHF UKP 0.53 9.75e-02 1.03e-01 2.33e-01 9.29e-02 DEM JPY 0.53 3.63e-01 5.40e-01 1.77e-02 6.54e-01 DEM MYR 0.18 3.55e-01 5.00e-01 5.84e-01 5.67e-01 DEM THA 0.28 1.28e-02 2.18e-02 1.08e-01 1.51e-02 DEM UKP 0.56 1.15e-01 1.10e-01 3.02e-01 1.06e-01 JPY MYR 0.29 7.63e-02 2.14e-01 6.67e-02 2.23e-01 JPY THA 0.38 0.00e+00 2.00e-04 3.09e-02 2.00e-04 JPY UKP 0.28 4.62e-01 2.30e-01 1.23e-01 2.07e-01 MYR THA 0.44 5.00e-04 1.20e-03 5.34e-02 1.20e-03 MYR UKP 0.11 5.94e-01 7.44e-01 6.95e-01 7.82e-01 THA UKP 0.12 1.26e-02 7.66e-02 1.19e-01 6.51e-02 Table 4: Same as table 2 for currencies over a 5 years time interval from January 12, 1994 to December 31, 1998. 31 223
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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 171 and 172: A Corcos et al Q UANTITATIVE F INAN
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272 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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