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212 8. Tests de copule gaussienne References Andersen, J.V. and D. Sornette, 2001, Have your cake and eat it too: increasing returns while lowering large risks! Journal of Risk Finance 2, 70-82. Anderson T. W. and D.A. Darling, 1952, Asymptotic theory of certain “goodness of fit” criteria, Annals of Mathematical Statistics 23, 193-212. Ang, A. and J. Chen, 2001, Asymmetric correlations of equity portfolio, Working Paper. Baig, T. and I. Goldfjn, 1998, Financial Markets Contagion in the Asian crisis, Mimeo, International Monetary Fund. Chen, K. and S.-H. Lo, 1997, On a Mapping Approach to Investigating the Bootstrap Accuracy, Probability Theory and Related Fields 107, 197-217. Cherubini, U. and E. Luciano, 2000, Multivariate option pricing with copulas, Working Paper. Efron, B., and R.Tibshirani, 1986, Bootstrap method for standard errors, confidence intervals and other measures of statistical accuracy, Statistical Science 1, 54-77. Embrechs P., A.J. McNeil and D. Straumann, 1999, Correlation : Pitfalls and Alternatives. Risk, 69-71. 2001. Embrechts, P., A. Hoeing, A. Juri, 2001, Using Copulae to bound the Value-at-Risk for functions of dependent risk, ETH Zurick Working Paper. Embrechts P., A.J. McNeil and D. Straumann, 2001, Correlation and Dependency in Risk Management : Properties and Pitfalls, in : Dempster, M., ed., Value at Risk and Beyond (Cambridge University Press). Frees, E. and E. Valdez, 1998, Understanding Relationships using copula,. North Americam Actuarial Journal 2, 1-25. Genest, C. and R. MacKay, 1986, The Joy of Copulas, American Statistician 40, 280-283. Genest, C., 1987, Frank’s Family of Bivariate Distributions, Biometrika 74, 549-555. Genest, C. and J.P. Rivest, 1993, Statistical Inference Procedures for Bivariate Archimedean Copulas, Journal of American Statistical Association 88, 1034-1043. Gopikrishnan, P., M. Meyer, L.A.N. Amaral and H.E. Stanley, 1998, Inverse Cubic Law for the Distribution of Stock Price Variation, European Physical Journal B 3, 139-140. Gouriéroux, C. and J. Jasiak, 1999, Truncated Local Likelyhood and Non-paarametric tail analysis, DP 99 CREST. Guillaume, D.M., M.M Dacorogna, R.R. Davé, J.A Muller, R.B. Olsen and O.V. Pictet, 1997, From the Bird Eye to the Microscope : A Survey of the New Stylized Facts of the Intra-Dayly Foreign Exchange Markets, Finance and Stochastics 1, 95-129. Haas, C.N., 1999, On Modeling Correlated Random Variables in Risk Assessment, Risk Analysis 19, 1205-1214. Joe, H., 1993, Parametric Families of Multivariate Distributions with Given Marginals, Journal of Multivariate Analysis 46, 262-282. 20
Kaminsky, G.L. and S.L. Schmukler, 1999, What Triggers Market Jitters? A Chronicle of the Asian Crisis, Journal of International Money and Finance 18, 537-560. Klugman, S.A. and R. Parsa, 1999, Fitting Bivariate Loss Distribution with Copulas, Insurance : Mathematics and Economics 24, 139-148. Laherrère, J. and D. Sornette, 1999, Stretched exponential distributions in Nature and Economy: “Fat tails” with characteristic scales, European Physical Journal B 2, 525-539. Longin F. and B. Solnik, Extreme Correlation of International Equity Markets, The Journal of Finance LVI, 649-676 (2001). Lindskog, F., 1999, Modelling Dependence with Copulas, http : //www.risklab.ch/P apers.html#MT Lindskog Lux, L., 1996, The Stable Paretian Hypothesis and the Frequency of Large Returns : an Examination of Major German Stocks, Applied Financial Economics 6, 463-475. Markovitz, H., 1959, Portfolio selection : Efficient diversification of investments (John Wiley and Sons, New York). Nelsen, R.B., 1998, An Introduction to Copulas. Lectures Notes in statistic 139 (Springer Verlag, New York). Pagan, A., 1996, The Econometrics of Financial Markets, Journal of Empirical Finance 3, 15-102. Rosenberg, J.V., 1999, Semiparametric pricing of multivariate contingent claims, NYU-Stern School of Business Working Paper. Sornette, D., P. Simonetti and J. V. Andersen, 2000, φ q -field theory for Portfolio optimization: “fat tails” and non-linear correlations, Physics Report 335, 19-92. Sornette, D., J. V. Andersen and P. Simonetti, 2000, Portfolio Theory for “Fat Tails”, International Journal of Theoretical and Applied Finance 3 , 523-535. Starica, C., 1999, Multivariate extremes for models with constant conditional correlations. Journal of Empirical Finance, 6, 515-553. Vries, C.G. de, 1994, Stylized Facts of Nominal Exchange Rate Returns, in : Van der Ploeg, F., ed., The Handbook of international Macroeconomics (Blackwell, Oxford) 348-389. 21 213
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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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262 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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