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328 9. Mesure de la dépendance extrême entre deux actifs financiers Nelsen, R.B., 1998, An introduction to copulas. (Springer Verlag New York). Pagan, A., 1996, The econometrics of financial markets, Journal of Empirical Finance 3, 15 – 102. Pagan, A., and A. Ullah, 1999, Non parametrics econometrics. (Cambridge University Press Cambridge). Patton, J.A., 2001, Estimation of copula models for time series of possibly different lengths, Working paper, University of California, Econ. Disc. Paper No. 2001-17. Roll, R., 1988, The International Crash of October 1987, Financial Analysts Journal pp. 19–35. Rootzén, H., M.R. Leadbetter, and L. de Haan, 1998, On the distribution tail array sums for strongly mixing stationary sequences, Annals of Applied Probability 8, 868–885. Ross, S.A., 1976, The arbitrage theory of capital asset pricing, Journal of Economic Theory 17, 254–286. Sharpe, W., 1964, Capital assets prices: a theory of market equilibrium under conditions of risk, Journal of Finance 19, 425–442. Shealter, S.J., and J.S. Marron, 1990, Kernel quantile estimators, Journal of the Americam Statistical Association 85, 410–415. Sklar, A., 1959, Fonction de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8, 229–231. Starica, C., 1999, Multivariate extremes for models with constant conditional correlations, Journal of Empirical Finance 6, 515–553. Vasicek, O., 1977, An equilibrium characterisation of the term structure of interest rates, Journal of Financial Economics 5, 177–188. Xu, Y., and B.G. Malkiel, 2002, Investigating the behavior of idiosyncratic volatility, forthcoming Journal of Business. 29
9.2. Estimation du coefficient de dépendance de queue 329 July 1962 - December 1979 January 1980 - December 2000 July 1962 - December 2000 Mean Std. Skew. Kurt. Mean Std. Skew. Kurt. Mean Std. Skew. Kurt. Abbott Labs 0.6677 0.0154 0.2235 2.192 0.9217 0.0174 -0.0434 2.248 0.8066 0.0165 0.0570 2.300 American Home Products Corp. 0.4755 0.0136 0.2985 3.632 0.8486 0.0166 0.1007 8.519 0.6803 0.0154 0.1717 7.557 Boeing Co. 0.8460 0.0228 0.6753 4.629 0.7752 0.0193 0.1311 4.785 0.8068 0.0209 0.4495 4.901 Bristol-Myers Squibb Co. 0.5342 0.0152 -0.0811 2.808 0.9353 0.0175 -0.3437 16.733 0.7546 0.0165 -0.2485 12.573 Chevron Corp. 0.4916 0.0134 0.2144 2.442 0.6693 0.0169 0.0491 4.355 0.5885 0.0154 0.1033 4.209 Du Pont (E.I.) de Nemours & Co. 0.2193 0.0126 0.3493 2.754 0.6792 0.0172 -0.1021 4.731 0.4715 0.0153 0.0231 4.937 Disney (Walt) Co. 0.9272 0.0215 0.2420 2.762 0.8759 0.0195 -0.6661 17.655 0.8997 0.0204 -0.1881 9.568 General Motors Corp. 0.3547 0.0126 0.4138 4.302 0.5338 0.0183 -0.0128 5.373 0.4538 0.0160 0.0872 6.164 Hewlett-Packard Co. 0.7823 0.0199 0.0212 3.063 0.8913 0.0238 0.0254 4.921 0.8420 0.0221 0.0256 4.624 Coca-Cola Co. 0.4829 0.0138 0.0342 5.436 0.9674 0.0170 -0.1012 14.377 0.7483 0.0157 -0.0513 12.611 Minnesota Mining & MFG Co. 0.3459 0.0139 0.3016 2.997 0.6885 0.0150 -0.7861 20.609 0.5333 0.0145 -0.3550 14.066 Philip Morris Cos Inc. 0.7930 0.0153 0.2751 2.799 0.9664 0.0180 -0.2602 10.954 0.8863 0.0169 -0.0784 8.790 Pepsico Inc. 0.4982 0.0147 0.2380 2.867 0.9443 0.0180 0.1372 4.594 0.7431 0.0166 0.1786 4.413 Procter & Gamble Co. 0.3569 0.0115 0.3911 4.343 0.7916 0.0164 -1.6610 46.916 0.5947 0.0144 -1.2408 44.363 Pharmacia Corp. 0.3801 0.0145 0.2699 3.508 0.9027 0.0191 -0.6133 13.587 0.6666 0.0172 -0.3773 12.378 Schering-Plough Corp. 0.6328 0.0163 0.2619 3.112 1.0663 0.0192 0.1781 7.9979 0.8703 0.0179 0.2139 6.757 Texaco Inc. 0.3416 0.0134 0.2656 2.596 0.6644 0.0166 0.1192 6.477 0.5197 0.0152 0.1725 5.829 Texas Instruments Inc. 0.6839 0.0198 0.2076 3.174 1.0299 0.0268 0.1595 7.848 0.8726 0.0239 0.1831 7.737 United Technologies Corp 0.5801 0.0185 0.3397 2.826 0.7752 0.0170 0.0396 3.190 0.6876 0.0177 0.1933 3.034 Walgreen Co. 0.5851 0.0165 0.3530 3.030 1.1996 0.0185 0.1412 3.316 0.9217 0.0176 0.2260 3.295 30 Standart & Poor’s 500 0.1783 0.0075 0.2554 3.131 0.5237 0.0101 -1.6974 36.657 0.3674 0.0090 -1.2236 32.406 Table 1: This table gives the main statistical features of the three samples we have considered. The columns Mean, Std., Skew. and Kurt. respectively give the average return multiplied by one thousand, the standard deviation, the skewness and the excess kurtosis of each asset over the time intervals form July 1962 to December 1979, January 1980 to Decemeber 2000 and July 1962 to December 2000. The excess kurtosis is given as indicative of the relative weight of large return amplitudes, and can always be calculated over a finite time series even if it may not be asymptotically defined for power tails with exponents less than 4.
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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 278 and 279: 278 9. Mesure de la dépendance ext
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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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