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104 3. Distributions exponentielles étirées contre distributions régulièrement variables Champenowne, D.G, 1953, Economic Journal 63, 318-51. Cont, R., Potters, M. and J.-P. Bouchaud, 1997, Scaling in stock market data: stable laws and beyond, in Scale Invariance and Beyond (Proc. CNRS Workshop on Scale Invariance, Les Houches, 1997), eds. B. Dubrulle, F. Graner and D. Sornette (Berlin: Springer). Cox, D.R., 1961, Test of separate families of hypotheses, in : Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probabilty 1, 105-123, University of California Press: Berkeley . Cox, D.R., 1962, Further results of separate families of hypotheses, journal of the Royal Statistical Society B 24, 406-424. Cromwell, J.B., W.C. Labys and M. Terraza, 1994, Univariate Tests for Time Series Models (Sage, Thousand Oaks, CA, pp. 20-22). Dacorogna M.M., U.A. Müller, O.V. Pictet and C.G. de Vries, 1992, The distribution of extremal foreign exchange rate returns in large date sets, Working Paper, Olsen and Associates Internal Documents UAM, 19921022. Dragulescu, A.A. and V.M. Yakovenko, 2002, Probability distribution of returns for a model with stochastic volatility, preprint at http://xxx.lanl.gov/abs/cond-mat/0203046 Eberlein, E., Keller, U. and Prause, K., 1998, New insights into smile, mispricing and value at risk: the hyperbolic model J. Business 71, 371-405. Embrechts P., C.P. Klüppelberg and T. Mikosh, 1997, Modelling Extremal Events (Springer-Verlag). Engle, R.F., 1984, Wald, Likelihood Ratio, and Lagrange Multiplier Tests in Econometrics , in: Z. Griliches and M.D. Intriligator, eds., Handbook of Econometrics, Vol. II. North-Holland: Amsterdam. Engle, R.F. and A.J. Patton, 2001, What good is a volatility model ?, Quantitative Finance 1, 237-245. Fama E.F., 1965, The Behavior of Stock Market Prices, J. Business 38, 34-105. Fama E.F. and K.R. French, 1996, Multifactor explanations of asset pricing anomalies, Journal of Finance 51. Fang, H. and T. Lai, 1997, Co-kurtosis and capital asset pricing, Financial Review 32, 293-307. Farmer J.D., 1999, Physicists Attempt to Scale the Ivory Towers of Finance, Computing in Science and Engineering, Nov/Dec 1999, 26-39. Feller, W., 1971, An Introduction to Probability Theory and its Applications, vol. II (John Wiley and sons, New York). Frisch, U. and D. Sornette, 1997, Extreme deviations and applications, J. Phys. I France 7, 1155-1171. Gabaix, X., 1999, Zipf’s law for cities: An explanation, Quaterly J. Econ. 114, 739-767. Gabaix, X., P. Gopikrishnan, V. Plerou and H.E. Stanley, 2002, Understanding Large Movements in Stock Market Activity, in press in Nature Gopikrishnan P., M. Meyer, L.A.N. Amaral and H.E. Stanley, 1998, Inverse Cubic Law for the Distribution of Stock Price Variations, European Physical Journal B 3, 139 –140. Gouriéroux C. and J. Jasiak, 1998, Truncated maximum likelihood, goodness of fit tests and tail analysis, Working paper, CREST. 40
Gouriéroux C. and A. Monfort, 1994, Testing non nested hypothesis, Handbook of Econometrics 4, 2585- 2637. Granger, C.W.J. and T. Teräsvirta, 1999, A simple nonlinear model with misleading properties, Economics Letter 62, 741-782. Guillaume D.M., M.M. Dacorogna, R.R. Davé, U.A. Müller, R.B. Olsen and O.V. Pictet, 1997, From the bird’s eye to the microscope: a survey of new stylized facts of the intra-day foreign exchange markets, Finance and Stochastics 1, 95-130. Hall, P.G, 1979, On the rate of convergence of normal extremes. Journal of Applied Probabilities 16, 433- 439. Hall, W.J. and J.A. Wellnel, 1979, The rate of convergence in law of the maximum of an exponential sample. Statistica Neerlandica 33, 151-154. Hill, B.M., 1975, A simple general approach to inference about the tailof a distribution, Annals of statistics 3, 1163-1174. Hwang, S. and S. Satchell, 1999, Modelling emerging market risk premia using higher moments, International Journal of Finance and Economics 4, 271-296. Joe, H, 1997, Multivariate models and dependence concepts, Chapman & Hall, London. Johansen, A. and D. Sornette, 2002, Large Stock Market Price Drawdowns Are Outliers, Journal of Risk 4 (2), 69-110. E. Jondeau and M. Rockinger, 2001, Testing for differences in the tails of stock-market returns. Working Paper available at htt p : //papers.ssrn.com/paper.ta f ?abstract id = 291399 Jurcenko, E. and B. Maillet, 2002, The four-moment capital asset pricing model: some basic results, Working Paper. Kearns P. and A. Pagan, 1997, Estimating the density tail index for financial time series, Review of Economics and Statistics 79, 171-175. Kon, S., 1984, Models of stock returns: a comparison J. Finance XXXIX, 147-165. 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. Levy, M., S. Solomon and G. Ram, 1996, Dynamical explanation of the emergence of power law in a stock market model, Int. J. Mod. Phys. C 7, 65-72. Longin F.M., 1996, The asymptotic distribution of extreme stock market returns, Journal of Business 96, 383-408. Lux T., 1996, The stable Paretian hypothesis and the frequency of large returns: an examination of major German stocks, Applied Financial Economics 6, 463-475. Lux T., 2000, The Limiting Extreme Behavior of Speculative Returns: An Analysis of Intra-Daily Data from the Francfurt Stock Exchange, preprint,March 2000, 29 p. Lux, L. and D. Sornette, 2002, On Rational Bubbles and Fat Tails, J. Money Credit and Banking, Part 1, 34, 589-610. 41 105
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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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Page 85 and 86: 5 Comparison of the descriptive pow
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Page 93 and 94: B Minimum Anderson-Darling Estimato
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Page 97 and 98: D Testing non-nested hypotheses wit
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Page 103: References Andersen, J.V. and D. So
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Page 123 and 124: Variation coefficient Variation coe
Page 125 and 126: Mean excess function Mean excess fu
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Page 139 and 140: 2 Long-range memory and distinction
Page 141 and 142: Figure 2: Measuring the conditional
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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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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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