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190 BIBLIOGRAPHY [9] O. E. Barndorff-Nielsen and N. Shephard, Non-Gaussian Ornstein-Uhlenbeck based models and some of their uses in financial econometrics, J. R. Statistic. Soc. B, 63 (2001), pp. 167–241. [10] D. Bates, Jumps and stochastic volatility: the exchange rate processes implicit in Deutschemark options, Rev. Fin. Studies, 9 (1996), pp. 69–107. [11] D. Bates, Post-87 crash fears in the S&P 500 futures option market, J. Econometrics, 94 (2000), pp. 181–238. [12] D. Bates, Maximum likelihood estimation of latent affine processes. Working paper, available from http://www.biz.uiowa.edu/faculty/dbates/, 2004. [13] D. S. Bates, Testing option pricing models, in Statistical Methods in Finance, vol. 14 of Handbook of Statistics, North-Holland, Amsterdam, 1996, pp. 567–611. [14] N. Baud, A. Frachot, and T. Roncalli, How to avoid over-estimating capital charge in operational risk. Download from gro.creditlyonnais.fr/content/fr/home_mc.htm, 2002. [15] S. Beckers, A note on estimating parameters of a jump-diffusion process of stock returns, J. Fin. and Quant. Anal., 16 (1981), pp. 127–140. [16] F. Bellini and M. Frittelli, On the existence of minimax martingale measures, Math. Finance, 12 (2002), pp. 1–21. [17] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. [18] J. Bouchaud and M. Potters, Théorie des Risques Financiers, Aléa, Saclay, 1997. [19] S. Boyarchenko and S. Levendorskiĭ, Non-Gaussian Merton-Black-Scholes Theory, World Scientific, River Edge, NJ, 2002. [20] R. Byrd, P. Lu, and J. Nocedal, A limited memory algorithm for bound constrained optimization, SIAM Journal on Scientific and Statistical Computing, 16 (1995), pp. 1190– 1208.
BIBLIOGRAPHY 191 [21] P. Carr, H. Geman, D. Madan, and M. Yor, The fine structure of asset returns: An empirical investigation, Journal of Business, 75 (2002), pp. 305–332. [22] P. Carr, H. Geman, D. Madan, and M. Yor, Stochastic volatility for Lévy processes, Math. Finance, 13 (2003), pp. 345–382. [23] P. Carr and D. Madan, Option valuation using the fast Fourier transform, J. Comput. Finance, 2 (1998), pp. 61–73. [24] T. Chan, Pricing contingent claims on stocks driven by Lévy processes, Ann. Appl. Probab., 9 (1999), pp. 504–528. [25] A. S. Cherny and A. N. Shiryaev, Change of time and measure for Lévy processes. MaPhySto lecture notes series 2002-13, 2002. [26] R. Cont, J.-P. Bouchaud, and M. Potters, Scaling in financial data: Stable laws and beyond, in Scale Invariance and Beyond, B. Dubrulle, F. Graner, and D. Sornette, eds., Springer, Berlin, 1997. [27] R. Cont and P. Tankov, Financial Modelling with Jump Processes, Chapman & Hall / CRC Press, 2004. [28] R. Cont and P. Tankov, Non-parametric calibration of jump-diffusion option pricing models, J. Comput. Finance, 7 (2004). [29] J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp., 19 (1965), pp. 297–301. [30] I. Csiszar, I-divergence geometry of probability distributions and minimization problems, Annals of Probability, 3 (1975), pp. 146–158. [31] M. H. A. Davis, Option pricing in incomplete markets, in Mathematics of Derivative Securities, M. H. A. Dempster and S. R. Pliska, eds., 1997. [32] P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, 1975.
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Thèse présentée pour obtenir le
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Abstract This thesis deals with the
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Contents Remarks on notation 11 Int
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CONTENTS 9 II Multidimensional mode
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12 For {P n } n≥1 , P ∈ P(Ω) t
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14 INTRODUCTION EN FRANCAIS corresp
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16 INTRODUCTION EN FRANCAIS Lévy p
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18 INTRODUCTION EN FRANCAIS Calibra
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20 INTRODUCTION EN FRANCAIS • Si
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22 INTRODUCTION EN FRANCAIS et Scai
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24 INTRODUCTION EN FRANCAIS Ce rés
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26 INTRODUCTION EN FRANCAIS dans un
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28 INTRODUCTION 7500 Taux de change
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30 INTRODUCTION Lévy models by Fou
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Chapter 1 Lévy processes and exp-L
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1.1. LEVY PROCESSES 35 Proposition
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1.1. LEVY PROCESSES 37 The characte
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1.1. LEVY PROCESSES 39 On the other
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1.2. EXPONENTIAL LEVY MODELS 41 (b)
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1.3. EXP-LEVY MODELS IN FINANCE 43
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1.3. EXP-LEVY MODELS IN FINANCE 45
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1.4. PRICING EUROPEAN OPTIONS 47 wi
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1.4. PRICING EUROPEAN OPTIONS 49 Pr
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1.4. PRICING EUROPEAN OPTIONS 51 Nu
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1.4. PRICING EUROPEAN OPTIONS 53 By
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1.4. PRICING EUROPEAN OPTIONS 55 Si
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Chapter 2 The calibration problem a
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2.1. LEAST SQUARES CALIBRATION 59 m
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2.1. LEAST SQUARES CALIBRATION 61 i
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2.1. LEAST SQUARES CALIBRATION 63 w
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2.1. LEAST SQUARES CALIBRATION 65 A
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2.1. LEAST SQUARES CALIBRATION 67 i
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2.2. SELECTION USING RELATIVE ENTRO
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2.2. SELECTION USING RELATIVE ENTRO
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2.3. RELATIVE ENTROPY IN THE LITERA
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2.4. RELATIVE ENTROPY OF LEVY PROCE
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2.4. RELATIVE ENTROPY OF LEVY PROCE
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2.5. REGULARIZING THE CALIBRATION P
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Chapter 3 Numerical implementation
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3.1. DISCRETIZING THE CALIBRATION P
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3.2. CHOICE OF THE PRIOR 99 Since
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3.2. CHOICE OF THE PRIOR 101 twice
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3.3. CHOICE OF THE REGULARIZATION P
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3.4. CHOICE OF THE WEIGHTS 111 Then
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3.5. NUMERICAL SOLUTION 113 have th
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3.5. NUMERICAL SOLUTION 115 of X t
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3.5. NUMERICAL SOLUTION 117 since
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3.6. NUMERICAL AND EMPIRICAL TESTS
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Part II Multidimensional modelling
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134 CHAPTER 4. DEPENDENCE OF LEVY P
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Page 140 and 141: 140 CHAPTER 4. DEPENDENCE OF LEVY P
Page 166 and 167: 166 CHAPTER 5. APPLICATIONS OF LEVY
Page 188 and 189: 188 CONCLUSIONS AND PERSPECTIVES ge
Page 192 and 193: 192 BIBLIOGRAPHY [33] F. Delbaen, P
Page 194 and 195: 194 BIBLIOGRAPHY [57] P. Jorion, On
Page 196 and 197: 196 BIBLIOGRAPHY [81] S. Raible, L
Page 198 and 199: 198 BIBLIOGRAPHY
Page 200: 200 INDEX tightness, 40 levycalibra
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