From local volatility to local Lévy models

References

References

• Andersen , L . 2000 . Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing . Rev. Derivatives Research , 4 : 231 – 62 .
   Google Scholar
• Andersen L Andreasen J 1999 Jumping smiles Risk 65 8
   Google Scholar
• Bakshi , G , Cao , C and Chen , Z . 1997 . Empirical performance of alternative option pricing models . J. Finance , 52 : 2003 – 49 .
   Web of Science ®Google Scholar
• Barndorff-Nielsen , O . 1998 . Processes of normal inverse gaussian type . Finance and Stochastics , 2 : 41 – 68 .
   Google Scholar
• Barndorff-Nielsen , O and Shephard , N . 2001 . Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics (with discussion) . J. Royal Statistical Society, Series B , 63 : 167 – 241 .
   Google Scholar
• Bates , D . 1996 . Jumps and stochastic volatility: exchange rate processes implicit in Deutschemark options . Rev. Financial Studies , 9 : 69 – 108 .
   Web of Science ®Google Scholar
• Bertoin J 1998 Lévy Processes Second Edition Cambridge Cambridge University Press
   Google Scholar
• Biane-Yor 1988 Sur la loi des temps locaux browniens pris en un temps exponentiel Séminaire de Probabilités, XXII Lecture Notes in Mathematics 1321 Springer-Verlag Berlin 454 66
   Google Scholar
• Carr , P , Geman , H , Madan , D and Yor , M . 2002 . The fine structure of asset returns: an empirical investigation . J. Business , 75 : 305 – 32 .
   Web of Science ®Google Scholar
• Carr , P , Geman , H , Madan , D and Yor , M . 2003 . Stochastic Volatility for Lévy Processes . Mathematical Finance , 13 : 345 – 82 .
   Web of Science ®Google Scholar
• Dellacherie C Meyer P 1980 Probabilités et Potentiel, Theorie des Martingales Paris Hermann
   Google Scholar
• Derman , E and Kani , I . 1994 . Riding on a smile . Risk , 7 : 32 – 9 .
   Google Scholar
• Dupire , B . 1994 . Pricing with a smile . Risk , 7 : 18 – 20 .
   Google Scholar
• Eberlein , E , Keller , U and Prause , K . 1998 . New insights into smile, mispricing and value at risk . J. Business , 71 : 371 – 406 .
   Web of Science ®Google Scholar
• Eberlein , E , Kallsen , J and Kristen , J . 2003 . Risk management based on stochastic volatility . J. Risk , 5 : 19 – 44 .
   Google Scholar
• Geman , H , Madan , D and Yor , M . 2001 . Time changes for lévy processes . Mathematical Finance , 11 : 79 – 96 .
   Web of Science ®Google Scholar
• Gyöngy , I . 1986 . Mimicking the one-dimensional marginal distributions of processes having an ito differential . Probability Theory and Related Fields , 71 : 501 – 16 .
   Web of Science ®Google Scholar
• Hirsch F Lacombe G 1999 Elements of Functional Analysis Graduate Texts in Mathematics Berlin Springer-Verlag
   Google Scholar
• Kou , S G . 2002 . A jump diffusion model for option pricing . Management Science , 48 : 1088 – 101 .
   Web of Science ®Google Scholar
• Kou , S G and Wang , H . 2003 . First passage times of a jump diffusion process . Adv. Appl. Probability , 35 : 504 – 31 .
   Web of Science ®Google Scholar
• Madan , D B , Carr , P and Chang , E . 1998 . The variance gamma process and option pricing . European Finance Review , 2 : 79 – 105 .
   Google Scholar
• Madan , D B and Yor , M . 2002 . Making markov martingales meet marginals . Bernoulli , 8 : 509 – 36 .
   Web of Science ®Google Scholar
• Meyer P 1976 Un Cours sur les Intégrales stochastiques Séminaire de Probabilités X Lecture Notes in Mathematics 511 Berlin Springer-Verlag
   Google Scholar
• Sato K 1999 Lévy Processes and Infinitely Divisible Distributions Cambridge Cambridge University Press
   Google Scholar
• Yor , M . 1978 . Rappels et Préliminaires Géné raux in Temps Locaux, Société Mathématique de France . Astérisque , 52–53 : 17 – 22 .
   Google Scholar