Some aspects of parameter identification in a mean reverting financial asset model with time-dependent volatility

References

• Achdou , Y. 2005 . An inverse problem for a parabolic variational inequality arising in volatility calibration with American options . SIAM J. Control Optim. , 43 : 1583 – 1615 .
   Google Scholar
• Avellaneda , M. , Friedman , C. , Holmes , R. and Samperi , D. 1997 . Calibrating volatility surfaces via relative entropy minimization . Appl. Math. Finance , 4 : 37 – 64 .
   Google Scholar
• Bouchouev , I. and Isakov , V. 1997 . The inverse problem of option pricing . Inverse Probl. , 13 : L11 – L17 .
   Web of Science ®Google Scholar
• Bouchouev , I. and Isakov , V. 1999 . Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets . Inverse Probl. , 15 : R95 – R116 .
   Web of Science ®Google Scholar
• Cohen , A. 2003 . Numerical analysis of wavelet methods, Studies in Mathematics and Its Applications , Amsterdam : Elsevier .
   Google Scholar
• Cont , R. and Tankov , P. 2004 . Financial Modelling with Jump Processes , Chapman & Hall/CRC Financial Mathematics Series Boca Raton, FL : Chapman & Hall/CRC .
   Google Scholar
• Cont , R. and Tankov , P. 2006 . Retrieving Lévy processes from option prices: regularization of an ill-posed inverse problem . SIAM J. Control Optim. , 45 : 1 – 25 .
   Web of Science ®Google Scholar
• Crépey , S. 2003 . Calibration of the local volatility in a generalized Black-Scholes model using Tikhonov regularization . SIAM J. Math. Anal. , 34 : 1183 – 1206 .
   Web of Science ®Google Scholar
• Dupire , B. 1994 . Pricing with a smile . RISK , 7 : 18 – 20 .
   Google Scholar
• Egger , H. and Engl , H. W. 2005 . Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates . Inverse Probl. , 21 : 1027 – 1045 .
   Web of Science ®Google Scholar
• Egger , H. , Hein , T. and Hofmann , B. 2006 . On decoupling of volatility smile and term structure in inverse option pricing . Inverse Prob. , 22 : 1247 – 1259 .
   Web of Science ®Google Scholar
• Engl , H. W. and Landl , G. 1993 . Convergence rates for maximum entropy regularization . SIAM J. Numer. Anal. , 30 : 1509 – 1536 .
   Web of Science ®Google Scholar
• Fouque , J.-P. , Papanicolaou , G. and Sircar , K. R. 2000 . Derivatives in Financial Markets with Stochastic Volatility , Cambridge : Cambridge University Press .
   Google Scholar
• Genon-Catalot , V. , Laredo , C. and Picard , D. 1990 . Estimation non parametrique de la variance d'une diffusion par methodes d'ondelettes . C. R. Acad. Sci. Paris , 311 : 397 – 382 .
   PubMedGoogle Scholar
• Genon-Catalot , V. , Laredo , C. and Picard , D. 1992 . Non-parametric estimation of the diffusion coefficient by wavelets methods . Scand. J. Statist. , 19 : 317 – 335 .
   Google Scholar
• Hein , T. and Hofmann , B. 2003 . On the nature of ill-posedness of an inverse problem arising in option pricing . Inverse Probl. , 19 : 1319 – 1338 .
   Web of Science ®Google Scholar
• Hofmann , B. , Kaltenbacher , B. , Pöschl , C. and Scherzer , O. 2007 . A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators . Inverse Problems , 23 : 987 – 1010 .
   Web of Science ®Google Scholar
• Hofmann , B. and Krämer , R. 2005 . On maximum entropy regularization for a specific inverse problem of option pricing . J. Inverse Ill-posed Probl. , 13 : 41 – 63 .
   Google Scholar
• Jackson , N. , Süli , E. and Howison , S. 1998 . Computation of deterministic volatility surfaces . J. Math. Financ. , 1 : 5 – 32 .
   Google Scholar
• Karatzas , I. and Shreve , S. E. 1991 . Brownian Motion and Stochastic Calculus , New York : Springer .
   Google Scholar
• Krämer , R. 2007 . Identification in financial models with time-dependent volatility and stochastic drift components , Chemnitz University of Technology . PhD thesis, Available at http://archiv.tu-chemnitz.de/pub/2007/0080
   Google Scholar
• Krämer , R. and Mathé , P. 2008 . Modulus of continuity of Nemytskii operators with application to the problem of option pricing . J. Inverse Ill-posed Probl. , 16 : 435 – 461 .
   Web of Science ®Google Scholar
• Krämer , R. , Reinhold , N. and Richter , M. 2007 . Einige Aspekte zur Parameterschätzung in einem verallgemeinerten Ornstein-Uhlenbeck Modell , Chemnitz : Chemnitz University of Technology . preprint 2007-5
   Google Scholar
• Krämer , R. and Richter , M. 2007 . A generalized bivariate Ornstein-Uhlenbeck model for financial assets , Chemnitz : Tagungsband zum Workshop ‘Stochastische Analysis’ . Available at http://archiv.tu-chemnitz.de/pub/2008/0057
   Google Scholar
• Krämer , R. and Richter , M. 2008 . Ill-posedness versus ill-conditioning-an example from inverse option pricing . Appl. Anal. , 87 : 465 – 478 .
   Web of Science ®Google Scholar
• Kwok , Y. K. 1998 . Mathematical Models of Financial Derivatives , Singapore : Springer .
   Google Scholar
• Lagnado , R. and Osher , S. 1997 . A technique for calibrating derivative security pricing models: numerical solution of the inverse problem . J. Comput. Finance , 1 : 13 – 25 .
   Google Scholar
• Liptser , R. S. and Shiryaev , A. N. 2001 . Statistics of Random Processes , Berlin, Heidelberg, New York : Springer .
   Google Scholar
• Lo , A. W. and Wang , J. 1995 . Implementing option pricing models when asset returns are predictable . J. Finance , 50 : 87 – 129 .
   Web of Science ®Google Scholar
• Pinheiro , A. , El-Dash , N. A. and Hotta , L. K. 2003 . Non-parametric volatility estimation in continuous time , Brasil : Report Universidade Estadual de Campinas .
   Google Scholar
• Richter , M. and Krämer , R. Proceedings of the Third Brazilian Conference on Statistical Modelling in Insurance and Finance . On some aspects of parameter identification in asset models with stochastic drift terms and time dependent volatility , pp. 230 – 235 . University of São Paulo .
   Google Scholar
• Rogers , L. C.G. and Satchell , S. E. 2000 . Does the behaviour of the asset tell us anything about the option price formula? A cautionary tale . Appl. Financ. Econ. , 10 : 37 – 39 .
   Google Scholar
• Samperi , D. 2002 . Calibrating a diffusion pricing model with uncertain volatility: regularization and stability . Math. Finance , 12 : 71 – 87 .
   Google Scholar
• Souza , M. O. and Zubelli , J. P. 2007 . On the asymptotics of fast mean-reversion stochastic volatility models . Int. J. Appl. Theor. Finance , 10 : 817 – 835 .
   Google Scholar
• Zubelli , J. P. Proceedings of the Second Brazilian Conference on Statistical Modelling in Insurance and Finance . Inverse problems in finance: a short survey of calibration techniques , pp. 64 – 76 . University of São Paulo .
   Google Scholar