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On the complete model with stochastic volatility by Hobson and Rogers

Author

Listed:
  • Andrea Pascucci
  • Marco Di Francesco

Abstract

We examine a recent model, proposed by Hobson and Rogers, which generalizes the classical one by Black and Scholes for pricing derivative securities such as options and futures. We treat the numerical solution of some degenerate partial differential equations governing this financial problem and propose some new numerical schemes which naturally apply in this degenerate setting. Then we aim to emphasize the mathematical tractability of the Hobson-Rogers model by presenting analytical and numerical results comparable with the known ones in the classical Black-Scholes environment.

Suggested Citation

  • Andrea Pascucci & Marco Di Francesco, 2005. "On the complete model with stochastic volatility by Hobson and Rogers," Finance 0503013, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpfi:0503013
    Note: Type of Document - pdf; pages: 12
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0503/0503013.pdf
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    References listed on IDEAS

    as
    1. Robert Peszek, 1995. "PDE Models for Pricing Stocks and Options With Memory Feedback," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(4), pages 211-224.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    3. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48.
    4. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    5. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    7. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    8. Fabio Antonelli & Andrea Pascucci, 2005. "On the viscosity solutions of a stochastic differential utility problem," Finance 0503021, University Library of Munich, Germany.
    9. Emilio Barucci & Paul Malliavin & Maria Elvira Mancino & Roberto Renò & Anton Thalmaier, 2003. "The Price-Volatility Feedback Rate: An Implementable Mathematical Indicator of Market Stability," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 17-35.
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    Citations

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    Cited by:

    1. Foschi, Paolo & Pascucci, Andrea, 2009. "Calibration of a path-dependent volatility model: Empirical tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2219-2235, April.
    2. Sekine, Jun, 2008. "Marginal distribution of some path-dependent stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1846-1850, September.
    3. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(1), pages 13-32, May.
    4. Andrea Pascucci & Paolo Foschi, 2005. "Calibration of the Hobson&Rogers model: empirical tests," Finance 0509020, University Library of Munich, Germany.
    5. Cristina Costantini & Marco Papi & Fernanda D’Ippoliti, 2012. "Singular risk-neutral valuation equations," Finance and Stochastics, Springer, vol. 16(2), pages 249-274, April.
    6. Mauro Rosestolato & Tiziano Vargiolu & Giovanna Villani, 2013. "Robustness for path-dependent volatility models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 137-167, November.

    More about this item

    Keywords

    Black-Scholes model; stochastic volatility; path-dependent option; hypoelliptic equation;

    JEL classification:

    • G - Financial Economics

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