IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpfi/0503013.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0503/0503013.pdf
    Download Restriction: no
    ---><---

    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. 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.
    3. Fabio Antonelli & Andrea Pascucci, 2005. "On the viscosity solutions of a stochastic differential utility problem," Finance 0503021, University Library of Munich, Germany.
    4. 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.
    5. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    6. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    7. 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.
    8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    9. Emanuel Derman & Iraj Kani, 1998. "Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 61-110.
    10. 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, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sekine, Jun, 2008. "Marginal distribution of some path-dependent stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1846-1850, September.
    2. Andrea Pascucci & Paolo Foschi, 2005. "Calibration of the Hobson&Rogers model: empirical tests," Finance 0509020, University Library of Munich, Germany.
    3. Cristina Costantini & Marco Papi & Fernanda D’Ippoliti, 2012. "Singular risk-neutral valuation equations," Finance and Stochastics, Springer, vol. 16(2), pages 249-274, April.
    4. 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.
    5. 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.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. Carey, Alexander, 2008. "Natural volatility and option pricing," MPRA Paper 6709, University Library of Munich, Germany.
    3. Darsinos, T. & Satchell, S.E., 2001. "Bayesian Forecasting of Options Prices: A Natural Framework for Pooling Historical and Implied Volatiltiy Information," Cambridge Working Papers in Economics 0116, Faculty of Economics, University of Cambridge.
    4. David Heath & Simon Hurst & Eckhard Platen, 1999. "Modelling the Stochastic Dynamics of Volatility for Equity Indices," Research Paper Series 7, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Duan, Jin-Chuan & Zhang, Hua, 2001. "Pricing Hang Seng Index options around the Asian financial crisis - A GARCH approach," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1989-2014, November.
    6. Liao, Wen Ju & Sung, Hao-Chang, 2020. "Implied risk aversion and pricing kernel in the FTSE 100 index," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    7. Pierdzioch, Christian, 2000. "Noise Traders? Trigger Rates, FX Options, and Smiles," Kiel Working Papers 970, Kiel Institute for the World Economy (IfW Kiel).
    8. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, May.
    9. Alexander, Carol, 2004. "Normal mixture diffusion with uncertain volatility: Modelling short- and long-term smile effects," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2957-2980, December.
    10. Alexander, Carol & Nogueira, Leonardo M., 2007. "Model-free hedge ratios and scale-invariant models," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1839-1861, June.
    11. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    12. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    13. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    14. Chang, Eric C. & Ren, Jinjuan & Shi, Qi, 2009. "Effects of the volatility smile on exchange settlement practices: The Hong Kong case," Journal of Banking & Finance, Elsevier, vol. 33(1), pages 98-112, January.
    15. Monteiro, Ana Margarida & Tutuncu, Reha H. & Vicente, Luis N., 2008. "Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity," European Journal of Operational Research, Elsevier, vol. 187(2), pages 525-542, June.
    16. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    17. Zhu, Ke & Ling, Shiqing, 2015. "Model-based pricing for financial derivatives," Journal of Econometrics, Elsevier, vol. 187(2), pages 447-457.
    18. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    19. Chalamandaris, Georgios & Tsekrekos, Andrianos E., 2010. "Predictable dynamics in implied volatility surfaces from OTC currency options," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1175-1188, June.
    20. Cheng Few Lee & Yibing Chen & John Lee, 2020. "Alternative Methods to Derive Option Pricing Models: Review and Comparison," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 102, pages 3573-3617, World Scientific Publishing Co. Pte. Ltd..

    More about this item

    Keywords

    Black-Scholes model; stochastic volatility; path-dependent option; hypoelliptic equation;
    All these keywords.

    JEL classification:

    • G - Financial Economics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:0503013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.