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Path dependent volatility

Author

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  • Pascucci, Andrea
  • Foschi, Paolo

Abstract

We propose a general class of non-constant volatility models with dependence on the past. The framework includes path-dependent volatility models such as that by Hobson&Rogers and also path dependent contracts such as options of Asian style. A key feature of the model is that market completeness is preserved. Some empirical analysis, based on the comparison with the performance of standard local volatility and Heston models, shows the effectiveness of the path dependent volatility.

Suggested Citation

  • Pascucci, Andrea & Foschi, Paolo, 2006. "Path dependent volatility," MPRA Paper 973, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:973
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    References listed on IDEAS

    as
    1. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    2. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 519-547.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    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.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Andrea Pascucci & Marco Di Francesco, 2005. "On the complete model with stochastic volatility by Hobson and Rogers," Finance 0503013, EconWPA.
    8. Andrea Pascucci & Paolo Foschi, 2005. "Calibration of the Hobson&Rogers model: empirical tests," Finance 0509020, EconWPA.
    9. Carl Chiarella & Oh-Kang Kwon, 2000. "A Complete Stochastic Volatility Model in the HJM Framework," Research Paper Series 43, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Carol Alexander & Leonardo M. Nogueira, 2006. "Hedging Options with Scale-Invariant Models," ICMA Centre Discussion Papers in Finance icma-dp2006-03, Henley Business School, Reading University.
    11. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    Full references (including those not matched with items on IDEAS)

    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. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
    3. repec:eee:spapps:v:127:y:2017:i:12:p:3997-4028 is not listed on IDEAS
    4. Sekine, Jun, 2008. "Marginal distribution of some path-dependent stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1846-1850, September.
    5. 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.
    6. repec:wsi:ijtafx:v:11:y:2008:i:07:n:s0219024908005007 is not listed on IDEAS
    7. Carey, Alexander, 2008. "Natural volatility and option pricing," MPRA Paper 6709, University Library of Munich, Germany.

    More about this item

    Keywords

    option pricing; stochastic volatility; path dependent option;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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