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A data-reconstructed fractional volatility model

Author

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  • Rui Vilela Mendes
  • M. J. Oliveira

Abstract

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes and a new option pricing formula are also obtained

Suggested Citation

  • Rui Vilela Mendes & M. J. Oliveira, 2006. "A data-reconstructed fractional volatility model," Papers math/0602013, arXiv.org, revised Jun 2007.
  • Handle: RePEc:arx:papers:math/0602013
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    References listed on IDEAS

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    1. 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..
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    5. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
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    7. R. Vilela Mendes & R. Lima & T. Araujo, 2001. "A process-reconstruction analysis of market fluctuations," Papers cond-mat/0102301, arXiv.org.
    8. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    9. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
    10. Silva, A. Christian & Prange, Richard E. & Yakovenko, Victor M., 2004. "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 227-235.
    11. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.
    12. Y. Malevergne & V. Pisarenko & D. Sornette, 2005. "Empirical distributions of stock returns: between the stretched exponential and the power law?," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 379-401.
    13. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    14. 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.
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    16. 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.
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    Citations

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    Cited by:

    1. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711, arXiv.org, revised Jan 2018.
    2. Philipp Harms & David Stefanovits, 2015. "Affine representations of fractional processes with applications in mathematical finance," Papers 1510.04061, arXiv.org, revised Feb 2018.
    3. Li Meng & Mei Wang, 2010. "Comparison of Black–Scholes Formula with Fractional Black–Scholes Formula in the Foreign Exchange Option Market with Changing Volatility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(2), pages 99-111, June.
    4. Vilela Mendes, R. & Oliveira, M.J. & Rodrigues, A.M., 2015. "No-arbitrage, leverage and completeness in a fractional volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 470-478.

    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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