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Estimation and pricing under long-memory stochastic volatility

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  • Alexandra Chronopoulou

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  • Frederi Viens

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Abstract

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Suggested Citation

  • Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, May.
  • Handle: RePEc:kap:annfin:v:8:y:2012:i:2:p:379-403
    DOI: 10.1007/s10436-010-0156-4
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    References listed on IDEAS

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    1. Offer Lieberman & Peter Phillips, 2008. "Refined Inference on Long Memory in Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 254-267.
    2. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    3. Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-1863, December.
    4. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.
    5. Michael Levine & Soledad Torres & Frederi Viens, 2009. "Estimators for the long-memory parameter in LARCH models, and fractional Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 12(3), pages 221-250, October.
    6. Casas, Isabel & Gao, Jiti, 2008. "Econometric estimation in long-range dependent volatility models: Theory and practice," Journal of Econometrics, Elsevier, vol. 147(1), pages 72-83, November.
    7. Esfandiar Maasoumi & Michael McAleer, 2008. "Realized Volatility and Long Memory: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 1-9.
    8. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
    9. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    10. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    11. 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.
    12. Bordignon, Silvano & Caporin, Massimiliano & Lisi, Francesco, 2007. "Generalised long-memory GARCH models for intra-daily volatility," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5900-5912, August.
    13. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
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    Citations

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    Cited by:

    1. Shi, Yanlin & Ho, Kin-Yip, 2015. "Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 189-204.
    2. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711, arXiv.org, revised Jan 2018.
    3. Shi, Yanlin & Ho, Kin-Yip, 2015. "Modeling high-frequency volatility with three-state FIGARCH models," Economic Modelling, Elsevier, vol. 51(C), pages 473-483.
    4. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    5. Ho, Kin-Yip & Shi, Yanlin & Zhang, Zhaoyong, 2013. "How does news sentiment impact asset volatility? Evidence from long memory and regime-switching approaches," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 436-456.
    6. Xiao, Weilin & Yu, Jun, 2018. "Asymptotic Theory for Rough Fractional Vasicek Models," Economics and Statistics Working Papers 7-2018, Singapore Management University, School of Economics.
    7. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175, arXiv.org, revised Mar 2017.

    More about this item

    Keywords

    Option pricing; Stochastic volatility; Long memory; Particle filtering; Estimation; Multinomial tree; C14; C5; C6; G13;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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