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An Asymptotic Estimation of the Coefficients of the Stochastic Volatility Model

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  • Lisok, Helen
  • Kritskiy, Oleg

Abstract

The method of evaluation of stochastic volatility (SV) model coefficients, with time approaching the infinity, is consid-ered. The problem of finding the solution of a system of stochastic differential equations is reduced to that of the ana-lytical solution of the Fokker–Planck–Kholmogorov asymptotic equation. The constructed algorithm is applied to economet-ric analysis of daily GAZPROM share prices and values of S&P500 Index options (SPX).

Suggested Citation

  • Lisok, Helen & Kritskiy, Oleg, 2007. "An Asymptotic Estimation of the Coefficients of the Stochastic Volatility Model," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 6(2), pages 3-12.
    • Handle: RePEc:ris:apltrx:0147
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    References listed on IDEAS

    as
    1. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 443-453.
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    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Fiorentini, Gabriele & Leon, Angel & Rubio, Gonzalo, 2002. "Estimation and empirical performance of Heston's stochastic volatility model: the case of a thinly traded market," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 225-255, March.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    More about this item

    Keywords

    stochastic volatility model; Fokker-Planck-Kolmogorov equation;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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