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Volatility and GMM: Monte Carlo studies and empirical estimations

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  • Nagel, Hartmut
  • Schöbel, Rainer

Abstract

In this paper we examine small sample properties of a generalized method of moments (GMM) estimation using Monte Carlo simulations. We assume that the generated time series describe the stochastic variance rate of a stock index. We use a mean reverting square-root prooess to simulate the dynamics of this instantaneous variance rate. The generated time series consist of 63, 250, and 1000 data points, respectively. They are used to estimate the Parameters of the assumed variance rate process by applying GMM. The results obtained are described and compared to our estimates from empirical volatility data. We use the German volatility index VDAX, historical volatilities of the German stock index DAX over 10, 22 and 33 trading days as well as daily volume data of the German stock market.

Suggested Citation

  • Nagel, Hartmut & Schöbel, Rainer, 1996. "Volatility and GMM: Monte Carlo studies and empirical estimations," Tübinger Diskussionsbeiträge 69, University of Tübingen, School of Business and Economics.
    • Handle: RePEc:zbw:tuedps:69
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    References listed on IDEAS

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    3. Jones, Charles M & Kaul, Gautam & Lipson, Marc L, 1994. "Transactions, Volume, and Volatility," Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 631-651.
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    5. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. 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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