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Estimating the distribution of volatility of realized stock returns and exchange rate changes

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  • Linden, Mikael

Abstract

Realized stock return volatility is modelled with a distribution based on the Laplace distribution. The moment properties of suggested volatility distribution, η(σ|λ), are derived. The properties of distribution correspond to the empirical regularities found in the finance literature. ML-estimator for λ is also provided. The advantage of Laplace approach lies in estimating λ from returns distribution f(x|λ) directly instead of volatility distribution based on bias sensitive standard deviation estimates. The goodness-to-fit tests with 5 day standard deviations of daily HEX closing price returns in period 3.1.1983–4.3.2003, daily S&P500 closing stock index returns in period 1.3.1950–27.3.2003 and daily USD/Euro exchange rate changes in period 28.12.1978–28.2.2003 support the suggested volatility distribution model.

Suggested Citation

  • Linden, Mikael, 2005. "Estimating the distribution of volatility of realized stock returns and exchange rate changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 573-583.
    • Handle: RePEc:eee:phsmap:v:352:y:2005:i:2:p:573-583
    DOI: 10.1016/j.physa.2004.12.024
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    4. Chao Zhang & Lu Huang, 2010. "A quantum model for the stock market," Papers 1009.4843, arXiv.org, revised Oct 2010.
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    7. López Martín, María del Mar & García, Catalina García & García Pérez, José, 2012. "Treatment of kurtosis in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2032-2045.

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