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Volatility estimation from short time series of stock prices

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  • Nikolai Dokuchaev

Abstract

We consider estimation of the historical volatility of stock prices. It is assumed that the stock prices are represented as time series formed as samples of the solution of a stochastic differential equation with random and time-varying parameters; these parameters are not observable directly and have unknown evolution law. The price samples are available with limited frequency only. In this setting, the estimation has to be based on short time series, and the estimation error can be significant. We suggest some supplements to the existing nonparametric methods of volatility estimation. Two modifications of the standard summation formula for the volatility are derived. In addition, a linear transformation eliminating the appreciation rate and preserving the volatility is suggested.

Suggested Citation

  • Nikolai Dokuchaev, 2014. "Volatility estimation from short time series of stock prices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 373-384, June.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:2:p:373-384
    DOI: 10.1080/10485252.2013.844805
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    Cited by:

    1. Chuong Luong & Nikolai Dokuchaev, 2018. "Forecasting of Realised Volatility with the Random Forests Algorithm," JRFM, MDPI, vol. 11(4), pages 1-15, October.
    2. Hong Ben Yee & Nikolai Dokuchaev, 2015. "Construction Of Models For Bounded Price Processes: The Case Of The Hkd Exchange Rate," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 1-23, December.
    3. Nikolai Dokuchaev, 2017. "A pathwise inference method for the parameters of diffusion terms," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 731-743, October.

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