On Estimation of Volatility for Short Time Series of Stock Prices

16 Pages Posted: 28 Nov 2010 Last revised: 12 Sep 2013

See all articles by Nikolai Dokuchaev

Nikolai Dokuchaev

Zhejiang University/University of Illinois at Urbana-Champaign Institute

Date Written: June 12, 2013

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 non-parametric 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.

Keywords: econometrics, continuous time price models, discretization, short time series, volatility estimation, non-parametric estimation

JEL Classification: C14, C15, C58

Suggested Citation

Dokuchaev, Nikolai, On Estimation of Volatility for Short Time Series of Stock Prices (June 12, 2013). Available at SSRN: https://ssrn.com/abstract=1716525 or http://dx.doi.org/10.2139/ssrn.1716525

Nikolai Dokuchaev (Contact Author)

Zhejiang University/University of Illinois at Urbana-Champaign Institute ( email )

Haining
Zhejiang
China

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