On Estimation of Volatility for Short Time Series of Stock Prices
Curtin University of Technology - Department of Mathematics and Statistics
June 12, 2013
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.
Number of Pages in PDF File: 16
Keywords: econometrics, continuous time price models, discretization, short time series, volatility estimation, non-parametric estimation
JEL Classification: C14, C15, C58working papers series
Date posted: November 28, 2010 ; Last revised: September 12, 2013
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