Volatility estimation from short time series of stock prices

Abstract

We consider estimation of the historicalvolatility of stock prices. It is assumed that the stock prices arerepresented as time series formed as samples of the solution of astochastic differential equation with random and time varyingparameters; these parameters are not observable directly and haveunknown evolution law. The price samples are available with limitedfrequency only. In this setting, the estimation has to be based onshort time series, and the estimation error can be significant. Wesuggest some supplements to the existing non-parametric methods ofvolatility estimation. Two modifications of the standard summationformula for the volatility are derived. In addition, a lineartransformation eliminating the appreciation rate and preserving thevolatility is suggested.