Francesco Croci: The World of Volatility Estimators

Adviser: Prof. Dr. Sara van de Geer

January 2008

Abstract:

  This thesis investigates the estimation of the volatility of an asset
  return process. The main concern is to give a general overview for how to
  estimate volatility non-parametrically and efficiently. First of all, I
  have introduced the basic notions of stochastic theory and a special and
  unusual limit theorem that I will use throughout the thesis. Then, I
  deal with several volatility estimators, from the easiest and worst one,
  the so called realized volatility (RV) estimator, to the so far best
  estimator, the so called multi-scale realized volatility (MSRV)
  estimator, which converges to the true volatility at the rate of
  n-1/4. Finally, in the last section, we consider microstructure as
  an arbitrary contamination of the underlying latent securities price,
  through a Markov kernel Q. The main result there is that, subject to
  smoothness conditions, the two scales realized volatility (TSRV) is
  robust to the form of contamination Q

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