Spot Volatility Estimation Using Delta Sequences

Cecilia Mancini (), Vanessa Mattiussi () and Roberto Renò
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Cecilia Mancini: Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze
Vanessa Mattiussi: Department of Economics, City University of London

No 2012-10, Working Papers - Mathematical Economics from Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa

Abstract: We introduce a class of nonparametric spot volatility estimators based on delta sequences and conceived to include many of the existing estimators in the field as special cases. The full limit theory is first derived when unevenly sampled observations under infill asymptotics and fixed time-horizon are considered, and the state variable is assumed to follow a Brownian semimartingale. We then extend our class of estimators to include Poisson jumps or financial microstructure noise in the observed price process. As an application of our results, we relate the Fourier estimator to a specific delta sequence obtained with the Feje'r function. The proposed estimators are applied to data from the S&P500 stock index futures market.

Keywords: spot volatility; estimation; central limit theorem; microtructure noises; jumps; delta sequances; kernels; Feje'r kernel; threshold estimator; Fourier estimator (search for similar items in EconPapers)
Pages: 40 pages
Date: 2012-07
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Citations: View citations in EconPapers (5)

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Journal Article: Spot volatility estimation using delta sequences (2015)
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