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on Econometric Time Series |
| By: | Michel Fliess (LIX - Laboratoire d'informatique de l'école polytechnique - CNRS : UMR7161 - Polytechnique - X); Cédric Join (INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - Ecole Centrale de Lille - CNRS : UMR8146, CRAN - Centre de recherche en automatique de Nancy - CNRS : UMR7039 - Université Henri Poincaré - Nancy I - Institut National Polytechnique de Lorraine (INPL)); Frédéric Hatt (Lucid Capital Management - Lucid Capital Management) |
| Abstract: | The Cartier-Perrin theorem, which was published in 1995 and is expressed in the language of nonstandard analysis, permits, for the first time perhaps, a clear-cut mathematical definition of the volatility of a financial asset. It yields as a byproduct a new understanding of the means of returns, of the beta coefficient, and of the Sharpe and Treynor ratios. New estimation techniques from automatic control and signal processing, which were already successfully applied in quantitative finance, lead to several computer experiments with some quite convincing forecasts. |
| Keywords: | Time series; quantitative finance; trends; returns; volatility; beta coefficient; Sharpe ratio; Treynor ratio; forecasts; estimation techniques; numerical differentiation; nonstandard analysis |
| Date: | 2011–04–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-00562488&r=ets |
| By: | Manabu Asai (Faculty of Economics, Soka University); Michael McAleer (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, and Institute of Economic Research, Kyoto University); Marcelo C. Medeiros (Department of Economics, Pontifical Catholic University of Rio de Janeiro) |
| Abstract: | Several methods have recently been proposed in the ultra high frequency financial literature to remove the effects of microstructure noise and to obtain consistent estimates of the integrated volatility (IV) as a measure of ex-post daily volatility. Even bias-corrected and consistent realized volatility (RV) estimates of IV can contain residual microstructure noise and other measurement errors. Such noise is called "realized volatility error". Since such errors are ignored, we need to take account of them in estimating and forecasting IV. This paper investigates through Monte Carlo simulations the effects of RV errors on estimating and forecasting IV with RV data. It is found that: (i) neglecting RV errors can lead to serious bias in estimators; (ii) the effects of RV errors on one-step ahead forecasts are minor when consistent estimators are used and when the number of intraday observations is large; and (iii) even the partially corrected R2 recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of R2 . An empirical example for S&P 500 data is used to demonstrate the techniques developed in the paper. |
| Keywords: | realized volatility; diffusion; financial econometrics; measurement errors; forecasting; model evaluation; goodness-of-fit.; realized volatility; diffusion; financial econometrics; measurement errors; forecasting; model evaluation; goodness-of-fit. |
| JEL: | G32 G11 C53 C22 |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:758&r=ets |
| By: | Isao Ishida (Center for the Study of Finance and Insurance, Osaka University); Michael McAleer (Erasmus University Rotterdam, Tinbergen Institute, The Netherlands, and Institute of Economic Research, Kyoto University); Kosuke Oya (Graduate School of Economics and Center for the Study of Finance and Insurance, Osaka University) |
| Abstract: | This paper proposes a new method for estimating continuous-time stochastic volatility (SV) models for the S&P 500 stock index process using intraday high-frequency observations of both the S&P 500 index and the Chicago Board of Exchange (CBOE) implied (or expected) volatility index (VIX). Intraday high-frequency observations data have become readily available for an increasing number of financial assets and their derivatives in recent years, but it is well known that attempts to estimate the parameters of popular continuous-time models can lead to nonsensical estimates due to severe intraday seasonality. A primary purpose of the paper is to estimate the leverage parameter, ρ , that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively. We show that, under the special case of Heston's (1993) square-root SV model without measurement errors, the "realized leverage", or the realized covariation of the price and VIX processes divided by the product of the realized volatilities of the two processes, converges to ρ in probability as the time intervals between observations shrink to zero, even if the length of the whole sample period is fixed. Finite sample simulation results show that the proposed estimator delivers accurate estimates of the leverage parameter, unlike existing methods. |
| Keywords: | Continuous time, high frequency data, stochastic volatility, S&P 500, implied volatility, VIX |
| JEL: | G13 G32 |
| Date: | 2011–02 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:759&r=ets |