Unbiased covariance estimation with interpolated data

We study covariance estimation when compelled to use evenly spaced data which have already been manipulated by previous-tick interpolation. We propose an un- biased covariance estimator, which is designed to correct for the two biases arising because of the interpolation: non-synchronous trading and zero-return bias. We show how these sources make usual realized covariance estimators biased, and that the traditional lead-lag modification does not correct these biases completely. The proposed estimator is also proved to be consistent with the Hayashi and Yoshida (2005)’s unbiased estimator under extremely high frequency situation. We illustrate the potential advantages of the method with both simulated and actual dataRealized covariance; Previous tick interpolation; Epps effect; Nonsynchronous trading; Bias-correction

Nonparametric Stochastic Volatility

Using recent advances in the nonparametric estimation of continuous-time processes under mild statistical assumptions as well as recent developments on nonparametric volatility estimation by virtue of market microstructure noise-contaminated high-frequency asset price data, we provide (i) a theory of spot variance estimation and (ii) functional methods for stochastic volatility modelling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, jumps in returns and volatility with possibly state-dependent jump intensities, as well as nonlinear risk-return trade-offs. Our identification approach and asymptotic results apply under weak recurrence assumptions and, hence, accommodate the persistence properties of variance in finite samples. Functional estimation of a generalized (i.e., nonlinear) version of the square-root stochastic variance model with jumps in both volatility and returns for the S&P500 index suggests the need for richer variance dynamics than in existing work. We find a linear specification for the variance's diffusive variance to be misspecified (and inferior to a more flexible CEV specification) even when allowing for jumps in the variance dynamics.Spot variance, stochastic volatility, jumps in returns, jumps in volatility, leverage effects, risk-return trade-offs, kernel methods, recurrence, market microstructure noise.

Threshold Bipower Variation and the Impact of Jumps on Volatility Forecasting

This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous component using estimators which are not only consistent, but also scarcely plagued by small-sample bias. To this purpose, we introduce the concept of threshold bipower variation, which is based on the joint use of bipower variation and threshold estimation. We show that its generalization (threshold multipower vari- ation) admits a feasible central limit theorem in the presence of jumps and provides less biased estimates, with respect to the standard multipower variation, of the continuous quadratic varia- tion in finite samples. We further provide a new test for jump detection which has substantially more power than tests based on multipower variation. Empirical analysis (on the S&P500 index, individual stocks and US bond yields) shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump.volatility estimation, jump detection, volatility forecasting, threshold estimation, financial markets

Volatility Forecasting: The Jumps Do Matter

This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is correctly separated into its continuous and discontinuous component. To this purpose, we introduce the concept of threshold multipower variation (TMPV), which is based on the joint use of bipower variation and threshold estimation. With respect to alternative methods, our TMPV estimator provides less biased and robust estimates of the continuous quadratic variation and jumps. This technique also provides a new test for jump detection which has substantially more power than traditional tests. We use this separation to forecast volatility by employing an heterogeneous autoregressive (HAR) model which is suitable to parsimoniously model long memory in realized volatility time series. Empirical analysis shows that the proposed techniques improve significantly the accuracy of volatility forecasts for the S&P500 index, single stocks and US bond yields, especially in periods following the occurrence of a jump.volatility forecasting, jumps, bipower variation, threshold estimation, stock, bond

A Comparison of Alternative Nonparametric Estimators of the Short Rate Diffusion Coefficient

In this paper we discuss the estimation of the diffusion coefficient of one-factor models for the short rate via non-parametric methods. We test the estimators proposed by Ait Sahalia (1996a), Stanton (1997) and Bandi and Phillips (2003) on Monte Carlo simulation of the Vasicek and CIR model and show that all estimators, especially that proposed by Ait-Sahalia (1996a), are problematic for values of the mean reversion coefficient typically displayed by interest rate data. Moreover all estimators depend crucially on the choice of the bandwith parameter. Data analysis shows that the estimators lead to different estimates on the data set analyzed by Ait-Sahalia (1996a) and Stanton (1997); moreover we show that the two data set are inherently different.

The Italian overnight market: microstructure effects, the martingale hypothesis and the payment system

This paper analyzes the Italian segment of the Eurozone money market since the start of the European Monetary Union. Some relevant variables are analyzed at different frequencies (intramonth, intraweek and intraday); both level and volatily of the overnight interest rate, volume exchanged in the Italian overnight market, domestic and cross-border large value payments channeled in the Italian real-time gross settlement system (BI-REL). Patterns against the martingale hypothesis on the short-term interest rate are detected, and the relationship between the payment flows and the rate itself is investigated. Overall, evidence comes out that in the new framework Italian banks seem to manage liquidity efficiently.overnight market, interest rate, payment system

Trading strategies in the Italian interbank market

Using a data set which includes all transactions among banks in the Italian money market, we study their trading strategies and the dependence among them. We use the Fourier method to compute the variance-covariance matrix of trading strategies. Our results indicate that well defined patterns arise. Two main communities of banks, which can be coarsely identified as small and large banks, emerge.Comment: 19 page

VIRTUE EDUCATION IN SUFFERING FROM SEXUAL VIOLENCE

Is education on theological virtues and moral virtues still relevant to help victims of sexual violence? This article was written to see the importance of education on theological and moral virtues to help victims of sexual violence. The method used for research includes descriptive qualitative research which is carried out by combining field research and literature. Based on the research conducted, it was found that all respondents stated that education on theological virtues and moral virtues was still relevant to helping sufferers because of sexual violence. Therefore, a concept of personal theological and moral virtue is needed as a strategy to maintain and develop the integrity of creation and to experience oneself as the image of God

Volatility estimate via Fourier analysis

From the preface: The aim of this Thesis is to study some selected topics on volatility estimation and modeling. Recently, these topics received great attention in the \ufb01nancial literature, since volatility modeling is crucial in practically all \ufb01nancial applications, including derivatives pricing, portfolio selection and risk management. Speci\ufb01cally, we focus on the concept of realized volatility, which became important in the last decade mainly thanks to the increased availability of high-frequency data on practically every \ufb01nancial asset traded in the main marketplaces. The concept of realized volatility traces back to an early idea of Merton (1980), and basically consists in the estimation of the daily variance via the sum of squared intraday returns, see Andersen et al. (2003). The work presented here is linked to this strand of literature but an alternative estimator is adopted. This is based on Fourier analysis of the time series, hence the term Fourier estimator, which has been recently proposed by Malliavin and Mancino (2002). Moreover, we start from this result to introduce a nonparametric estimator of the di\ufb00usion coe\ufb03cient. The Thesis has two main objectives. After introducing the concept of quadratic variation and the Fourier estimator, we compare the properties of this estimator with realized volatility in a univariate and multivariate setting. This leads us to some applications in which we exploit the fact that we can regard volatility as an observable instead of a latent variable. We pursue this objective in Chapters 3 and 4. The second objective is to prove two Theorems on the estimation of the di\ufb00usion coe\ufb03cient of a stochastic di\ufb00usion in a univariate setting, and this is pursued in Chapter 5. [...