Dacheng Xiu

High Frequency Covariance Estimates with Noisy and Asynchronous Financial Data

This paper proposes a consistent and efficient estimator of the high frequency covariance (quadratic covariation) of two arbitrary assets, observed asynchronously with market microstructure noise. This estimator is built upon the marriage of the quasi-maximum likelihood estimator of the quadratic variation and the proposed Generalized Synchronization scheme. It is therefore not influenced by the Epps effect. Moreover, the estimation procedure is free of tuning parameters or bandwidths and readily implementable. The Monte Carlo simulations show the advantage of this estimator by comparing it with a variety of estimators with specific synchronization methods. The empirical studies of six foreign exchange future contracts illustrate the time-varying correlations of the currencies during the global financial crisis in 2008, discovering the similarities and differences in their roles as key currencies in the global market.

Quasi-Maximum Likelihood Estimation of Volatility with High Frequency Data

This paper investigates the properties of the well-known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise, by extending the classic asymptotic results of quasi-maximum likelihood estimation. When trying to estimate the integrated volatility and the variance of noise, this parametric approach remains consistent, efficient and robust as a quasi-estimator under misspecified assumptions. Moreover, it shares the model-free feature with nonparametric alternatives, for instance realized kernels, while being advantageous over them in terms of finite sample performance. In light of quadratic representation, this estimator behaves like an iterative exponential realized kernel asymptotically. Comparisons with a variety of implementations of the Tukey-Hanning2 kernel are provided using Monte Carlo simulations, and an empirical study with the Euro/US Dollar future illustrates its application in practice.

Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods

The non-Gaussian maximum likelihood estimator is frequently used in GARCH models with the intention of capturing heavy-tailed returns. However, unless the parametric likelihood family contains the true likelihood, the estimator is inconsistent due to density misspecification. To correct this bias, we identify an unknown scale parameter ηf that is critical to the identification for consistency and propose a three-step quasi-maximum likelihood procedure with non-Gaussian likelihood functions. This novel approach is consistent and asymptotically normal under weak moment conditions. Moreover, it achieves better efficiency than the Gaussian alternative, particularly when the innovation error has heavy tails. We also summarize and compare the values of the scale parameter and the asymptotic efficiency for estimators based on different choices of likelihood functions with an increasing level of heaviness in the innovation tails. Numerical studies confirm the advantages of the proposed approach.

Incorporating Global Industrial Classification Standard into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator with High Frequency Data

We document a striking block-diagonal pattern in the factor model residual covariances of the S&P 500 Equity Index constituents, after sorting the assets by their assigned Global Industry Classification Standard (GICS) codes. Cognizant of this structure, we propose combining a location-based thresholding approach based on sector inclusion with the Fama-French and SDPR sector Exchange Traded Funds (ETF’s). We investigate the performance of our estimators in an out-of-sample portfolio allocation study. We find that our simple and positive-definite covariance matrix estimator yields strong empirical results under a variety of factor models and thresholding schemes. Conversely, we find that the Fama-French factor model is only suitable for covariance estimation when used in conjunction with our proposed thresholding technique. Theoretically, we provide justification for the empirical results by jointly analyzing the in-fill and diverging dimension asymptotics.

Hermite Polynomial Based Expansion of European Option Prices

We seek a closed-form series approximation of European option prices under a variety of diffusion models. The proposed convergent series are derived using the Hermite polynomial approach. Departing from the usual option pricing routine in the literature, our model assumptions have no requirements for affine dynamics or explicit characteristic functions. Moreover, convergent expansions provide a distinct insight into how and on which order the model parameters affect option prices, in contrast with small-time asymptotic expansions in the literature. With closed-form expansions, we explicitly translate model features into option prices, such as mean-reverting drift and self-exciting or skewed jumps. Numerical examples illustrate the accuracy of this approach and its advantage over alternative expansion methods.

Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data

This paper constructs an estimator for the number of common factors in a setting where both the sampling frequency and the number of variables increase. Empirically, we document that the covariance matrix of a large portfolio of US equities is well represented by a low rank common structure with sparse residual matrix. When employed for out-of-sample portfolio allocation, the proposed estimator largely outperforms the sample covariance estimator.

Increased Correlation Among Asset Classes: Are Volatility or Jumps to Blame, or Both?

We develop estimators and asymptotic theory to decompose the quadratic covariation between two assets into its continuous and jump components, in a manner that is robust to the presence of market microstructure noise. Using high frequency data on different assets classes, we find that the recent financial crisis led to an increase in both the quadratic variations of the assets and their correlations. However, we find little evidence to suggest a change between the relative contributions of the Brownian and jump components, as both comove. Co-jumps stem from surprising news announcements that occur primarily before the opening of the U.S. market, and are also accompanied by an increase in Brownian-driven correlations.

Nonparametric Estimation of the Leverage Effect: A Trade-off between Robustness and Efficiency

ABSTRACT We consider two new approaches to nonparametric estimation of the leverage effect. The first approach uses stock prices alone. The second approach uses the data on stock prices as well as a certain volatility instrument, such as the Chicago Board Options Exchange (CBOE) volatility index (VIX) or the Black–Scholes implied volatility. The theoretical justification for the instrument-based estimator relies on a certain invariance property, which can be exploited when high-frequency data are available. The price-only estimator is more robust since it is valid under weaker assumptions. However, in the presence of a valid volatility instrument, the price-only estimator is inefficient as the instrument-based estimator has a faster rate of convergence.We consider an empirical application, in which we study the relationship between the leverage effect and the debt-to-equity ratio, credit risk, and illiquidity. Supplementary materials for this article are available online.

A Hausman Test for the Presence of Market Microstructure Noise in High Frequency Data

We develop tests that help assess whether a high frequency data sample can be treated as reasonably free of market microstructure noise at a given sampling frequency for the purpose of implementing high frequency volatility and other estimators. The tests are based on the Hausman principle of comparing two estimators, one that is efficient but not robust to the deviation being tested, and one that is robust but not as efficient. We investigate the asymptotic properties of the test statistic in a general nonparametric setting, and compare it with several alternatives that are also developed in the paper. Empirically, we find that improvements in stock market liquidity over the past decade have increased the frequency at which simple, uncorrected, volatility estimators can be safely employed.

Spot Variance Regressions

We study a nonlinear vector regression model for discretely sampled high-frequency data with the latent spot variance of an asset as a covariate. We propose a two-stage inference procedure by first nonparametrically recovering the volatility path from asset returns and then conducting inference based on the generalized method of moments (GMM). The GMM estimator is nonstandard in that the second-order asymptotics is dominated by a bias term, rendering the standard inference implausible. We propose several bias-correction methods and show that the bias-corrected estimators have the parametric rate of convergence with mixture normal asymptotic distributions. We provide estimators for the asymptotic variance, as well as Anderson-Rubin-type confidence sets for the true parameter. Tests for overidentification and parameter stability are constructed. An empirical application on VIX pricing provides substantive evidence against conventional risk-neutral models for volatility dynamics.