This chapter contains sections titled: * Introduction * Model * Price Jump Detection Method * Simulation Study * Comparison on NYSE Stock Prices * Conclusion

A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.

We propose three residual-based tests for conditional asymmetry. The distribution is assumed to fall into the class of skewed distributions of Fernández and Steel (1998). In this class, asymmetry is measured by the ratio between the probabilities of being larger and smaller than the mode. Estimation is performed under the null hypothesis of constant asymmetry of the innovations and, in a second step, tests for conditional asymmetry are performed on generalized residuals through parametric and nonparametric methods. We derive the asymptotic distribution of the tests that incorporates the uncertainty of the estimated parameters. A Monte Carlo study shows that neglecting this uncertainty severely biases the tests. An empirical application on a basket of daily returns reveals that financial data often present dynamics in the conditional skewness.

This paper addresses the question of the selection of multivariate GARCH models in terms of variance matrix forecasting accuracy with a particular focus on relatively large scale problems. We consider 10 assets from NYSE and NASDAQ and compare 125 model based one-step-ahead conditional variance forecasts over a period of 10 years using the model confidence set (MCS) and the Superior Predictive Ability (SPA) tests. Model performances are evaluated using four statistical loss functions which account for different types and degrees of asymmetry with respect to over/under predictions. When considering the full sample, MCS results are strongly driven by short periods of high market instability during which multivariate GARCH models appear to be inaccurate. Over relatively unstable periods, i.e. dot-com bubble, the set of superior models is composed of more sophisticated specifications such as orthogonal and dynamic conditional correlation (DCC), both with leverage effect in the conditional variances. However, unlike the DCC models, our results show that the orthogonal specifications tend to underestimate the conditional variance. Over calm periods, a simple assumption like constant conditional correlation and symmetry in the conditional variances cannot be rejected. Finally, during the 2007-2008 financial crisis, accounting for non-stationarity in the conditional variance process generates superior forecasts. The SPA test suggests that, independently from the period, the best models do not provide significantly better forecasts than the DCC model of Engle (2002) with leverage in the conditional variances of the returns.