A Multivariate Asymmetric Long Memory Conditional Volatility Model with X, Regularity and Asymptotics

The paper derives a Multivariate Asymmetric Long Memory conditional volatility model with Exogenous Variables (X), or the MALMX model, with dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. The underlying vector random coefficient autoregressive process, which has well established regularity conditions and associated asymptotic properties, is discussed, and a simple explanation is given as to why only the diagonal BEKK model, and not the Hadamard, triangular or full BEKK models, has regularity conditions and asymptotic properties. Various special cases, including the diagonal BEKK model of Baba et al. (1985) and Engle and Kroner (1995), VARMA- GARCH model of Ling and McAleer (2003), and VARMA-AGARCH model of McAleer et al. (2009), are discussed. There does not seem to have been a derivation of a univariate conditional volatility model with exogenous variables (X) that has dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. Therefore, the derivation of a multivariate conditional volatility model with exogenous variables (X) that has regularity conditions and asymptotic theory would seem to be a significant extension of the existing literature

Forecasting the Volatility of Nikkei 225 Futures

For forecasting volatility of futures returns, the paper proposes an indirect method based on the relationship between futures and the underlying asset for the returns and time-varying volatility. For volatility forecasting, the paper considers the stochastic volatility model with asymmetry and long memory, using high frequency data for the underlying asset. Empirical results for Nikkei 225 futures indicate that the adjusted R2 supports the appropriateness of the indirect method, and that the new method based on stochastic volatility models with the asymmetry and long memory outperforms the forecasting model based on the direct method using the pseudo long time series

Leverage and Feedback Effects on Multifactor Wishart Stochastic Volatility for Option Pricing

The paper proposes a general asymmetric multifactor Wishart stochastic volatility (AMWSV) diffusion process which accommodates leverage, feedback effects and multifactor for the covariance process. The paper gives the closed-form solution for the conditional and unconditional Laplace transform of the AMWSV models. The paper also suggests estimating the AMWSV model by the generalized method of moments using information not only of stock prices but also of realized volatilities and co-volatilities. The empirical results for the bivariate data of the NASDAQ 100 and S&P 500 indices show that the general AMWSV model is preferred among several nested models

The Impact of Jumps and Leverage in Forecasting Co-Volatility

__Abstract__ The paper investigates the impact of jumps in forecasting co-volatility, accommodating leverage effects. We modify the jump-robust two time scale covariance estimator of Boudt and Zhang (2013) such that the estimated matrix is positive definite. Using this approach we can disentangle the estimates of the integrated co-volatility matrix and jump variations from the quadratic covariation matrix. Empirical results for three stocks traded on the New York Stock Exchange indicate that the co-jumps of two assets have a significant impact on future co-volatility, but that the impact is negligible for forecasting weekly and monthly horizons

Forecasting Value-at-Risk Using Block Structure Multivariate Stochastic Volatility Models

Most multivariate variance or volatility models suffer from a common problem, the “curse of dimensionality”. For this reason, most are fitted under strong parametric restrictions that reduce the interpretation and flexibility of the models. Recently, the literature has focused on multivariate models with milder restrictions, whose purpose was to combine the need for interpretability and efficiency faced by model users with the computational problems that may emerge when the number of assets is quite large. We contribute to this strand of the literature proposing a block-type parameterization for multivariate stochastic volatility models. The empirical analysis on stock returns on US market shows that 1% and 5 % Value-at-Risk thresholds based on one-step-ahead forecasts of covariances by the new specification are satisfactory for the period includes the global financial crisis

Modelling and Forecasting Noisy Realized Volatility

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 recently proposed in the literature should be fully corrected for evaluating forecasts. This paper proposes a full correction of . An empirical example for S&P 500 data is used to demonstrate the techniques developed in the paper

Asymmetry and Long Memory in Volatility Modelling

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In this paper, we propose a new long memory asymmetric volatility model which captures more flexible asymmetric patterns as compared with existing models. We extend the new specification to realized volatility by taking account of measurement errors, and use the Efficient Importance Sampling technique to estimate the model. As an empirical example, we apply the new model to the realized volatility of Standard and Poor’s 500 Composite Index to show that the new specification of asymmetry significantly improves the goodness of fit, and that the out-of-sample forecasts and Value-at-Risk (VaR) thresholds are satisfactory. Overall, the results of the out-of-sample forecasts show the adequacy of the new asymmetric and long memory volatility model for the period including the global financial crisis

Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model

Asymmetry and leverage in realized volatility

A wide variety of conditional and stochastic variance models has been used to estimate latent volatility (or risk). In both the conditional and stochastic volatility literature, there has been some confusion between the definitions of asymmetry and leverage. In this paper, we first show the relationship among conditional, stochastic, integrated and realized volatilities. Then we develop a new asymmetric volatility model, which takes account of small and large, and positive and negative, shocks. Using the new specification, we examine alternative volatility models that have recently been developed and estimated in order to understand the differences and similarities in the definitions of asymmetry and leverage. We extend the new specification to realized volatility by taking account of measurement errors. As an empirical example, we apply the new model to the realized volatility of Standard and Poor’s 500 Composite Index using Efficient Importance Sampling to show the new specification of asymmetry significantly improves the goodness of fit

A Fractionally Integrated Wishart Stochastic Volatility Model

There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. We conduct a two-step procedure, namely estimating the parameter of fractional integration via log-periodgram regression in the first step, and estimating the remaining parameters via the generalized method of moments in the second step. Monte Carlo results for the procedure shows reasonable performances in finite samples. The empirical results for the bivariate data of the S&P 500 and FTSE 100 indexes show that the data favor the new FIWSV processes rather than one-factor and two-factor models of Wishart autoregressive processes for the covariance structure