Borus Jungbacker

Forecasting Daily Variability of the S&P 100 Stock Index using Historical, Realised and Implied Volatility Measurements

In this paper we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First we consider unobserved components and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility models and generalised autoregressive conditional heteroskedasticity models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard \& Poors 100 stock index series for which trading data (tick by tick) of almost seven years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts

Monte Carlo Likelihood Estimation for Three Multivariate Stochastic Volatility Models

Estimating parameters in a stochastic volatility (SV) model is a challenging task. Among other estimation methods and approaches, efficient simulation methods based on importance sampling have been developed for the Monte Carlo maximum likelihood estimation of univariate SV models. This paper shows that importance sampling methods can be used in a general multivariate SV setting. The sampling methods are computationally efficient. To illustrate the versatility of this approach, three different multivariate stochastic volatility models are estimated for a standard data set. The empirical results are compared to those from earlier studies in the literature. Monte Carlo simulation experiments, based on parameter estimates from the standard data set, are used to show the effectiveness of the importance sampling methods.

Smooth Dynamic Factor Analysis with Application to the U.S. Term Structure of Interest Rates

SUMMARY We consider the dynamic factor model and show how smoothness restrictions can be imposed on factor loadings by using cubic spline functions. We develop statistical procedures based on Wald, Lagrange multiplier and likelihood ratio tests for this purpose. The methodology is illustrated by analyzing a newly updated monthly time series panel of US term structure of interest rates. Dynamic factor models with and without smooth loadings are compared with dynamic models based on Nelson–Siegel and cubic spline yield curves. We conclude that smoothness restrictions on factor loadings are supported by the interest rate data and can lead to more accurate forecasts. Copyright

Likelihood‐Based Dynamic Factor Analysis for Measurement and Forecasting

We present new results for the likelihood‐based analysis of the dynamic factor model. The latent factors are modelled by linear dynamic stochastic processes. The idiosyncratic disturbance series are specified as autoregressive processes with mutually correlated innovations. The new results lead to computationally efficient procedures for the estimation of the factors and for the parameter estimation by maximum likelihood methods. We also present the implications of our results for models with regression effects, for Bayesian analysis, for signal extraction, and for forecasting. An empirical illustration is provided for the analysis of a large panel of macroeconomic time series.

Model-based Measurement of Actual Volatility in High-frequency Data

In this paper we aim to measure actual volatility within a model-based framework using high-frequency data. In the empirical finance literature it is known that tick-by-tick prices are subject to market micro-structure such as bid-ask bounces and trade information. Such market micro-structure effects become more and more apparent as prices or returns are sampled at smaller and smaller time intervals. High-frequency returns are used for the computation of realised volatility. Recent theoretical results have shown that realised volatility is a consistent estimator of actual volatility but when it is subject to micro-structure noise, the estimator diverges. Parametric and nonparametric methods can be adopted to account for the micro-structure bias. Here we measure actual volatility using a model that takes account of micro-structure noise together with intra-daily volatility patterns and stochastic volatility. The coefficients of this model are estimated by maximum likelihood methods that are based on importance sampling techniques. It is shown that such Monte Carlo techniques can be employed successfully for our purposes in a feasible way. As far as we know, this is a first serious attempt to model the basic components of the mean and variance of high-frequency prices simultaneously. An illustration is given for three months of tick-by-tick transaction prices of the IBM stock traded at the New York Stock Exchange.

On Importance Sampling for State Space Models

We consider likelihood inference and state estimation by means of importance sampling for state space models with a nonlinear non-Gaussian observation y ~ p(y|alpha) and a linear Gaussian state alpha ~ p(alpha). The importance density is chosen to be the Laplace approximation of the smoothing density p(alpha|y). We show that computationally efficient state space methods can be used to perform all necessary computations in all situations. It requires new derivations of the Kalman filter and smoother and the simulation smoother which do not rely on a linear Gaussian observation equation. Furthermore, results are presented that lead to a more effective implementation of importance sampling for state space models. An illustration is given for the stochastic volatility model with leverage.

Parameter Estimation and Practical Aspects of Modeling Stochastic Volatility

Estimating parameters in a stochastic volatility (SV) model is a challenging task and therefore much research is devoted in this area of estimation. This chapter presents an overview and a practical guide of the quasi-likelihood and the Monte Carlo likelihood methods of estimation. The concepts of the methods are straightforward and the implementation is based on Kalman filter, smoothing, simulation smoothing, mode calculation and Monte Carlo simulation. These methods are general, transparent and computationally fast; therefore, they provide a feasible way for the estimation of parameters in SV models. Various extensions of the SV model are considered and some details are provided for the effective implementation of the Monte Carlo methods. Some empirical illustrations are given to show that the methods can be successful in measuring the unobserved volatility in financial time series.