Yasuhiro Omori

Multivariate Stochastic Volatility

We provide a detailed summary of the large and vibrant emerging literature that deals with the multivariate modeling of conditional volatility of financial time series within the framework of stochastic volatility. The developments and achievements in this area represent one of the great success stories of financial econometrics. Three broad classes of multivariate stochastic volatility models have emerged: one that is a direct extension of the univariate class of stochastic volatility model, another that is related to the factor models of multivariate analysis and a third that is based on the direct modeling of time-varying correlation matrices via matrix exponential transformations, Wishart processes and other means. We discuss each of the various model formulations, provide connections and differences and show how the models are estimated. Given the interest in this area, further significant developments can be expected, perhaps fostered by the overview and details delineated in this paper, especially in the fitting of high-dimensional models.

Estimating stochastic volatility models using daily returns and realized volatility simultaneously

Realized volatility, which is the sum of squared intraday returns over a certain interval such as a day, has recently attracted the attention of financial economists and econometricians as an accurate measure of the true volatility. In the real market, however, the presence of non-trading hours and market microstructure noise in transaction prices may cause bias in the realized volatility. On the other hand, daily returns are less subject to noise and therefore may provide additional information on the true volatility. From this point of view, modeling realized volatility and daily returns simultaneously based on the well-known stochastic volatility model is proposed. Empirical studies using intraday data of Tokyo stock price index show that this model can estimate realized volatility biases and parameters simultaneously. The Bayesian approach is taken and an efficient sampling algorithm is proposed to implement the Markov chain Monte Carlo method for our simultaneous model. The result of the model comparison between the simultaneous models using both naive and scaled realized volatilities indicates that the effect of non-trading hours is more essential than that of microstructure noise and that asymmetry is crucial in stochastic volatility models. The proposed Bayesian approach provides an estimate of the entire conditional predictive distribution of returns under consideration of the uncertainty in the estimation of both biases and parameters. Hence common risk measures, such as value-at-risk and expected shortfall, can be easily estimated.

Block sampler and posterior mode estimation for asymmetric stochastic volatility models

This article introduces a new efficient simulation smoother and disturbance smoother for asymmetric stochastic volatility models where there exists a correlation between todays return and tomorrows volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable.

Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors

An efficient Bayesian estimation using a Markov chain Monte Carlo method is proposed in the case of a multivariate stochastic volatility model as a natural extension of the univariate stochastic volatility model with leverage and heavy-tailed errors. The cross-leverage effects are further incorporated among stock returns. The method is based on a multi-move sampler that samples a block of latent volatility vectors. Its high sampling efficiency is shown using numerical examples in comparison with a single-move sampler that samples one latent volatility vector at a time, given other latent vectors and parameters. To illustrate the proposed method, empirical analyses are provided based on five-dimensional S&P500 sector indices returns.

Generalized extreme value distribution with time-dependence using the AR and MA models in state space form

A new state space approach is proposed to model the time-dependence in an extreme value process. The generalized extreme value distribution is extended to incorporate the time-dependence using a state space representation where the state variables either follow an autoregressive (AR) process or a moving average (MA) process with innovations arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm is proposed to implement Markov chain Monte Carlo method where we exploit a very accurate approximation of the Gumbel distribution by a ten-component mixture of normal distributions. The methodology is illustrated using extreme returns of daily stock data. The model is fitted to a monthly series of minimum returns and the empirical results support strong evidence for time-dependence among the observed minimum returns.

Panel Data Analysis of Japanese Residential Water Demand Using a Discrete/Continuous Choice Approach

Block rate pricing is often applied to income taxation, telecommunication services, and brand marketing in addition to its best-known application in public utility services. Under block rate pricing, consumers face piecewise-linear budget constraints. A discrete/continuous choice approach is usually used to account for piecewise-linear budget constraints for demand and price endogeneity. A recent study proposed a methodology to incorporate a separability condition that previous studies ignore, by implementing a Markov chain Monte Carlo simulation based on a hierarchical Bayesian approach. To extend this approach to panel data, our study proposes a Bayesian hierarchical model incorporating the individual effect. The random coefficients model result shows that the price and income elasticities are estimated to be negative and positive, respectively, and the coefficients of the number of members and the number of rooms per household are estimated to be positive. Furthermore, the AR(1) error component model suggests that the Japanese residential water demand does not have serial correlation.

Realized stochastic volatility with leverage and long memory

The daily return and the realized volatility are simultaneously modeled in the stochastic volatility model with leverage and long memory. The dependent variable in the stochastic volatility model is the logarithm of the squared return, and its error distribution is approximated by a mixture of normals. In addition, the logarithm of the realized volatility is incorporated into the measurement equation, assuming that the latent log volatility follows an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process to describe its long memory property. The efficient Bayesian estimation method using Markov chain Monte Carlo method (MCMC) was proposed and implemented in the state space representation. Model comparisons are performed based on the marginal likelihood, and the volatility forecasting performances are investigated using S&P500 stock index returns.

Panel Data Analysis Of Japanese Residential Water Demand Using A Discrete/Continuous Choice Approach

Block rate pricing is often applied to income taxation, telecommunication services, and brand marketing in addition to its best-known application in public utility services. Under block rate pricing, consumers face piecewise-linear budget constraints. A discrete/continuous choice approach is usually used to account for piecewise-linear budget constraints for demand and price endogeneity. A recent study proposed a methodology to incorporate a separability condition that previous studies ignore, by implementing a Markov chain Monte Carlo simulation based on a hierarchical Bayesian approach. To extend this approach to panel data, our study proposes a Bayesian hierarchical model incorporating the individual effect. The random coefficients model result shows that the price and income elasticities are estimated to be negative and positive, respectively, and the coefficients of the number of members and the number of rooms per household are estimated to be positive. Furthermore, the AR(1) error component model suggests that the Japanese residential water demand does not have serial correlation.

Estimation for unequally spaced time series of counts with serially correlated random effects

A generalized model for time series count data with serially correlated random effects is introduced to establish robust inference procedures. Observations are taken at possibly unequally spaced time intervals and random effects are assumed to have a stationary ergodic continuous time first-order autoregressive process. This is a generalization of Zeger (Biometrika 75 (1988) 621) where observations are taken at equally spaced time intervals and random effects are assumed to follow a discrete autoregressive process. For reasons of robustness, the distributional forms of random effects is not specified. The central limit theorem is established to prove asymptotic normality of estimators.

Duopoly in the Japanese Airline Market : Bayesian Estimation for the Entry Game

This paper provides an econometric analysis of a duopoly game in the Japanese domestic airline market. We establish a novel Bayesian estimation approach for the entry game, which allows the incorporation of flexible inference techniques. We find asymmetric strategic interactions between Japanese firms. This result implies that competition is still influenced by the former regulation regime. Furthermore, our prediction analysis indicates that the new Shizuoka airport will suffer from a lack of demand in the future.