Bayesian Target Zones

Several authors have postulated econometric models for exchange rates restricted to lie within known target zones. However, it is not uncommon to observe exchange rate data with known limits that are not fully 'credible'; that is, where some of the observations fall outside the stated range. An empirical model for exchange rates in a soft target zone where there is a controlled probability of the observed rates exceeding the stated limits is developed in this paper. A Bayesian approach is used to analyse the model, which is then demonstrated on Deutschemark-French franc and ECU-French franc exchange rate data.

Non-linear Modelling of the Australian Business Cycle using a Leading Indicator

This paper develops a new non-linear model to analyse the business cycle by exploiting the relationship between the asymmetrical behaviour of the cycle and leading indicators. The model proposed is an innovations form of the structural model underlying simple exponential smoothing that is augmented by a latent Markov switching process. Furthermore, the probabilities that drive the Markov process vary with the growth of the leading indicator. The proposed model is used to analyse the Australian business cycle using the gross domestic product as a proxy and the industrial materials prices index as the exogenous leading indicator influencing the transition probabilities. Model parameters are estimated using a Gibbs sampling algorithm and subsequently used for forecasting purposes.Structural model; Markov switching regime; Gibbs sampling; Business cycle; Leading indicator.

Low level remote sensing: The Doppler Radar wind profiler

Mesoscale phenomena such as thunderstorm and sea breeze frontal circulations are being investigated using a 50 MHz Doppler wind profiler at the Kennedy Space Center. The profiler installation will begin October 1, 1988 and will be completed by February 17, 1989. The focus of current research and plans for next year include: examination of vertical velocities associated with local thunderstorm activity and sea breeze frontal circulations and compare the vertical velocities to conceptual mesoscale models; implementation of space-time conversion analysis techniques to blend profiler data with National Meteorological Center's model output and other wind data such as jimsphere, windsonde and rawinsonde for mesoscale analysis; development of suggestions for use of wind profiler data in mesoscale analysis and forecasting at Kennedy Space Center; and problems detection in the quality of the profiler data during this research project. Researchers will work closely with MSFC to identify and solve the data quality problems

Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices: Application of a Bivariate Kalman Filter

In this paper Bayesian methods are applied to a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Posterior densities for all model parameters, latent volatilities and the market price of volatility risk are produced via a hybrid Markov Chain Monte Carlo sampling algorithm. Candidate draws for the unobserved volatilities are obtained by applying the Kalman filter and smoother to a linearization of a state-space representation of the model. The method is illustrated using the Heston (1993) stochastic volatility model applied to Australian News Corporation spot and option price data. Alternative models nested in the Heston framework are ranked via Bayes Factors and via fit, predictive and hedging performance.Option Pricing; Volatility Risk; Markov Chain Monte Carlo; Nonlinear State Space Model; Kalman Filter and Smoother.

Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models

The impact of parameterisation on the simulation efficiency of Bayesian Markov chain Monte Carlo (MCMC) algorithms for two non-Gaussian state space models is examined. Specifically, focus is given to particular forms of the stochastic conditional duration (SCD) model and the stochastic volatility (SV) model, with four alternative parameterisations of each model considered. A controlled experiment using simulated data reveals that relationships exist between the simulation efficiency of the MCMC sampler, the magnitudes of the population parameters and the particular parameterisation of the state space model. Results of an empirical analysis of two separate transaction data sets for the SCD model, as well as equity and exchange rate data sets for the SV model, are also reported. Both the simulation and empirical results reveal that substantial gains in simulation efficiency can be obtained from simple reparameterisations of both types of non-Gaussian state space models.Bayesian methodology, stochastic volatility, durations, non-centred in location, non-centred in scale, inefficiency factors.

Diversification Meltdown or the Impact of Fat tails on Conditional Correlation?

A perceived increase in correlation during turbulent market conditions implies a reduction in the benefits arising from portfolio diversification. Unfortunately, it is exactly then that these benefits are most needed. To determine whether diversification truly breaks down, we investigate the robustness of a popular conditional correlation estimator against alternative distributional assumptions. Analytical results show that the apparent meltdown in the benefits from diversification could be a consequence of assuming normally distributed returns. A more realistic assumption - the bivariate Student-t distribution - suggests that constant correlation may be sustained over the full support of the multivariate return distributionConditional correlation, Truncated correlation, Bivariate Student-t correlation.

Bayesian Analysis of the Stochastic Conditional Duration Model

A Bayesian Markov Chain Monte Carlo methodology is developed for estimating the stochastic conditional duration model. The conditional mean of durations between trades is modelled as a latent stochastic process, with the conditional distribution of durations having positive support. The sampling scheme employed is a hybrid of the Gibbs and Metropolis Hastings algorithms, with the latent vector sampled in blocks. The suggested approach is shown to be preferable to the quasi-maximum likelihood approach, and its mixing speed faster than that of an alternative single-move algorithm. The methodology is illustrated with an application to Australian intraday stock market data.Transaction data, Latent factor model, Non-Gaussian state space model, Kalman filter and simulation smoother.

Implicit Bayesian Inference Using Option Prices

A Bayesian approach to option pricing is presented, in which posterior inference about the underlying returns process is conducted implicitly via observed option prices. A range of models allowing for conditional leptokurtosis, skewness and time-varying volatility in returns are considered, with posterior parameter distributions and model probabilities backed out from the option prices. Models are ranked according to several criteria, including out-of-sample fit, predictive and hedging performance. The methodology accommodates heteroscedasticity and autocorrelation in the option pricing errors, as well as regime shifts across contract groups. The method is applied to intraday option price data on the S&P500 stock index for 1995. Whilst the results provide support for models which accommodate leptokurtosis, no one model dominates according to all criteria considered.Bayesian Option Pricing; Leptokurtosis; Skewness; GARCH Option Pricing; Option Price Prediction; Hedging Errors.