Bayesian Analysis of Continuous Time Models of the Australian Short Rate

This paper provides an empirical analysis of a range of alternative single-factor continuous time models for the Australian short-term interest rate. The models are indexed by the level effect parameter for the volatility in the short rate process. The inferential approach adopted is Bayesian, with estimation of the models proceeding via a Markov Chain Monte Carlo simulation scheme. Discrimination between the alternative models is based on Bayes factors, estimated from the simulation output using the Savage-Dickey density ratio. A data augmentation approach is used to improve the accuracy of the discrete time approximation of the continuous time models. An empirical investigation is conducted using weekly observations on the Australian 90 day interest rate from January 1990 to July 2000. The Bayes factors indicate that the square root diffusion model has the highest posterior probability of all the nested models.Interest Rate Models, Markov Chain Monte Carlo, Data Augmentation

Simulation-Based Bayesian Estimation of Affine Term Structure Models

This paper demonstrates the application of Bayesian simulation-based estimation to a class of interest rate models known as Affine Term Structure (ATS) models. The technique used is based on a Markov Chain Monte Carlo algorithm, with the discrete observations on yields augmented by additional higher frequency latent data. The introduction of augmented yield data reduces the bias associated with estimating a continuous time model using discretely observed data. The technique is demon-strated using a one-factor ATS model, with the latent factor process that underlies the yields sampled via a single-move algorithm. Numerical application of the method is demonstrated using both simulated and empirical data. Extension of the method to a three-factor ATS model is also discussed, as well as the application of a multi-move sampler based on a Kalman Filtering and Smoothing algorithm.Interest Rate Models, Markov Chain Monte Carlo, Data Augmentation, Nonlinear State Space Models, Kalman Filtering.

Testing for Dependence in Non-Gaussian Time Series Data

This paper provides a general methodology for testing for dependence in time series data, with particular emphasis given to non-Gaussian data. A dynamic model is postulated for a continuous latent variable and the dynamic structure transferred to the non-Gaussian, possibly discrete, observations. Locally most powerful tests for various forms of dependence are derived, based on an approximate likelihood function. Invariance to the distribution adopted for the data, conditional on the latent process, is shown to hold in certain cases. The tests are applied to various financial data sets, and Monte Carlo experiments used to gauge their finite sample propertiesLatent variable model; locally most powerful tests; approximate likelihood; correlation tests; stochastic volatility tests

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.

Assessing the Impact of Market Microstructure Noise and Random Jumps on the Relative Forecasting Performance of Option-Implied and Returns-Based Volatility

This paper presents a comprehensive empirical evaluation of option-implied and returns-based forecasts of volatility, in which new developments related to the impact on measured volatility of market microstructure noise and random jumps are explicitly taken into account. The option-based component of the analysis also accommodates the concept of model-free implied volatility, such that the forecasting performance of the options market is separated from the issue of misspecification of the option pricing model. The forecasting assessment is conducted using an extensive set of observations on equity and option trades for News Corporation for the 1992 to 2001 period, yielding certain clear results. According to several different criteria, the model-free implied volatility is the best performing forecast, overall, of future volatility, with this result being robust to the way in which alternative measures of future volatility accommodate microstructure noise and jumps. Of the volatility measures considered, the one which is, in turn, best forecast by the option-implied volatility is that measure which adjusts for microstructure noise, but which retains some information about random jumps.Volatility Forecasts; Quadratic Variation; Intraday Volatility Measures; Model-free Implied Volatility.