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.

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.

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.

Probabilistic Forecasts of Volatility and its Risk Premia

The object of this paper is to produce distributional forecasts of physical volatility and its associated risk premia using a non-Gaussian, non-linear state space approach. Option and spot market information on the unobserved variance process is captured by using dual 'model-free' variance measures to define a bivariate observation equation in the state space model. The premium for diffusive variance risk is defined as linear in the latent variance (in the usual fashion) whilst the premium for jump variance risk is specified as a conditionally deterministic dynamic process, driven by a function of past measurements. The inferential approach adopted is Bayesian, implemented via a Markov chain Monte Carlo algorithm that caters for the multiple sources of non-linearity in the model and the bivariate measure. The method is applied to empirical spot and option price data for the S&P500 index over the 1999 to 2008 period, with conclusions drawn about investors' required compensation for variance risk during the recent financial turmoil. The accuracy of the probabilistic forecasts of the observable variance measures is demonstrated, and compared with that of forecasts yielded by more standard time series models. To illustrate the benefits of the approach, the posterior distribution is augmented by information on daily returns to produce Value at Risk predictions, as well as being used to yield forecasts of the prices of derivatives on volatility itself. Linking the variance risk premia to the risk aversion parameter in a representative agent model, probabilistic forecasts of relative risk aversion are also produced.Volatility Forecasting; Non-linear State Space Models; Non-parametric Variance Measures; Bayesian Markov Chain Monte Carlo; VIX Futures; Risk Aversion.

Non-Parametric Estimation of Forecast Distributions in Non-Gaussian, Non-linear State Space Models

The object of this paper is to produce non-parametric maximum likelihood estimates of forecast distributions in a general non-Gaussian, non-linear state space setting. The transition densities that define the evolution of the dynamic state process are represented in parametric form, but the conditional distribution of the non-Gaussian variable is estimated non-parametrically. The filtering and prediction distributions are estimated via a computationally efficient algorithm that exploits the functional relationship between the observed variable, the state variable and a measurement error with an invariant distribution. Simulation experiments are used to document the accuracy of the non-parametric method relative to both correctly and incorrectly specified parametric alternatives. In an empirical illustration, the method is used to produce sequential estimates of the forecast distribution of realized volatility on the S&P500 stock index during the recent financial crisis. A resampling technique for measuring sampling variation in the estimated forecast distributions is also demonstrated.Probabilistic Forecasting; Non-Gaussian Time Series; Grid-based Filtering; Penalized Likelihood; Subsampling; Realized Volatility.

Extended X-Ray Emission from QSOs

We report Chandra ACIS observations of the fields of 4 QSOs showing strong extended optical emission-line regions. Two of these show no evidence for significant extended X-ray emission. The remaining two fields, those of 3C 249.1 and 4C 37.43, show discrete (but resolved) X-ray sources at distances ranging from ~10 to ~40 kpc from the nucleus. In addition, 4C 37.43 also may show a region of diffuse X-ray emission extending out to ~65 kpc and centered on the QSO. It has been suggested that extended emission-line regions such as these may originate in the cooling of a hot intragroup medium. We do not detect a general extended medium in any of our fields, and the upper limits we can place on its presence indicate cooling times of at least a few 10^9 years. The discrete X-ray emission sources we detect cannot be explained as the X-ray jets frequently seen associated with radio-loud quasars, nor can they be due to electron scattering of nuclear emission. The most plausible explanation is that they result from high-speed shocks from galactic superwinds resulting either from a starburst in the QSO host galaxy or from the activation of the QSO itself. Evidence from densities and velocities found from studies of the extended optical emission around QSOs also supports this interpretation.Comment: Accepted by ApJ. 9 pages including 5 figure

Designing social networking sites for older adults

The importance of older adults’ social networks in providing practical, emotional and informational support is well documented. In this paper, we reflect on the personal social networks of older adults, and the shortcomings of existing online Social Networking Sites (SNSs) in supporting their needs. We report findings from ethnographic interviews, focus groups and hands-on demonstrations with older adults, where we find key themes affecting adoption of SNSs. We then consider design aspects that should be taken into account for future SNSs, if they are to meet the preferences of older users