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 which allow 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. Fit, predictive and hedging densities associated with the different models are produced. Models are ranked according to several criteria, including their ability to fit observed option prices, predict future option prices and minimize hedging errors. In addition to model-specific results, averaged predictive and hedging densities are produced, the weights used in the averaging process being the posterior model probabilities. The method is applied to option price data on the S&P500 stock index. Whilst the results provide some support for the Black-Scholes model, no one model dominates according to all criteria considered.Bayesian Implicit Inference; Option Pricing Errors; Option Price Prediction; Hedging Errors; Nonnormal Returns Models; GARCH; Bayesian Model averaging.

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.

A Multiwavelength View at the Heart of the Superwind in NGC 253

Here we present new optical data from the Hubble Space Telescope of the NGC 253 central region, which reveal numerous discrete sources in a ring--like structure. This is combined with data at infrared, millimeter, radio and X-ray wavelengths to examine the nature of these discrete sources and the nucleus itself. We find that the majority of optical/IR/mm sources are young star clusters which trace out a ~50 pc ring, that defines the inner edge of a cold gas torus. This reservoir of cold gas has probably been created by gas inflow from a larger scale bar and deposited at the inner Lindblad resonance. The family of compact radio sources lie interior to the starburst ring, and in general do not have optical or IR counterparts. They are mostly SNRs. The radio nucleus, which is probably an AGN, lies near the centre of the ring. The X-ray emission from the nuclear source is extended in the ROSAT HRI detector indicating that not all of the X-ray emission can be associated with the AGN. The lack of X-ray variability and the flat radio spectrum of the nucleus, argues against an ultraluminous SN as the dominant energetic source at the galaxy core. The diffuse emission associated with the outflowing superwind is present in the central region on a size scale consistent with the idea of collimation by the gas torus.Comment: 26 pages, Latex, 6 figures, 4 tables, submitted to MNRA

Rapid thermal processing of CuAISe2

CuAl thin film metallic precursors were selenised using a tube furnace or a rapid thermal processor (RTP). A comparison is made between the two processes for slightly Cu rich films and best crystallographic and elemental properties are obtained for films selenised by RTP: it was found that ternary compound could only be formed using the RTP. In both cases a large amount of CuxSey grains are found to develop at the surface of the films. Only samples processed in the RTP showed cathodoluminscence excitation at 2.68 eV characteristics of the electronic bandgap. Al rich samples were used to study the effect of etching the CuxSey phases from the surface in order to reveal the underlying CuAlSe2 material