An empirical Bayesian forecast in the threshold stochastic volatility models

In the area of finance, the stochastic volatility (SV) model is a useful tool for modelling stock market returns. However, there is evidence that asymmetric behaviour of stock returns exists. A threshold SV (THSV) model is provided to capture this behaviour. In this study, we introduce a robust model created through empirical Bayesian analysis to deal with the uncertainty between the SV and THSV models. A Markov chain Monte Carlo algorithm is applied to empirically select the hyperparameters of the prior distribution. Furthermore, the value at risk from the resulting predictive distribution is also given. Simulation studies show that the proposed empirical Bayes model not only clarifies the acceptability of prediction but also reduces the risk of model uncertainty.     

Forecasting interest rates volatilities by GARCH (1,1) and stochastic volatility models

In this paper, we compare the forecast ability of GARCH(1,1) and stochastic volatility models for interest rates. The stochastic volatility is estimated using Markov chain Monte Carlo methods. The comparison is based on daily data from 1994 to 1996 for the ten year swap rates for Deutsch Mark, Japanese Yen, and Pound Sterling. Various forecast horizons are considered. It turns out that forecasts based on stochastic volatility models are in most cases superiour to those obtained by GARCH(1,1) models.     

Value at risk estimation under stochastic volatility models using adaptive PMCMC methods

In this paper, we propose a value-at-risk (VaR) estimation technique based on a new stochastic volatility model with leverage effect, nonconstant conditional mean and jump. In order to estimate the model parameters and latent state variables, we integrate the particle filter and adaptive Markov Chain Monte Carlo (MCMC) algorithms to develop a novel adaptive particle MCMC (A-PMCMC) algorithm. Comprehensive simulation experiments based on three stock indices and two foreign exchange time series show effectiveness of the proposed A-PMCMC algorithm and the VaR estimation technique.     

A fractionally integrated Wishart stochastic volatility model

There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process, and derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. A two-step procedure is used, namely estimating the parameter of fractional integration via the local Whittle estimator in the first step, and estimating the remaining parameters via the generalized method of moments in the second step. Monte Carlo results for the procedure show a reasonable performance in finite samples. The empirical results for the S&P 500 and FTSE 100 indexes show that the data favor the new FIWSV process rather than the one-factor and two-factor models of the Wishart autoregressive process for the covariance structure.     

Pricing arithmetic Asian option under a two-factor stochastic volatility model with jumps

This paper presents an efficient Monte Carlo simulation scheme based on the variance reduction methods to evaluate arithmetic average Asian options in the context of the double Heston's stochastic volatility model with jumps. This paper consists of two essential parts. The first part presents a new flexible stochastic volatility model, namely, the double Heston model with jumps. In the second part, by combining two variance reduction procedures via Monte Carlo simulation, we propose an efficient Monte Carlo simulation scheme for pricing arithmetic average Asian options under the double Heston model with jumps. Numerical results illustrate the efficiency of our method.     

Modelling stochastic volatility using generalized t distribution

In modelling financial return time series and time-varying volatility, the Gaussian and the Student-t distributions are widely used in stochastic volatility (SV) models. However, other distributions such as the Laplace distribution and generalized error distribution (GED) are also common in SV modelling. Therefore, this paper proposes the use of the generalized t (GT) distribution whose special cases are the Gaussian distribution, Student-t distribution, Laplace distribution and GED. Since the GT distribution is a member of the scale mixture of uniform (SMU) family of distribution, we handle the GT distribution via its SMU representation. We show this SMU form can substantially simplify the Gibbs sampler for Bayesian simulation-based computation and can provide a mean of identifying outliers. In an empirical study, we adopt a GT–SV model to fit the daily return of the exchange rate of Australian dollar to three other currencies and use the exchange rate to US dollar as a covariate. Model implementation relies on Bayesian Markov chain Monte Carlo algorithms using the WinBUGS package.     

Stochastic volatility models for exchange rates and their estimation using quasi-maximum-likelihood methods: an application to the South African Rand

This paper is concerned with the volatility modeling of a set of South African Rand (ZAR) exchange rates. We investigate the quasi-maximum-likelihood (QML) estimator based on the Kalman filter and explore how well a choice of stochastic volatility (SV) models fits the data. We note that a data set from a developing country is used. The main results are: (1) the SV model parameter estimates are in line with those reported from the analysis of high-frequency data for developed countries; (2) the SV models we considered, along with their corresponding QML estimators, fit the data well; (3) using the range return instead of the absolute return as a volatility proxy produces QML estimates that are both less biased and less variable; (4) although the log range of the ZAR exchange rates has a distribution that is quite far from normal, the corresponding QML estimator has a superior performance when compared with the log absolute return.     

Methodology for stochastic volatility process calibration application to the CAC 40 index

In considering volatility as a stochastic, the aim of this paper is to estimate the four parameters related to a particular stochastic process named P1 and based on a Wiener–Levy process. We present the methodology to estimate its four parameters. We calibrate this theoretical model P1 to the CAC 40 index real data. In the same time, we test the normality of the random variables related to the two Wiener–Levy processes. The calibration is performed using the implemented aforesaid algorithm. We compare the stochastic process P1 with another process named P2 and to the Heston [Closed form solution for options with stochastic volatility with application to bonds and currency options, Rev. Financ. Stud. 6(2) (1993), pp. 327–343] process named H0 and to two other improved Heston processes named H1 and H2. For the empirical study, the same algorithm is used to calibrate the five processes. The calibration is based on a database including the CAC 40 index daily ‘closing fixing’ values for the time period from 3rd January 2005 to 22nd January 2007. The data are divided into 18 classes relative to 18 different contracts of European calls on the CAC 40 index. As a result, we find that, the normality test of the CAC 40 index is rejected which is in accordance with the previous original works dealing with this problem. For the five volatility processes, the normality test is verified almost for the same contracts. We also find that according to the used data, the process P1 and its equivalent H1 are the best for calibration.     

GMM estimation of a realized stochastic volatility model: A Monte Carlo study

This article investigates alternative generalized method of moments (GMM) estimation procedures of a stochastic volatility model with realized volatility measures. The extended model can accommodate a more general correlation structure. General closed form moment conditions are derived to examine the model properties and to evaluate the performance of various GMM estimation procedures under Monte Carlo environment, including standard GMM, principal component GMM, robust GMM and regularized GMM. An application to five company stocks and one stock index is also provided for an empirical demonstration.     

On periodic autoregressive stochastic volatility models: structure and estimation

To capture both the volatility evolution and the periodicity feature in the autocorrelation structure exhibited by many nonlinear time series, a Periodic AutoRegressive Stochastic Volatility (PAR-SV ) model is proposed. Some probabilistic properties, namely the strict and second-order periodic stationarity, are provided. Furthermore, conditions for the existence of higher-order moments are established. The autocovariance structure of the squares and higher order powers of the PAR-SV process is studied. Its dynamic properties are shown to be consistent with financial time series empirical findings. Ways in which the model may be estimated are discussed. Finally, a simulation study of the performance of the proposed estimation methods is provided and the PAR-SV is applied to model the spot rates of the euro and US dollar both against the Algerian dinar. The empirical analysis shows that the proposed PAR-SV model can be considered as a viable alternative to the periodic generalized autoregressive conditionally heteroscedastic (PGARCH) model.     

Detecting T cell activation using a varying dimension Bayesian model

The detection of T cell activation is critical in many immunological assays. However, detecting T cell activation in live tissues remains a challenge due to highly noisy data. We developed a Bayesian probabilistic model to identify T cell activation based on calcium flux, a increase in intracellular calcium concentration that occurs during T cell activation. Because a T cell has unknown number of flux events, the implementation of posterior inference requires trans-dimensional posterior simulation. The model is able to detect calcium flux events at the single cell level from simulated data, as well as from noisy biological data.     

Bayesian inference for nonlinear stochastic SIR epidemic model

ABSTRACT

Inference for epidemic parameters can be challenging, in part due to data that are intrinsically stochastic and tend to be observed by means of discrete-time sampling, which are limited in their completeness. The problem is particularly acute when the likelihood of the data is computationally intractable. Consequently, standard statistical techniques can become too complicated to implement effectively. In this work, we develop a powerful method for Bayesian paradigm for susceptible–infected–removed stochastic epidemic models via data-augmented Markov Chain Monte Carlo. This technique samples all missing values as well as the model parameters, where the missing values and parameters are treated as random variables. These routines are based on the approximation of the discrete-time epidemic by diffusion process. We illustrate our techniques using simulated epidemics and finally we apply them to the real data of Eyam plague.     

Energy performance evaluation of OECD countries using Bayesian stochastic frontier analysis and Bayesian network classifiers

More recently a large amount of interest has been devoted to the use of Bayesian methods for deriving parameter estimates of the stochastic frontier analysis. Bayesian stochastic frontier analysis (BSFA) seems to be a useful method to assess the efficiency in energy sector. However, BSFA results do not expose the multiple relationships between input and output variables and energy efficiency. This study proposes a framework to make inferences about BSFA efficiencies, recognizing the underlying relationships between variables and efficiency, using Bayesian network (BN) approach. BN classifiers are proposed as a method to analyze the results obtained from BSFA.     

Bayesian parameter inference for stochastic SIR epidemic model with hyperbolic diffusion

This paper is concerned with the Bayesian estimation parameters of the stochastic SIR (Susceptible-Infective-Removed) epidemic model from the trajectory data. Specifically, the data from the count of both infectives and susceptibles is assumed to be available on some time grid as the epidemic progresses. The diffusion approximation of the appropriate jump process is then used to estimate missing data between every pair of observation times. If the time step of imputations is small enough, we derive the posterior distributions of the infection and recovery rates using the Milstein scheme. The paper also presents Markov-chain Monte Carlo (MCMC) simulation that demonstrates that the method provides accurate estimates, as illustrated by the synthetic data from SIR epidemic model and the real data.     

Pricing longevity-linked derivatives using a stochastic mortality model

Abstract

We propose a 2-factor MBMM model with exponential Lévy process to develop a stochastic mortality process. The two components are fitted by two independent NIG distributions. Compared to Lee–Carter model or 1-factor MBMM model, our mortality model explains more variation and improves the goodness of fit by including the second time component. Based on the improved model, we price three longevity-linked financial instruments, namely the longevity bond, q-forward and s-forward. The pricing is demonstrated on English and Welsh males aged 65 in 2013. Results indicate that the 2-factor MBMM model gives the highest price for mortality-related type of contract.     

Application of a stochastic model to response assessments in a study of squamous cell carcinoma of the head and neck

This paper discusses the application of a stochastic model in the analysis of response assessments made at various time points in a clinical trial of patients with squamous cell carcinoma of the head and neck. The transition rates and probabilities during treatment administration are derived using maximum likelihood methods. The results are then compared with the standard analyses used in solid tumour studies. Stochastic modelling is considered to complement the standard analyses, provide a holistic approach and better explain the underlying disease process. Copyright © 2012 John Wiley & Sons, Ltd.     

Bayesian item response model: a generalized approach for the abilities' distribution using mixtures

Traditional Item Response Theory models assume the distribution of the abilities of the population in study to be Gaussian. However, this may not always be a reasonable assumption, which motivates the development of more general models. This paper presents a generalized approach for the distribution of the abilities in dichotomous 3-parameter Item Response models. A mixture of normal distributions is considered, allowing for features like skewness, multimodality and heavy tails. A solution is proposed to deal with model identifiability issues without compromising the flexibility and practical interpretation of the model. Inference is carried out under the Bayesian Paradigm through a novel MCMC algorithm. The algorithm is designed in a way to favour good mixing and convergence properties and is also suitable for inference in traditional IRT models. The efficiency and applicability of our methodology is illustrated in simulated and real examples.     

A generalised stochastic model for the most recent inter-arrival time

The analysis of intervals between successive arrivals is an important component in any study of point processes. In this context, the most recent inter-arrival time (MRIAT), that is, the interval between last and second-last arrivals has a prominent place in the characterization of such a process if the study is made only for a limited period of time. In this paper, a general probability model for MRIAT is derived under some realistic assumptions. Some particular cases of the model have also been obtained which might be applicable in real data sets.     

Bayesian inference for a discretely observed stochastic kinetic model

The ability to infer parameters of gene regulatory networks is emerging as a key problem in systems biology. The biochemical data are intrinsically stochastic and tend to be observed by means of discrete-time sampling systems, which are often limited in their completeness. In this paper we explore how to make Bayesian inference for the kinetic rate constants of regulatory networks, using the stochastic kinetic Lotka-Volterra system as a model. This simple model describes behaviour typical of many biochemical networks which exhibit auto-regulatory behaviour. Various MCMC algorithms are described and their performance evaluated in several data-poor scenarios. An algorithm based on an approximating process is shown to be particularly efficient.