Common volatility and correlation clustering in asset returns

We present a new multivariate framework for the estimation and forecasting of the evolution of financial asset conditional correlations. Our approach assumes return innovations with time dependent covariances. A Cholesky decomposition of the asset covariance matrix, with elements written as sines and cosines of spherical coordinates allows for modelling conditional variances and correlations and guarantees its positive definiteness at each time t. As in Christodoulakis and Satchell [Christodoulakis, G.A., Satchell, S.E., 2002. Correlated ARCH (CorrARCH): Modelling the time-varying conditional correlation between financial asset returns. European Journal of Operational Research 139 (2), 350–369] correlation is generated by conditionally autoregressive processes, thus allowing for an autocorrelation structure for correlation. Our approach allows for explicit out-of-sample forecasting and is consistent with stylized facts as time-varying correlations and correlation clustering, co-movement between correlation coefficients, correlation and volatility as well as between volatility processes (co-volatility). The latter two are shown to depend on correlation and volatility persistence. Empirical evidence on a trivariate model using monthly data from Dow Jones Industrial, Nasdaq Composite and the 3-month US Treasury Bill yield supports our theoretical arguments.     

On the dynamics of a finite buffer queue conditioned on the amount of loss

This paper is concerned with computing large-deviation asymptotics for the loss process in a stylized queueing model that is fed by a Brownian input process. In addition, the dynamics of the queue, conditional on such a large deviation in the loss, is calculated. Finally, the paper computes the quasi-stationary distribution of the system and the corresponding dynamics, conditional on no loss occurring.     

An application of vector GARCH model in semiconductor demand planning

Demand planning has been the key to supply chain management in semiconductor industry. With an appropriate weight assignment scheme, the planning accuracy resulting from combinational forecasts can be improved by merging several individual candidate methods. In this paper we discuss the applicability of vector generalized autoregressive conditional heteroskedasticity (GARCH) model to determine the optimal combinational weights of component forecasts, where the conditional variances and correlations of forecast errors from candidate methods are represented and estimated by a maximum-likelihood procedure. The asymptotical properties of parameter estimators for GARCH model are investigated by simulation experiments. An example of the proposed method to real time series of electronic products demonstrates that this weight-varying combinational method produces less prediction errors, compared to other commonly used forecasting approaches that are based on single model selection criteria or fixed weights.     

Real options approach-based demand forecasting method for a range of products with highly volatile and correlated demand

To achieve a competitive edge needed for marketing highly competitive products, modern enterprises have actively sought to provide the marketplace with an expansive range of products with high random volatility of demand and correlations between demands of product. Consequently, traditional forecasting methods for separately forecasting demand for these products are likely to yield significant deviations. Therefore, this study develops a real options approach-based forecasting model to accurately predict future demand for a given range of products with highly volatile and correlated demand. Additionally, this study also proposes using Monte Carlo simulation to solve the demand forecasting model. The real options approach associated with Monte Carlo simulation not only deals effectively with random variation involving a particular demand stochastic diffusion process, but can handle the correlations in product demand.     

A mean reverting process for pricing treasury bills and futures contracts

An analytically tractable, discrete-time single-factor model is developed for valuing treasury bills and futures contracts. It uses a multiplicative binomial foward process that creates neither negative nor implausibly large positive interest factors, and which can incorporate different possible degrees of mean reversion. The paper derives explicit formulae for bill prices, futures prices, their conditional variances and risk premia in a setting that relates the evolution of the term structure more closely to both model and data than do other similar works. In contrast to other term-structure constrained models, this paper emphasizes that in a one-factor model the martingale probabilities cannot be treated independently of the perturbation functions. The paper's empirical methods also differ from the customary approaches. Instead of comparing differences between model-predicted and observed prices, the paper applies ARCH methodology to test model-predicted ratios of conditional variances to risk premia. Our tests find influences exogenous to the model, but these factors do not seem capable of being explained with two-factor models using only interest rates.     

Capital budgeting and optimal timing of investments in flexible manufacturing systems

This paper investigates the financial-economic decision process for investments in flexible manufacturing systems (FMS). Contrary to popular belief, we show that conventional capital budgeting techniques can be used to make such investment decisions. First, we identify theoverall impact of installing an FMS and present guidelines for a cash flow forecasting model. We then present ways in which to incorporate uncertainty in these cash flows within a risk-adjusted discount rate. These expected cash flows and the discount rate are used in calculating the net present value (NPV). Once the capital budgeting analysis is completed, a critical issue facing the firm is the optimal timing of the installation. We reinterpret the general results on optimal timing of investments within the special context of an FMS project. Finally, we illustrate the above technique via a stylized example.     

Conditional sampling for max-stable processes with a mixed moving maxima representation

This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using the Poisson point process structure of such processes. For explicit calculations we restrict ourselves to the one-dimensional case and use a finite number of shape functions satisfying some regularity conditions. For more general shape functions approximation techniques are presented. Our algorithm is applied to the Smith process and the Brown-Resnick process. Finally, we compare our computational results to other approaches. Here, the algorithm for Gaussian processes with transformed marginals turns out to be surprisingly competitive.     

A model of HIV population to seropositivity

HIV population is modelled as a point process with a time-dependent birth rate. A method of phases is introduced to analyse special types of time-dependencies. The conditional life time of HIV population is assumed to be hypothetical in phases, the life span of the process being distributed independently and exponentially. The analysis leads to an explicit differential equations for generating functions of the population size. The detection process of the antibodies (against the antigen of the virus) is analysed and an explicit expression for the correlation functions are also provided. The same model is attacked by using the product density approach which leads to the same result. Finally, some applications to the product density approach are given.     

马氏调制费率复合Poisson-Geometric风险模型的预警区问题

考虑了一类具有马氏调制费率的复合Poisson-Geometric过程风险模型,充分利用盈余过程的强马氏性,得到第一个预警区的一个条件矩母函数所满足的微积分方程,并进一步在两状态情形下,当理赔额的分布为指数分布时得到了第一个预警区的一个条件矩母函数的具体表达式以解释结果.需要特别指出的是,所研究模型的盈余过程不具有平稳增量性,只能充分运用盈余过程的强马氏性,研究了一类具有马氏调制费率的复合Poisson-Geometric过程风险模型的预警区问题,丰富了保险公司对预警区问题的研究,对保险公司考虑财务预警系统以及保险监管部门设计某些监管指标系统具有一定的参考指导价值.     

The GARCH(1,1)-M model: results for the densities of the variance and the mean

This paper starts from the GARCH(1,1)-M model of Bollerslev [Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 31 (1986) 307–327], and investigates the limit diffusion form as it is presented in Nelson [ARCH models as diffusion approximations, Journal of Econometrics 45 (1990) 7–38]. The distribution for the conditional variance process is derived, and in the limit for t going to infinity is shown to coincide with the stationary distribution given in Nelson [ARCH models as diffusion approximations, Journal of Econometrics 45 (1990) 7–38]. In addition it is shown how the distribution for the complete model can be arrived at; explicit calculations are given in case the conditional variance is a martingale.     

Tail dependence of random variables from ARCH and heavy-tailed bilinear models

Discussed in this paper is the dependent structure in the tails of distributions of random variables from some heavy-tailed stationary nonlinear time series. One class of models discussed is the first-order autoregressive conditional heteroscedastic (ARCH) process introduced by Engle (1982). The other class is the simple first-order bilinear models driven by heavy-tailed innovations. We give some explicit formulas for the asymptotic values of conditional probabilities used for measuring the tail dependence between two random variables from these models. Our results have significant meanings in finance.     

Computing conditional expectations of multidimensional diffusion processes

We study multidimensional diffusion processes and give an explicit representation for their conditional expectation. Starting from the solution formula for one dimensional stochastic differential equations found in Lanconelli and Proske [8], we compute the conditional expectation of a certain class of multidimensional diffusions without resorting to the Markov property of the process and therefore without requiring an explicit expression for the semi group associated to it.     

Bayesian modeling and forecasting of Value‐at‐Risk via threshold realized volatility

This study proposes a threshold realized generalized autoregressive conditional heteroscedastic (GARCH) model that jointly models daily returns and realized volatility, thereby taking into account the bias and asymmetry of realized volatility. We incorporate this threshold realized GARCH model with skew Student‐t innovations as the observation equation, view this model as a sharp transition model, and treat the realized volatility as a proxy for volatility under this nonlinear structure. Through the Bayesian Markov chain Monte Carlo method, the model can jointly estimate the parameters in the return equation, the volatility equation, and the measurement equation. As an illustration, we conduct a simulation study and apply the proposed method to the US and Japan stock markets. Based on quantile forecasting and volatility estimation, we find that the threshold heteroskedastic framework with realized volatility successfully models the asymmetric dynamic structure. We also investigate the predictive ability of volatility by comparing the proposed model with the traditional GARCH model as well as some popular asymmetric GARCH and realized GARCH models. This threshold realized GARCH model with skew Student‐t innovations outperforms the competing risk models in out‐of‐sample volatility and Value‐at‐Risk forecasting.     

马氏调制费率的带干扰风险模型

考虑了一类具有马氏调制的带干扰连续时间风险模型,得到了该模型下其条件Gerber-Shiu折现罚金函数所满足的积分方程,Laplace变换及渐近解.在两状态情形下,当索赔额的分布为有理数情况时得到了条件Gerber-Shiu折现罚金函数的具体表达式并给出了数值例子     

Optimal dynamic management of the population mix

In this paper we present an optimal control model that addresses a central challenge of modern housing policy: deconcentrating poverty via “housing mobility programs”, which move poor families into middle-class neighborhoods. The tension is that helping poor families is clearly an opportunity, but pursuing these programs too aggressively increases the risk of inducing middle-class flight. Previous studies in this area of research considered only one state variable representing the middle-class families; here, we add one more state variable to allow for an explicit consideration of the poor families. While our model is still somewhat stylized given the sophisticated structure of the real world problem, we show that it exhibits complex behavior including multiple equilibria, (strong and weak) DNSS curves, and indifference points for which there exist two different paths approaching one and the same steady state in the long run.     

Improving density forecast by modeling asymmetric features: An application to S&P500 returns

A density forecast is an estimate of the probability distribution of the possible future values of a random variable. From the current literature, an economic time series may have three types of asymmetry: asymmetry in unconditional distribution, asymmetry in conditional distribution, volatility asymmetry. In this paper, we propose three density forecasting methods under two-piece normal assumption to capture these asymmetric features. A GARCH model with two-piece normal distribution is developed to capture asymmetries in the conditional distributions. In this approach, we first estimate parameters of a GARCH model by assuming normal innovations, and then fit a two-piece normal distribution to the empirical residuals. Block bootstrap procedure, and moving average method with two-piece normal distribution are presented for volatility asymmetry and asymmetry in the conditional distributions. Application of the developed methods to the weekly S&P500 returns illustrates that forecast quality can be significantly improved by modeling these asymmetric features.     

Finding market structure by sales count dynamics—Multivariate structural time series models with hierarchical structure for count data—

In this paper, we propose a multivariate time series model for sales count data. Based on the fact that setting an independent Poisson distribution to each brand’s sales produces the Poisson distribution for their total number, characterized as market sales, and then, conditional on market sales, the brand sales follow a multinomial distribution, we first extend this Poisson–multinomial modeling to a dynamic model in terms of a generalized linear model. We further extend the model to contain nesting hierarchical structures in order to apply it to find the market structure in the field of marketing. As an application using point of sales time series in a store, we compare several possible hypotheses on market structure and choose the most plausible structure by using several model selection criteria, including in-sample fit, out-of-sample forecasting errors, and information criterion.     

Volatility forecasting using stochastic conditional range model with leverage effect

In this paper, we propose a stochastic conditional range model with leverage effect (henceforth SCRL) for volatility forecasting. A maximum likelihood method based on the particle filters is developed to estimate the parameters of the SCRL model. Simulation results show that the proposed methodology performs well. We apply the proposed model and methodology to four stock market indices, the Shanghai Stock Exchange Composite Index of China, the Hang Seng Index of Hong Kong, the Nikkei 225 Index of Japan, and the S&P 500 Index of US. Empirical results highlight the value of incorporating leverage effect into range modeling and forecasting. In particular, the results show that our SCRL model outperforms the conditional autoregressive range model, the conditional autoregressive range model with leverage effect, and the stochastic conditional range model in both in‐sample fit and out‐of‐sample forecast.     

复合Poisson-Geometric风险模型的预警区问题

应用有别于传统鞅方法的方法,充分利用盈余过程的强马氏性,在一类复合Poisson-Geometric风险模型下讨论预警区问题,得到第一个预警区的一个条件矩母函数所满足的微积分方程,并在指数索赔情形下给出其精确解.     

遗传算法与神经网络相结合的降水预报模型

针对目前BP神经网络在实际应用中,网络结构难以确定以及网络极易陷入局部解问题,用遗传算法优化神经网络的连接权和网络结构,在遗传进化过程中采取保留最佳个体的方法,建立基于遗传算法的BP网络模型,同时通过实例说明该模型在降水预测中的应用,计算结果表明该方法的预测精度较高。