Catastrophe equity put options with target variance

In this study, we consider a new class of catastrophe equity put options, whose payoff depends on the ratio of the realized variance of the stock over the life of the option and the target variance, which represents the insurance company’s expectation of the future realized variance. This kind of options could help insurance companies raise more equity capital when a large number of catastrophic events occur during the life of the option. We employ a compound doubly stochastic Poisson process with lognormal intensity to describe accumulated catastrophe losses and assume the volatility varies stochastically. Finally, numerical results are presented to investigate the values of this class of options.     

Bayesian analysis of constant elasticity of variance models

This paper focuses on the estimation of some models in finance and in particular, in interest rates. We analyse discretized versions of the constant elasticity of variance (CEV) models where the normal law showing up in the usual discretization of the diffusion part is replaced by a range of heavy‐tailed distributions. A further extension of the model is to allow the elasticity of variance to be a parameter itself. This generalized model allows great flexibility in modelling and simplifies the model implementation considerably using the scale mixtures representation. The mixing parameters provide a means to identify possible outliers and protect inference by down‐weighting the distorting effects of these outliers. For parameter estimation, Bayesian approach is adopted and implemented using the software WinBUGS (Bayesian inference using Gibbs sampler). Results from a real data analysis show that an exponential power distribution with a random shape parameter, which is highly leptokurtic compared with the normal distribution, forms the best CEV model for the data. Copyright © 2006 John Wiley & Sons, Ltd.     

Automatic model selection for partially linear models

We propose and study a unified procedure for variable selection in partially linear models. A new type of double-penalized least squares is formulated, using the smoothing spline to estimate the nonparametric part and applying a shrinkage penalty on parametric components to achieve model parsimony. Theoretically we show that, with proper choices of the smoothing and regularization parameters, the proposed procedure can be as efficient as the oracle estimator [J. Fan, R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of American Statistical Association 96 (2001) 1348–1360]. We also study the asymptotic properties of the estimator when the number of parametric effects diverges with the sample size. Frequentist and Bayesian estimates of the covariance and confidence intervals are derived for the estimators. One great advantage of this procedure is its linear mixed model (LMM) representation, which greatly facilitates its implementation by using standard statistical software. Furthermore, the LMM framework enables one to treat the smoothing parameter as a variance component and hence conveniently estimate it together with other regression coefficients. Extensive numerical studies are conducted to demonstrate the effective performance of the proposed procedure.     

Options on Realized Variance in Log-OU Models

Abstract

We study the pricing of options on realized variance in a general class of Log-OU (Ornstein–Ühlenbeck) stochastic volatility models. The class includes several important models proposed in the literature. Having as common feature the log-normal law of instantaneous variance, the application of standard Fourier–Laplace transform methods is not feasible. We derive extensions of Asian pricing methods, to obtain bounds, in particular, a very tight lower bound for options on realized variance.     

"已实现"波动率在VaR计算中的实证研究

本文根据“已实现”波动率的性质用ARF IM A模型对其进行模拟,并在此基础上研究了V aR,发现在学生T分布和GED分布下有比较好的预测效果.     

Industry structural inefficiency and potential gains from mergers and break-ups: A comprehensive approach

An efficiency indicator of industry configuration (allowing for entry/exit of firms) is presented which accounts for four sources components: (1) size inefficiencies arising from firms which can be conveniently split into smaller units; (2) efficiency gains realized through merger of firms; (3) re-allocation of inputs and outputs among firms; (4) technical inefficiencies. The indicator and its components are computed using linear and mixed-integer programming (data envelopment analysis models). A method to monitor the evolution of these components in time is introduced. Data on hospitals in Australia show that technical inefficiency of hospitals accounts for less than 15% of total industry inefficiency, with 40% attributable to size inefficiencies and the rest to potential mergers and re-allocation effects.     

Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors

We explore simultaneous modeling of several covariance matrices across groups using the spectral (eigenvalue) decomposition and modified Cholesky decomposition. We introduce several models for covariance matrices under different assumptions about the mean structure. We consider ‘dependence’ matrices, which tend to have many parameters, as constant across groups and/or parsimoniously modeled via a regression formulation. For ‘variances’, we consider both unrestricted across groups and more parsimoniously modeled via log-linear models. In all these models, we explore the propriety of the posterior when improper priors are used on the mean and ‘variance’ parameters (and in some cases, on components of the ‘dependence’ matrices). The models examined include several common Bayesian regression models, whose propriety has not been previously explored, as special cases. We propose a simple approach to weaken the assumption of constant dependence matrices in an automated fashion and describe how to compute Bayes factors to test the hypothesis of constant ‘dependence’ across groups. The models are applied to data from two longitudinal clinical studies.     

Medium‐term horizon volatility forecasting: A comparative study

In this paper, volatility is estimated and then forecast using unobserved components‐realized volatility (UC‐RV) models as well as constant volatility and GARCH models. With the objective of forecasting medium‐term horizon volatility, various prediction methods are employed: multi‐period prediction, variable sampling intervals and scaling. The optimality of these methods is compared in terms of their forecasting performance. To this end, several UC‐RV models are presented and then calibrated using the Kalman filter. Validation is based on the standard errors on the parameter estimates and a comparison with other models employed in the literature such as constant volatility and GARCH models. Although we have volatility forecasting for the computation of Value‐at‐Risk in mind the methodology presented has wider applications. This investigation into practical volatility forecasting complements the substantial body of work on realized volatility‐based modelling in business. Copyright © 2007 John Wiley & Sons, Ltd.     

Exact investigation of all effects for extensions of one-way ANOVA model with random effects

Consider the standard one-way analysis of variance model with random effects (variance components model). The customary assumptions of zero means, zero correlations, and equal variances are made for the random terms of this balanced model. The customary normality assumptions are also made when other than point estimates are desired. This standard model is generalized, in several ways, by addition of one or two types of “error” terms. The extended models are applicable to much more general situations than the standard model. However, exact results are developed for investigating the mean and both variance components (of the standard model) and for investigating subsets of these parameters. The generality level for an extended model depends on which parameters are investigated. Customary procedures for the standard model remain usable for some investigations and extensions, but more general models are applicable when use of customary results is not required. A method for rejection of outliers by use of the standard model is described and shown to be applicable for some of the extensions. Partially supported by Air Force Contract AFOSR F33615-71-C-1178 and by Mobil Research and Development Corporation. Also associated with ONR Contract N00014-68-A-0515 and NASA Grant NGR 44-007-028. Research performed at the University of Cape Town.     

一类线性混合模型的谱分解估计

谱分解估计(SDE)是新近提出的关于线性混合模型参数的一种新的估计方法,此方法的一个突出特点是同时给出固定效应参数和方差分量的显式解估计．本文就含两个方差分量的线性混合模型,对谱分解估计的性质做了进一步的研究,获得了方差分量的SDE和方差分析估计相等的充分必要条件,证明了在一定的条件下方差分量的SDE为一致最小方差无偏估计．     

Large deviations of realized volatility

This paper studies large and moderate deviation properties of a realized volatility statistic of high frequency financial data. We establish a large deviation principle for the realized volatility when the number of high frequency observations in a fixed time interval increases to infinity. Our large deviation result can be used to evaluate tail probabilities of the realized volatility. We also derive a moderate deviation rate function for a standardized realized volatility statistic. The moderate deviation result is useful for assessing the validity of normal approximations based on the central limit theorem. In particular, it clarifies that there exists a trade-off between the accuracy of the normal approximations and the path regularity of an underlying volatility process. Our large and moderate deviation results complement the existing asymptotic theory on high frequency data. In addition, the paper contributes to the literature of large deviation theory in that the theory is extended to a high frequency data environment.     

Restricted expected multivariate least squares

A new approach of estimating parameters in multivariate models is introduced. A fitting function will be used. The idea is to estimate parameters so that the fitting function equals or will be close to its expected value. The function will be decomposed into two parts. From one part, which will be independent of the mean parameters, the dispersion matrix is estimated. This estimator is inserted in the second part which then yields the estimators of the mean parameters. The Growth Curve model, extended Growth Curve model and a multivariate variance components model will illustrate the approach.     

Dynamic Index Tracking and Risk Exposure Control Using Derivatives

We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of derivatives in order to gain exposure to an index and/or market factors that may be not directly tradable. Among our results, we establish a general tracking condition that relates the portfolio drift to the desired exposure coefficients under any given model. We also derive a slippage process that reveals how the portfolio return deviates from the targeted return. In our multi-factor setting, the portfolio’s realized slippage depends not only on the realized variance of the index but also the realized covariance among the index and factors. We implement our trading strategies under a number of models, and compare the tracking strategies and performances when using different derivatives, such as futures and options.     

Shriknage estimators with general quadratic loss and differentiable or paratially differentiable shrinkage function

We place ourselves in the n–dimensional normal linear model, for which the variance is known up to a multiplicative factor

If y is observed, we denote by x the associated maximum likelihood estimator and z=y-x. We denote H(x,z) the realized Shrinkage. One is dealing here with an unbiased estimator of the risk using either the differentiability with respect to x and z of H, or the partially differentiability of H with respect to x     

Confidence Regions on Variance Components in an Extended ANOVA Model for Combining Information

In this paper we consider a general variance components model for combining experiments that allows for a possible interaction of responses with groups. The variance estimate from each experiment cannot take into account this interaction which can additionally be different from experiment to experiment. The interaction term can be interpreted as an additional variance component so that we consider an extended ANOVA model. We derive confidence regions and test of hypotheses on the variance components which – at least approximately – hold the nominal significance level.     

The Herd Behavior Index: A new measure for the implied degree of co-movement in stock markets

We introduce a new and easy-to-calculate measure for the expected degree of herd behavior or co-movement between stock prices. This forward looking measure is model-independent and based on observed option data. It is baptized the Herd Behavior Index (HIX).The degree of co-movement in a stock market can be determined by comparing the observed market situation with the extreme (theoretical) situation under which the whole system is driven by a single factor. The HIX is then defined as the ratio of an option-based estimate of the risk-neutral variance of the market index and an option-based estimate of the corresponding variance in case of the extreme single factor market situation.The HIX can be determined for any market index provided an appropriate series of vanilla options is traded on this index as well as on its components. As an illustration, we determine historical values of the 30-days HIX for the Dow Jones Industrial Average, covering the period January 2003 to October 2009.     

Model selection via adaptive shrinkage with t priors

We discuss a model selection procedure, the adaptive ridge selector, derived from a hierarchical Bayes argument, which results in a simple and efficient fitting algorithm. The hierarchical model utilized resembles an un-replicated variance components model and leads to weighting of the covariates. We discuss the intuition behind this type estimator and investigate its behavior as a regularized least squares procedure. While related alternatives were recently exploited to simultaneously fit and select variablses/features in regression models (Tipping in J Mach Learn Res 1:211–244, 2001; Figueiredo in IEEE Trans Pattern Anal Mach Intell 25:1150–1159, 2003), the extension presented here shows considerable improvement in model selection accuracy in several important cases. We also compare this estimator’s model selection performance to those offered by the lasso and adaptive lasso solution paths. Under randomized experimentation, we show that a fixed choice of tuning parameter leads to results in terms of model selection accuracy which are superior to the entire solution paths of lasso and adaptive lasso when the underlying model is a sparse one. We provide a robust version of the algorithm which is suitable in cases where outliers may exist.     

Optimal inspection of a complex system subject to periodic and opportunistic inspections and preventive replacements

This paper proposes two optimization models for the periodic inspection of a system with “hard-type” and “soft-type” components. Given that the failures of hard-type components are self-announcing, the component is instantly repaired or replaced, but the failures of soft-type components can only be detected at inspections. A system can operate with a soft failure, but its performance may be reduced. Although a system may be periodically inspected, a hard failure creates an opportunity for additional inspection (opportunistic inspection) of all soft-type components. Two optimization models are discussed in the paper. In the first, soft-type components undergo both periodic and opportunistic inspections to detect possible failures. In the second, hard-type components undergo periodic inspections and are preventively replaced depending on their condition at inspection. Soft-type and hard-type components are either minimally repaired or replaced when they fail. Minimal repair or replacement depends on the state of a component at failure; this, in turn, depends on its age. The paper formulates objective functions for the two models and derives recursive equations for their required expected values. It develops a simulation algorithm to calculate these expected values for a complex model. Several examples are used to illustrate the models and the calculations. The data used in the examples are adapted from a real case study of a hospital’s maintenance data for a general infusion pump.     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)^α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.     

Analysis of Multi-Unit Variance Components Models with State Space Profiles

We apply the Kalman Filter to the analysis of multi-unit variance components models where each unit's response profile follows a state space model. We use mixed model results to obtain estimates of unit-specific random effects, state disturbance terms and residual noise terms. We use the signal extraction approach to smooth individual profiles. We show how to utilize the Kalman Filter to efficiently compute the restricted loglikelihood of the model. For the important special case where each unit's response profile follows a continuous structural time series model with known transition matrix we derive an EM algorithm for the restricted maximum likelihood (REML) estimation of the variance components. We present details for the case where individual profiles are modeled as local polynomial trends or polynomial smoothing splines.