Modelling the persistence of conditional variances

This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The discussion will be motivated by a simple asset pricing theory which is particularly appropriate for examining futures contracts with risk averse agents. A new class of models defined to be integrated in variance is then introduced. This new class of models includes the variance analogue of a unit root in the mean as a special case. The models are argued to be both theoretically important for the asset pricing models and empirically relevant. The conditional density is then generalized from a normal to a Student-t with unknown degrees of freedom. By estimating the degrees of freedom, implications about the conditional kurtosis of these models and time aggregated models can be drawn. A further generalization allows the conditional variance to be a non-linear function of the squared innovations. Throughout empirical e imates of the logarithm of the exchange rate between the U.S. dollar and the Swiss franc are presented to illustrate the models.     

保险产品中最低收益保证的均衡定价

在同时考虑保险公司和投保人的利益下,研究保险产品中最低收益保证的均衡定价,给出了不同效用函数下的定价区间,最后从再保险风险交换的角度给出了Pareto最优下的最低收益保证需要满足的条件。     

Stochastic Spanning

ABSTRACT

This study develops and implements methods for determining whether introducing new securities or relaxing investment constraints improves the investment opportunity set for all risk averse investors. We develop a test procedure for “stochastic spanning” for two nested portfolio sets based on subsampling and linear programming. The test is statistically consistent and asymptotically exact for a class of weakly dependent processes. A Monte Carlo simulation experiment shows good statistical size and power properties in finite samples of realistic dimensions. In an application to standard datasets of historical stock market returns, we accept market portfolio efficiency but reject two-fund separation, which suggests an important role for higher-order moment risk in portfolio theory and asset pricing. Supplementary materials for this article are available online.     

The least concave majorant of the empirical distribution function

The author compares two estimators of a continuous, concave distribution function having support on the positive half line. In terms of samples from uniform distributions, he gives stochastic bounds for the pointwise and sup‐norm differences between the least concave majorant of the empirical distribution function and the underlying distribution function. He also offers evidence demonstrating the almost paradoxical result that the empirical distribution function is not as good an estimator as its least concave majorant in terms of sup‐norm error but a better pointwise estimator of the true distribution function in terms of mean squared error.     

Risk preference and employment contract type

Summary.  We explore the possibility that a systematic relationship exists between employment within a particular type of contract and risk preference. We exploit a set of proxies for risk preference, whereby some of the proxies capture risk loving behaviour (expenditure on gambling, smoking and alcohol) whereas others capture risk averse behaviour (expenditure on life and contents insurance, and unearned income). The empirical analysis, based on pooled cross-section data from the UK Family Expenditure Survey, 1997–2000, provides evidence of a systematic relationship between employment contract type and risk preference, with, for example, self-employed workers being more or less likely to engage in the consumption of 'risky' or financial security products respectively. The results are based on the ordered generalized extreme value model, a relatively infrequently used discrete choice model, which allows for ordering and correlation in the alternatives observed.     

Asset Prices Under Habit Formation and Reference-Dependent Preferences

This article explains the high level and the countercyclical variation of the equity premium in a consumption-based asset pricing model with low large-scale risk aversion. Investors have gain-loss utility over consumption relative to slowly time-varying habit. Stocks deliver low returns in recessions when consumption falls below habit; investors therefore require a high premium for holding stocks. The model's conditional moment restrictions are tested on consumption and asset returns data. The empirical estimate of large-scale risk aversion is low, whereas the estimate of loss aversion agrees with prior experimental evidence.     

A flexible parametric survival model which allows a bathtub-shaped hazard rate function

A new parametric (three-parameter) survival distribution, the lognormal–power function distribution, with flexible behaviour is introduced. Its hazard rate function can be either unimodal, monotonically decreasing or can exhibit a bathtub shape. Special cases include the lognormal distribution and the power function distribution, with finite support. Regions of parameter space where the various forms of the hazard-rate function prevail are established analytically. The distribution lends itself readily to accelerated life regression modelling. Applications to five data sets taken from the literature are given. Also it is shown how the distribution can behave like a Weibull distribution (with negative aging) for certain parameter values.     

A robust test for non-nested hypotheses

This paper uses a modified rank score test for non-nested linear regression models. The modified rank score test is robust with respect to models with non-normal distributions and can be viewed as a robust version of the J test of Davidson and MacKinnon (Econometrica 49:781–793, 1981). Therefore, this test does not require a specification of error density function and is easy to implement. Also, a modified rank score test for multiple non-nested models is provided. Monte Carlo simulation results show that the test has good finite sample performances. Financial applications for two competing theories, the capital asset pricing model and the arbitrage pricing theory, are considered herein. Empirical evidence from the modified rank score test shows that the former is a better model for asset pricing.     

Exact Estimation of Demand Functions under Block-Rate Pricing

This article proposes an exact estimation of demand functions under block-rate pricing by focusing on increasing block-rate pricing. This is the first study that explicitly considers the separability condition which has been ignored in previous literature. Under this pricing structure, the price changes when consumption exceeds a certain threshold and the consumer faces a utility maximization problem subject to a piecewise-linear budget constraint. Solving this maximization problem leads to a statistical model in which model parameters are strongly restricted by the separability condition. In this article, by taking a hierarchical Bayesian approach, we implement a Markov chain Monte Carlo simulation to properly estimate the demand function. We find, however, that the convergence of the distribution of simulated samples to the posterior distribution is slow, requiring an additional scale transformation step for parameters to the Gibbs sampler. These proposed methods are then applied to estimate the Japanese residential water demand function.     

A discrete/continuous choice model on a nonconvex budget set

Decreasing block rate pricing is a nonlinear price system often used for public utility services. Residential gas services in Japan and the United Kingdom are provided under this price schedule. The discrete/continuous choice approach is used to analyze the demand under decreasing block rate pricing. However, the nonlinearity problem, which has not been examined in previous studies, arises because a consumer’s budget set (a set of affordable consumption amounts) is nonconvex, and hence, the resulting model includes highly nonlinear functions. To address this problem, we propose a feasible, efficient method of demand estimation on the nonconvex budget. The advantages of our method are as follows: (i) the construction of an Markov chain Monte Carlo algorithm with an efficient blanket based on the Hermite–Hadamard integral inequality and the power-mean inequality, (ii) the explicit consideration of the (highly nonlinear) separability condition, which often makes numerical likelihood maximization difficult, and (iii) the introduction of normal disturbance into the discrete/continuous choice model on the nonconvex budget set. The proposed method is applied to estimate the Japanese residential gas demand function and evaluate the effect of price schedule changes as a policy experiment.     

RISK PREFERENCES UNDER PRICE UNCERTAINTIES AND PRODUCTION RISK

This paper deals with estimation of risk preferences of producers when they face uncertainties in output and input prices, in addition to uncertainty in production (usually labeled as production risk). All these uncertainty components are modeled in the context of production theory where the producers maximize expected utility of anticipated profit. Risk preference functions associated with these uncertainties are derived without assuming a specific form of the utility function. Moreover, no distributional assumptions are made on the distributions of the random variables representing price and production uncertainties. A multi-stage estimation procedure is developed to estimate the parameters of the production function and risk preference functions associated with output price uncertainty, input price uncertainty and production risk. Production risk is specified in such a way that one can identify inputs with increasing, decreasing and constant production risks. Similarly, risk aversion behavior is specified in such a way that one can test for different types of risk aversion behavior.     

沪深300股指期货定价模型的改进及实证研究

根据沪深300股指期货市场的实际情况,将交易成本、冲击成本、借贷利率不等、融资融券、间断股利发放等因素纳入考虑,对克莱蒙考斯基和李无套利区间定价模型进行改进,推导出一个不完美市场下适用于沪深300股指期货定价的无套利区间定价模型。该模型克服了持有成本定价模型和隐含增长率定价模型假设条件太强的缺陷,在对11份沪深300股指期货合约日收盘价数据的实证后发现,该模型无套利区间定价模型定价效率最高。     

A permutation test for umbrella alternatives

There is a wide variety of stochastic ordering problems where K groups (typically ordered with respect to time) are observed along with a (continuous) response. The interest of the study may be on finding the change-point group, i.e. the group where an inversion of trend of the variable under study is observed. A change point is not merely a maximum (or a minimum) of the time-series function, but a further requirement is that the trend of the time-series is monotonically increasing before that point, and monotonically decreasing afterwards. A suitable solution can be provided within a conditional approach, i.e. by considering some suitable nonparametric combination of dependent tests for simple stochastic ordering problems. The proposed procedure is very flexible and can be extended to trend and/or repeated measure problems. Some comparisons through simulations and examples with the well known Mack & Wolfe test for umbrella alternative and with Page’s test for trend problems with correlated data are investigated.     

A class of distortion measures generated from expectile and its estimation

We construct a specific form of piecewise distortion function which can distort a random risk to its expectile. After analyzing this kind of distortion functions, we define a class of distortion functions which are generated from random variables. The consistent estimation of the expectile distortion parameter is given by the maximum empirical likelihood method. The expectile distortion not only inherits the good properties of concave distortion measures but also has its own advantages. Since that, we discuss the potential usage of this measure and imagine a new premium principle based on the non self form of this measure.     

非线性定价、家庭人口特征和收入再分配效应调整

本文以分时阶梯定价为例,在人口老龄化及生育政策逐渐放宽的背景下,通过建立结构计量模型,实证分析了引入家庭人口特征后,非线性定价对收入再分配效应这一政策目标的影响。通过构建引入家庭人口特征的二次近乎理想需求（QUAIDS）函数,基于相对等价补偿方法建立收入再分配效应调整的测度模型。估计了为保持相同效用增加家庭不同类型的人口需要增加的电费补偿率及其金额。研究结论表明,引入家庭人口特征后收入再分配效应得到了强化;家庭人口特征对消费者行为选择有显著影响;不同人口规模的家庭的电费补贴结构存在明显差异;动态分析显示,随着预算水平的提高,家庭人口特征对收入再分配效应的影响在减小。     

A variable selection approach to monotonic regression with Bernstein polynomials

One of the standard problems in statistics consists of determining the relationship between a response variable and a single predictor variable through a regression function. Background scientific knowledge is often available that suggests that the regression function should have a certain shape (e.g. monotonically increasing or concave) but not necessarily a specific parametric form. Bernstein polynomials have been used to impose certain shape restrictions on regression functions. The Bernstein polynomials are known to provide a smooth estimate over equidistant knots. Bernstein polynomials are used in this paper due to their ease of implementation, continuous differentiability, and theoretical properties. In this work, we demonstrate a connection between the monotonic regression problem and the variable selection problem in the linear model. We develop a Bayesian procedure for fitting the monotonic regression model by adapting currently available variable selection procedures. We demonstrate the effectiveness of our method through simulations and the analysis of real data.     

EUROPEAN OPTION PRICING WITH GENERAL TRANSACTION COSTS AND SHORT-SELLING CONSTRAINTS

In this paper, we study the problem of European Option Pricing in a market with short-selling constraints and transaction costs having a very general form. We consider two types of proportional costs and a strictly positive fixed cost. We study the problem within the framework of the theory of stochastic impulse control. We show that determining the price of a European option involves calculating the value functions of two stochastic impulse control problems. We obtain explicit expressions for the quasi-variational inequalities satisfied by the value functions and derive the solution in the case where the parameters of the price processes are constants and the investor's utility function is linear. We use this result to obtain a price for a call option on the stock and prove that this price is a nontrivial lower bound on the hedging price of the call option in the presence of general transaction costs and short-selling constraints. We then consider the situation where the investor's utility function has a general form and characterize the value function as the pointwise limit of an increasing sequence of solutions to associated optimal stopping problems. We thereby devise a numerical procedure to calculate the option price in this general setting and implement the procedure to calculate the option price for the class of exponential utility functions. Finally, we carry out a qualitative investigation of the option prices for exponential and linear-power utility functions.     

综合评价中一种凹性指数型功效函数

目前主流功效函数多为凸性,在处理社会经济数据集中常见的右偏样本时效果难以令人满意。通过系统探讨凸性和凹性功效函数各自的适用特征,指出凹性函数在应用中有其必要性。归纳并使用偏度、区分度、P-P图三种方法作为分布形态的评判标准,比较了常见功效函数对指标原始数据分布形态的调整作用。在分析基础上,提出一种改进的凹性指数功效函数,能有效地处理右偏数据,且相比使用对数预处理的凸性功效函数更具适用性与便利性。     

A test for the variance residual life

In this paper we develop a test based on the empirical distribution function for the alternative representing 'decreasing variance residual life1 property. The test is consistent with asymptotically normal test statistic and is shown to perform well in the Pitman's asymptotic relative efficiency sense.     

Testing Symmetry of the Error Distribution in Nonlinear Heteroscedastic Models

Using the empirical characteristic function, we derive a Cramér-von Mises test for symmetry of the error distribution in a class of nonlinear parametric heteroscedastic models. We study the convergence of the residual-based empirical distribution function. We establish a functional limit theorem for an empirical process of residuals, and investigate the asymptotic null distribution function of our test statistic. A simulation experiment is conducted to evaluate small-sample performances of our test.