资产定价的数学模型

随着资本市场的发展,投资者越来越关注资产价格预期问题,理论研究者对这一问题给出不同的解决方法.Sharpe等给出了资本资产定价模型(CAPM),Ross提出了套利定价理论(APT),Black和Scholes给出了期权定价公式.Cochrane提出了随机折线因子模型的定价理论.在对资产定价问题研究的同时,风险投资公司还需要密切关注投资中的市场风险,以期更有效地进行风险管理,但是风险管理离不开投资收益的合理有效分析,给出的折线因子模型能够很好的反映收益在资产定价中的作用,Robert F.Engle指出资产定价是当今资本市场的研究关键.以下对这些模型从数学角度进行分析.     

Knight不确定性与一般风险资产的动态最小定价

文章研究了具有Knight不确定性的金融市场,利用倒向随机微分方程(BSDE)的重要理论以及时间-风险折现方法,探讨了一般风险资产的动态定价公式,求出了一般风险资产在Knight不确定性控制集合上的动态最小定价.最后通过研究某种风险资产的动态最小定价公式,借助于数值分析,揭示了Knight不确定性对风险资产定价的重要影响.     

资本资产定价模型CAPM在中国资本市场中的实证检验

采用中国上海资本市场交易数据对资本资产定价模型（CAPM）的适用性进行了三个方面的检验：资产的风险和收益之间是否存在线性关系;系统风险是否是资产风险的唯一度量;资产的风险和收益是否正相关。结果发现：2003年8月1日至2006年7月31日期间,上海资本市场股票组合的平均超额收益率与其系统风险之间存在正相关关系,与非系统风险不存在显著的线性关系,基本符合标准形式的CAPM。这与国内许多学者对2001年以前中国资本市场CAPM的实证检验结果不太一致。     

中国商品期货市场波动性研究

在金融领域中,波动性一直是个非常重要的方面,其对资产定价、投资组合选择及风险管理起着极其重要的作用,而且波动性也是直接影响金融市场稳定性的重要风险因素,普遍受到各国政府的重视。本文利用GARcH（1,1）和EGARCH（1,1）模型对中国商品期货市场的波动性进行研究,试图寻找发现我国商品期货市场运行机制和风险控制具有启发意义的结论。     

分形理论下的定价模型及实证检验

文章依据分形理论对资产收益率的惯性现象进行了经济学阐释,在Fama-French三因子定价模型的基础之上,构造了含有惯性因子的定价模型,并结合中国证券市场对模型的有效性和稳定性进行了实证检验,为证券监管机构的监管和广大投资者的风险控制提供了依据。     

第一HJ距离的理论分析

模型设定检验是资产定价的核心环节,作为模型误设的新指标,第一HJ距离受到学术界的广泛关注。然而,鲜有文献比较第一HJ距离和传统的误设测度的异同。本文系统地分析第一HJ距离的性质,并与传统的模型设定误差测度进行比较发现：（1）第一HJ距离将基于模型所用SDF的欧氏空间距离和最大定价误相联系,有丰富的经济含义;（2）第一HJ距离关注定价误差,相较于传统的模型误设测度,倾向于选择大的零Beta收益率和小的因子风险溢酬,对模型的排序有差异;（3）第一HJ距离的加权矩阵具有模型独立性和对测试资产组合选择的一致性。     

中国无风险和率与居民消费增长实证分析

文章根据基于消费的资产定价理论建立了无风险利率与消费之间的关系模型,并对中国1998～2008年的数据进行实证分析.     

基于多元GARCH的动态CAPM

资本资产定价模型(CAPM)是一种评估风险的重要模型,但该模型是基于静态分析,实践效用较低.文章从资本资产定价模型的理论定义入手,使用多元GARCH模型分析资产收益率的时变方差和协方差,并在此基础之上动态估计CAPM中β系数.实证结果表明,时变β系数较好的体现了风险是时变波动的状况,而且实证结果同理论和经验研究保持了一致.     

多阶段贷款担保价值及其影响因素研究

鉴于目前贷款担保经验定价方法的准确性太低和单阶段期权定价未考虑担保方资产变化过程的现实,文章通过吸收存款保险的多阶段风险定价的优点,考虑到担保期内的债务方资产的变化过程,构建了多阶段贷款担保定价模型,并通过蒙特卡罗模拟测算了多阶段贷款担保价值及资产负债比、担保比例、担保期限以及被担保方资产波动率对担保价值的影响作用,为担保方规避风险,进行科学的担保定价提供了决策依据.     

土地资产证券化产品设计与风险防范

文章在对土地资产证券化进行界定的基础上,着重研究土地资产证券化的产品设计,创造性引入跳-扩散模型对土地资产证券化进行定价,解决产品设计中的核心问题。最后对土地资产证券化的风险控制和制度环境建设进行前瞻性探讨。     

Highly Efficient Designs to Handle the Incorrect Specification of Linear Mixed Models

The asymptotic chi-square test for testing the Hardy–Weinberg law is unreliable in either small or unbalanced samples. As an alternative, either the unconditional or conditional exact test might be used. It is known that the unconditional exact test has greater power than the conditional exact test in small samples. In this article, we show that the conditional exact test is more powerful than the unconditional exact test in large samples. This result is useful in extremely unbalanced cases with large sample sizes which are often obtained when a rare allele exists.     

Confidence intervals following Box-Cox transformation

What is the interpretation of a confidence interval following estimation of a Box-Cox transformation parameter λ? Several authors have argued that confidence intervals for linear model parameters ψ can be constructed as if λ. were known in advance, rather than estimated, provided the estimand is interpreted conditionally given $\hat \lambda$. If the estimand is defined as $\psi \left( {\hat \lambda } \right)$, a function of the estimated transformation, can the nominal confidence level be regarded as a conditional coverage probability given $\hat \lambda$, where the interval is random and the estimand is fixed? Or should it be regarded as an unconditional probability, where both the interval and the estimand are random? This article investigates these questions via large-n approximations, small- σ approximations, and simulations. It is shown that, when model assumptions are satisfied and n is large, the nominal confidence level closely approximates the conditional coverage probability. When n is small, this conditional approximation is still good for regression models with small error variance. The conditional approximation can be poor for regression models with moderate error variance and single-factor ANOVA models with small to moderate error variance. In these situations the nominal confidence level still provides a good approximation for the unconditional coverage probability. This suggests that, while the estimand may be interpreted conditionally, the confidence level should sometimes be interpreted unconditionally.     

Evaluation of Conditional Weight Approximations for Two-Level Models

This article evaluates two methods of approximating cluster-level and conditional sampling weights when only unconditional sampling weights are available. For estimation of a multilevel analysis that does not include all facets of a sampling design, conditional sampling weights at each stage of the model should be used, but typically only the unconditional sampling weight of the ultimate sampling unit is provided on federal publicly-released datasets. Methods of approximating these conditional weights have been suggested but there has been no study of their adequacy. This demonstration and simulation study examines the feasibility of using these weight approximations.     

The Generalized Conditional Autoregressive Wishart Model for Multivariate Realized Volatility

It is well known that in finance variances and covariances of asset returns move together over time. Recently, much interest has been aroused by an approach involving the use of the realized covariance (RCOV) matrix constructed from high-frequency returns as the ex-post realization of the covariance matrix of low-frequency returns. For the analysis of dynamics of RCOV matrices, we propose the generalized conditional autoregressive Wishart (GCAW) model. Both the noncentrality matrix and scale matrix of the Wishart distribution are driven by the lagged values of RCOV matrices, and represent two different sources of dynamics, respectively. The GCAW is a generalization of the existing models, and accounts for symmetry and positive definiteness of RCOV matrices without imposing any parametric restriction. Some important properties such as conditional moments, unconditional moments, and stationarity are discussed. Empirical examples including sequences of daily RCOV matrices from the New York Stock Exchange illustrate that our model outperforms the existing models in terms of model fitting and forecasting.     

Generalized L-statistics: Correction to the Form of the Asymptotic Variance Presented by Helmers et al. (1990)

We show that the asymptotic variance of a "generalized L -statistic" is a function of the difference between the conditional and unconditional cumulative distribution functions of the kernel used to form the statistic.     

Conditional Correlation Models of Autoregressive Conditional Heteroscedasticity With Nonstationary GARCH Equations

In this article, we investigate the effects of careful modeling the long-run dynamics of the volatilities of stock market returns on the conditional correlation structure. To this end, we allow the individual unconditional variances in conditional correlation generalized autoregressive conditional heteroscedasticity (CC-GARCH) models to change smoothly over time by incorporating a nonstationary component in the variance equations such as the spline-GARCH model and the time-varying (TV)-GARCH model. The variance equations combine the long-run and the short-run dynamic behavior of the volatilities. The structure of the conditional correlation matrix is assumed to be either time independent or to vary over time. We apply our model to pairs of seven daily stock returns belonging to the S&P 500 composite index and traded at the New York Stock Exchange. The results suggest that accounting for deterministic changes in the unconditional variances improves the fit of the multivariate CC-GARCH models to the data. The effect of careful specification of the variance equations on the estimated correlations is variable: in some cases rather small, in others more discernible. We also show empirically that the CC-GARCH models with time-varying unconditional variances using the TV-GARCH model outperform the other models under study in terms of out-of-sample forecasting performance. In addition, we find that portfolio volatility-timing strategies based on time-varying unconditional variances often outperform the unmodeled long-run variances strategy out-of-sample. As a by-product, we generalize news impact surfaces to the situation in which both the GARCH equations and the conditional correlations contain a deterministic component that is a function of time.     

Derivative Pricing With Wishart Multivariate Stochastic Volatility

This paper deals with the pricing of derivatives written on several underlying assets or factors satisfying a multivariate model with Wishart stochastic volatility matrix. This multivariate stochastic volatility model leads to a closed-form solution for the conditional Laplace transform, and quasi-explicit solutions for derivative prices written on more than one asset or underlying factor. Two examples are presented: (i) a multiasset extension of the stochastic volatility model introduced by Heston (1993), and (ii) a model for credit risk analysis that extends the model of Merton (1974) to a framework with stochastic firm liability, stochastic volatility, and several firms. A bivariate version of the stochastic volatility model is estimated using stock prices and moment conditions derived from the joint unconditional Laplace transform of the stock returns.     

Some remarks on conditional and unconditional inference for location-scale models

Conditional and unconditional confidence intervals have been compared by Grice, Bain, and Engelhardt (Commun. Statist. B7 (1978), 515–524) in terms of the location-scale model with double-exponential distribution form. Preference was found for the conditional intervals based on mean length and coverage probability for untrue parameters values. These two criteria for a location-scale system are shown to be inappropriate criteria for assessing the conditional versus unconditional approaches to inference. The usual ancillarity concept is also noted to be inappropriate. Support for many conditional analyses, however, is found in a more careful formulation of the statistical model.     

Extending permutation conditional inference to unconditional ones

In this presentation we discuss the extension of permutation conditional inferences to unconditional or population ones. Within the parametric approach this extension is possible when the data set is randomly selected by well-designed sampling procedures on well-defined population distributions, provided that their nuisance parameters have boundely complete statistics in the null hypothesis or are provided with invariant statistics. When these conditions fail, especially if selection-bias procedures are used for data collection processes, in general most of the parametric inferential extensions are wrong or misleading. We will see that, since they are provided with similarity and conditional unbiasedness properties and if correctly applicable, permutation tests may extend, at least in a weak sense, conditional to unconditional inferences.     

Tests for Equality of Parameters of Two Exponential Distributions with Common Known Coefficient of Variation

ABSTRACT

This article considers the problem of testing equality of parameters of two exponential distributions having common known coefficient of variation, both under unconditional and conditional setup. Unconditional tests based on BLUE'S and LRT are considered. Using the Conditionality Principle of Fisher, an UMP conditional test for one-sided alternative is derived by conditioning on an ancillary. This test is seen to be uniformly more powerful than unconditional tests in certain given ranges of ancillary. Simulation studies on the power functions of the tests are done for this purpose.