Price bias and common practice in option pricing

Generally, the semiclosed-form option pricing formula for complex financial models depends on unobservable factors such as stochastic volatility and jump intensity. A popular practice is to use an estimate of these latent factors to compute the option price. However, in many situations this plug-and-play approximation does not yield the appropriate price. This article examines this bias and quantifies its impacts. We decompose the bias into terms that are related to the bias on the unobservable factors and to the precision of their point estimators. The approximated price is found to be highly biased when only the history of the stock price is used to recover the latent states. This bias is corrected when option prices are added to the sample used to recover the states' best estimate. We also show numerically that such a bias is propagated on calibrated parameters, leading to erroneous values. The Canadian Journal of Statistics 48: 8–35; 2020 © 2019 Statistical Society of Canada     

陕北方言的疑问句

陕北方言的疑问句和普通话的疑问句不同 ,只有是非问句、特指问句和选择问句三种 ,且结构格式也不一样。是非问句通常用类似于正反问的“体标记 否定词”格式表示 ;选择问句是在选择项之间嵌入“是”字 ,并于选项末缀体标记 ;特指问句则表现为一系列不同于普通话的特殊疑问代词的使用。同时三种问句格式在语义、语用方面也和普通话的相应形式有一些差别     

Book Reviews

Books reviewed:
M Hollander and D Wolfe, Nonparametric Statistical Methods
T Leonard and J.S.J Hsu, Bayesian Methods     

Quadratic estimators of covariance components in a multivariate mixed linear model

It is known that the Henderson Method III (Biometrics 9:226–252, 1953) is of special interest for the mixed linear models because the estimators of the variance components are unaffected by the parameters of the fixed factor (or factors). This article deals with generalizations and minor extensions of the results obtained for the univariate linear models. A MANOVA mixed model is presented in a convenient form and the covariance components estimators are given on finite dimensional linear spaces. The results use both the usual parametric representations and the coordinate-free approach of Kruskal (Ann Math Statist 39:70–75, 1968) and Eaton (Ann Math Statist 41:528–538, 1970). The normal equations are generalized and it is given a necessary and sufficient condition for the existence of quadratic unbiased estimators for covariance components in the considered model.     

国民党对日派遣占领军问题浅析

战后国民党政府对日派遣占领军问题是在美国的亚洲政策及对日政策的影响下提出的,是国民党政府忙于打内战使此问题未果而终。这一结局影响中国战后对日处置一些问题的实施,进而影响战后一段时期亚太地区的国际关系。     

DBF系统的通道校正技术

描述了影响DBF系统特性的主要因素,研究了阵元间互耦对自适应方向图旁瓣和零深的影响及校正方法,讨论了在DBF阵中校正接收通道幅、相误差和I/Q支路正交误差的技术途径。计算机模拟和测试证明,按照所述方法进行校正可以得到满意的结果。另外,为了减小I/Q支路产生正交误差,建议采用中频直接采样和数字化的接收机方案。     

MODEL-ASSISTED HIGHER-ORDER CALIBRATION OF ESTIMATORS OF VARIANCE

In survey sampling, interest often centres on inference for the population total using information about an auxiliary variable. The variance of the estimator used plays a key role in such inference. This study develops a new set of higher‐order constraints for the calibration of estimators of variance for various estimators of the population total. The proposed strategy requires an appropriate model for describing the relationship between the response and auxiliary variable, and the variance of the auxiliary variable. It is therefore referred to as a model‐assisted approach. Several new estimators of variance, including the higher‐order calibration estimators of the variance of the ratio and regression estimators suggested by Singh, Horn & Yu and Sitter & Wu are special cases of the proposed technique. The paper presents and discusses the results of an empirical study to compare the performance of the proposed estimators and existing counterparts.     

The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

“安乐死”的合法性分析

安乐死历来是个敏感的话题,有关安乐死的争论除在哲学、伦理学、医学等领域展开外,法学界对安乐死从不同的角度发表了不同的观点。近期对这一问题的讨论尤其引人注目,笔者想就此进行分析并进而提出一些自己的看法。     

均值绝对偏差资产组合选择模型的算法

对均值绝对偏差模型进行了简化,并利用一种旋转算法求解。这种算法比单纯形算法的计算简便,且计算量更小。利用上海和深圳股市1 072支股票70期周末收盘价所作的实验结果表明,对于资产无上界限制的模型,计算20个不同最优投资组合需要1 274次旋转运算,上界为10%时需要1 570次旋转运算,每 次旋转运算约需1 14171次加法和乘法运算。