Sequential calibration of options

Robust calibration of option valuation models to quoted option prices is non-trivial but crucial for good performance. A framework based on the state-space formulation of the option valuation model is introduced. Non-linear (Kalman) filters are needed to do inference since the models have latent variables (e.g. volatility). The statistical framework is made adaptive by introducing stochastic dynamics for the parameters. This allows the parameters to change over time, while treating the measurement noise in a statistically consistent way and using all data efficiently. The performance and computational efficiency of standard and iterated extended Kalman filters (EKF and IEKF) are investigated. These methods are compared to common calibration such as weighted least squares (WLS) and penalized weighted least squares (PWLS). A simulation study, using the Bates model, shows that the adaptive framework is capable of tracking time varying parameters and latent processes such as stochastic volatility processes. It is found that the filter estimates are the most accurate, followed by the PWLS estimates. The estimates from all of the advanced methods are significantly closer to the true parameters than the WLS estimates which overfits data. The filters are also faster than least squares methods. All calibration methods are also applied to daily European option data on the S&P 500 index, where the Heston, Bates and NIG-CIR models are considered. The results are similar to the simulation study and it can be seen that the overfitting is a real problem for the WLS estimator when applied complex models.     

Computation of estimates in segmented regression and a liquidity effect model

Weighted least squares (WLS) estimation in segmented regression with multiple change points is considered. A computationally efficient algorithm for calculating the WLS estimate of a single change point is derived. Then, iterative methods of approximating the global solution of the multiple change-point problem based on estimating change points one-at-a-time are discussed. It is shown that these results can also be applied to a liquidity effect model in finance with multiple change points. The liquidity effect model we consider is a generalization of one proposed by Çetin et al. [2006. Pricing options in an extended Black Scholes economy with illiquidity: theory and empirical evidence. Rev. Financial Stud. 19, 493-529], allowing that the magnitude of liquidity effect depends on the size of a trade. Two data sets are used to illustrate these methods.     

A majorization algorithm for simultaneous parameter estimation in robust exploratory factor analysis

A new approach for fitting the exploratory factor analysis (EFA) model is considered. The EFA model is fitted directly to the data matrix by minimizing a weighted least squares (WLS) goodness-of-fit measure. The WLS fitting problem is solved by iteratively performing unweighted least squares fitting of the same model. A convergent reweighted least squares algorithm based on iterative majorization is developed. The influence of large residuals in the loss function is curbed using Huber’s criterion. This procedure leads to robust EFA that can resist the effect of outliers in the data. Applications to real and simulated data illustrate the performance of the proposed approach.     

Fast two-dimensional weighted least squares techniques for the design of two-dimensional finite impulse response filters

This paper focuses on the design of two-dimensional (2D) quadrantally symmetric finite impulse response (FIR) filters, and presents three very efficient algorithms for the weighted least squares (WLS) design with a weight matrix that assigns four different weights to four different frequency bands. The first algorithm seeks for iterative solutions to the matrix equation describing the optimality condition of the design problem. The second algorithm aims at the limit solution of the solution sequence to the first algorithm, analytically obtained by using matrix diagonalization techniques. The third algorithm belongs to the category of iterative reweighting techniques. It uses the second algorithm as its iteration core, and aims at reducing the maximum magnitude error of the filter by iteratively adjusting the four entry values of the weight matrix. Design examples are provided to demonstrate the performance of the proposed algorithms.     

GPU-based model predictive control for continuous casting spray cooling control system using particle swarm optimization

Model predictive control (MPC) for spray cooling control system requires a repeated online solution of an optimization problem that includes partial differential equations (PDEs). To simulate the future temperature behavior of steel billets, 3D dynamic heat transfer model is used. The special solution domain of PDEs has led to large computation cost, which is the main challenge in the real-time practical application of spray cooling control system. Meanwhile, the heat transfer coefficients need to be identified using the measured surface temperature. This work presents a two-level parallel solution method implemented on a Graphics processing unit (GPU) for MPC of spray cooling control systems and a weighted least squares modified conjugate gradient method (WLS–MCG) for identification of heat transfer coefficients. Two-level parallel solution method consists of parallel-based heat transfer model and stream parallel particle swarm optimization (PSO). PSO is used to solve the optimization problem. WLS–MCG consists of the weighted least squares (WLS) and modified conjugate gradient method (MCG). The experimental results show that the two-level parallel solution method has good computational performance and achieves satisfactory control performance.     

一种改进的三边定位算法

针对基于加权最小二乘(WLS)的三边定位算法在线性化过程中损失定位信息的问题,提出了一种改进的三边定位算法。该算法利用WLS算法粗略估计未知节点的坐标,并利用损失的定位信息构建定位模型,通过求解该定位模型实现精确定位。仿真结果表明,与基于WLS的三边定位算法相比,该算法有效提高了定位精度,且巷道长宽比越大,定位性能越好。     

加速度计几种模型辨识方法的比较研究

加速度计离心试验中,为了更精确的得到加速度计的模型系数,比较研究了3种辨识方法:最小二乘方法(加权最小二乘)、总体最小二乘方法和EV模型方法.通过仿真得出在输出噪声和输入噪声为白噪声或者近似白噪声且离心机精度优于1×10-5的情况下,最小二乘与其他2种辨识方法辨识精度相当.最后通过试验对比了最小二乘方法与加权最小二乘方...     

基于准最小二乘法的光伏阵列模型鲁棒参数估计方法

光伏阵列的模型参数估计在光伏发电系统的仿真、输出功率预测、最大功率点跟踪等方面有重要意义。当测量数据中只含随机误差时,以加权最小二乘（WLS）为优化函数的参数估计方法有较好的辩识效果。但是当测量数据中含有显著误差时,WLS参数辩识的效果较差。为解决此问题,本文提出了一种以准加权最小二乘法（QWLS）为优化函数的参数估计方法来减小显著误差的影响,采用了赤池信息量准则(AIC)设计QWLS最优参数,将该方法应用于光伏阵列中构造模型鲁棒参数估计问题。最后将WLS和QWLS分别结合序列二次规划（SQP）算法,进行光伏阵列模型的参数估计仿真与实验测试。测试结果显示QWLS参数估计结果更准确,验证了准最小二乘法的鲁棒性与有效性。     

多基地声纳系统中目标位置与速度联合估计

在多基地声呐系统中,为了利用时间和与多普勒频率量测同时估计运动目标的位置与速度,设计了一种闭式的估计器.其中,使用误差修正的方法,改善了传统的多步加权最小二乘估计器.该估计器只涉及线性加权最小二乘运算,在量测高斯噪声较小的情况下,均方误差可以达到克拉美罗下界(CRLB).通过计算机模拟对比了该估计器的均方误差与CRLB,并比较了其与传统多步加权最小二乘估计器的性能,结果表明:估计器的均方误差小于传统多步加权最小二乘估计器.     

联合TDOA-AOA无线传感器网络半定规划定位算法研究

在无线传感器网络定位中,TDOA和AOA联合定位可有效利用多种位置信息提高定位精度.由于传统联合加权最小二乘(WLS)的目标函数非线性,在应用于无线传感器网络定位时,会产生多个局部最优解.因此,针对该问题本文将约束加权最小二乘问题转化为二次约束二次规划问题,之后通过引入半定松弛(SDR)方法将联合定位问题转换为低复杂度的半定规划问题(SDP),进而寻找全局最优解.并且针对实际应用中参考节点带误差的情形分析和推导了定位算法.与已有算法相比,提出的算法在参考节点无误差和有误差时都有更高的精度.此外,提出的SDP算法还能够实现只有两个参考节点下的目标定位.     

A novel weighted least squares PET image reconstruction method using adaptive variable index sets

In this paper, we present a novel image reconstruction method based on weighted least squares (WLS) objective function for positron emission tomography (PET). Unlike a usual WLS algorithm, the proposed method, which we call it SA-WLS, combines the SAGE algorithm with WLS algorithm. It minimized the WLS objective function using single coordinate descent (SCD) method in a sequence of small “hidden” data spaces (HDS). Although SA-WLS used a strategy to update parameter sequentially just like common SCD method, the use of these small HDS makes it converge much faster and produce the reconstructed images with greater contrast and detail than the usual WLS method. In order to decrease further the actual CPU time per iteration, the adaptive variable index sets were introduced to modify SA-WLS (MSA-WLS). Instead of optimizing each pixel, this MSA-WLS method sequentially optimizes many pixels located in an index set at one time. The index sets were automatically modified during each iteration step. MSA-WLS gathers the virtue of simultaneously and sequentially updating the parameters so that it achieves a good compromise between the convergence rate and the computational cost in PET reconstruction problem. Details of these algorithms were presented and the performances were evaluated by a simulated head phantom.     

The Koul–Susarla–Van Ryzin and weighted least squares estimates for censored linear regression model: A comparative study

The Koul–Susarla–Van Ryzin (KSV) and weighted least squares (WLS) methods are simple to use techniques for handling linear regression models with censored data. They do not require any iterations and standard computer routines can be employed for model fitting. Emphasis has been given to the consistency and asymptotic normality for both estimators, but the finite sample performance of the WLS estimator has not been thoroughly investigated. The finite sample performance of these two estimators is compared using an extensive simulation study as well as an analysis of the Stanford heart transplant data. The results demonstrate that the WLS approach performs much better than the KSV method and is reliable for use with censored data.     

The Koul-Susarla-Van Ryzin and weighted least squares estimates for censored linear regression model: A comparative study

The Koul-Susarla-Van Ryzin (KSV) and weighted least squares (WLS) methods are simple to use techniques for handling linear regression models with censored data. They do not require any iterations and standard computer routines can be employed for model fitting. Emphasis has been given to the consistency and asymptotic normality for both estimators, but the finite sample performance of the WLS estimator has not been thoroughly investigated. The finite sample performance of these two estimators is compared using an extensive simulation study as well as an analysis of the Stanford heart transplant data. The results demonstrate that the WLS approach performs much better than the KSV method and is reliable for use with censored data.     

Sequential weighted least squares algorithm for PET image reconstruction

The weighted least squares (WLS) algorithm has proven useful for modern positron emission tomography (PET) scanners to approach reconstructions with non-Poisson precorrected measurement data. In this paper, we propose a new time recursive sequential WLS algorithm whose derivation uses the time-varying property of data acquisition of PET scanning. It ties close relationship with the time-varying Kalman filtering and can be extended appropriately to an iteration fashion as the absence of proper a priori initializations. The performance of sequential WLS is evaluated experimentally. The results show its fast convergence over both the multiplicative and coordinate-based iterative WLS methods. It also produces relative uniform estimate variances that makes it more suitable for routine applications.     

一种传感网时间同步和定位的联合线性估计方法

采用时间测量以估计节点位置的方法实现简单,在传感网中得到了广泛的使用。然而节点计时时钟存在漂移和偏离,导致时间测量不准确。为此文本以节点时钟漂移和偏离模型为基础,提出了一种时间同步和节点定位的联合线性估计方法,包括最小平方（LS）及权重最小平方（WLS）方法。仿真测试了所设计算法的运行时间,分析了噪声对联合估计方法的估计误差影响。结果表明,LS及WLS线性估计方法运算速度较半正定（SDP）算法快,在低噪声条件下LS及WLS线性估计方法具有较高的稳定性和定位精度。     

Received signal strength based positioning for multiple nodes in wireless sensor networks

We address the problem of locating multiple nodes in a wireless sensor network with the use of received signal strength (RSS) measurements. In RSS based positioning, transmit power and path-loss factor are two environment dependent parameters which may be uncertain or unknown. For unknown transmit powers, we devise two-step weighted least squares (WLS) and maximum likelihood (ML) algorithms for node localization. The mean square error of the former is analyzed in the presence of zero-mean white Gaussian disturbances. When both transmit powers and path-loss factors are unavailable, two nonlinear least squares estimators, namely, the direct ML approach and combination of linear least squares and ML algorithm, are developed. Numerical examples are also included to evaluate the localization accuracy of the proposed estimators by comparing with two existing node positioning methods and the Cramér–Rao lower bound.     

Weighted least squares based recursive parametric identification for the submodels of a PWARX system

A piecewise affine autoregressive system with exogenous inputs (PWARX) is composed of a finite number of ARX subsystems, each of which corresponds to a polyhedral partition of the regression space. In this work a weighted least squares (WLS) estimator is suggested to recursively estimate the parameters of the ARX submodels, in which a sequence of kernel functions are introduced. Conditions on the input signal and the PWARX system are imposed to guarantee the almost sure convergence of the WLS estimates. Some numerical examples are included to illustrate performances of the algorithm.     

On the choice of test for a unit root when the errors are conditionally heteroskedastic

It is well known that in the context of the classical regression model with heteroskedastic errors, while ordinary least squares (OLS) is not efficient, the weighted least squares (WLS) and quasi-maximum likelihood (QML) estimators that utilize the information contained in the heteroskedasticity are. In the context of unit root testing with conditional heteroskedasticity, while intuition suggests that a similar result should apply, the relative performance of the tests associated with the OLS, WLS and QML estimators is not well understood. In particular, while QML has been shown to be able to generate more powerful tests than OLS, not much is known regarding the relative performance of the WLS-based test. By providing an in-depth comparison of the tests, the current paper fills this gap in the literature.     

多变量离散时间系统的自适应LQ控制

考虑了多变量离散系统的自适应ＬＱ（线性二次）控制问题,利用ＬＳ（最小二乘）算法和ＷＬＳ（加权最小二乘）算法的自收敛性和随机正则化的思想「１」,证明了修改的估计模型是几乎处处自收敛的、一致可控和一致可观的,基于上面的估计,提出了两种自适应ＬＱ控制律,证明了闭环系统是稳定的和最优的。