Digital contracts-driven method for pricing complex derivatives

In this paper, we propose a hybrid method of nonparametric and parametric methods, that is a digital contracts-driven (DCD) method, for pricing various complex options. Differing from general nonparametric data-driven methods, in which usually the observed data are used as training data directly, in the DCD method the European-style digital contracts of the underlying assets are used as basic inputs for a learning network. The digital contracts calculated from the observed data based upon the parametric method are used as hints in the learning process, and then enable the DCD method to have superior pricing accuracy to the common data-driven method in practical applications. Some Monte Carlo simulation experiments are performed and the results demonstrate that the proposed hybrid method not only has the advantages of generality and superior accuracy as the nonparametric method, but also the robust property to financial data with noise as the parametric method.     

基于中国地震的损失模型(英文)

对损失分布的估计一直是保险公司的重要问题. 有多种参数方法以及非参数方法拟合损失分布. 本文作者提出了结合参数和非参数的方法来解决损失分布拟合问题. 首先通过超额均值图确定大小损失之间的阈限,再利用广义Pareto分布拟合阈值以上损失, 转换后的核密度估计拟合阈值以下损失. 最后, 通过实证分析将该方法和其他方法进行了误差分析比较, 取得了理想的结果.     

GAM在汽车保险定价中的应用研究

汽车保险定价的基础在于风险分析,车辆、驾驶人以及行车环境等因素构成汽车保险定价所倚赖的一个风险系统.本文引入广义加法模型(GAM).将非参数平滑方法应用于到GAM中,结合贝叶斯理论(Bayes)和马尔可夫蒙特卡罗(MCMC)方法得到参数估计,构建汽车保险定价模型,并以国外某保险数据为样本进行实证分析,得到了较好的效果.     

Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation

Isotonic nonparametric least squares (INLS) is a regression method for estimating a monotonic function by fitting a step function to data. In the literature of frontier estimation, the free disposal hull (FDH) method is similarly based on the minimal assumption of monotonicity. In this paper, we link these two separately developed nonparametric methods by showing that FDH is a sign-constrained variant of INLS. We also discuss the connections to related methods such as data envelopment analysis (DEA) and convex nonparametric least squares (CNLS). Further, we examine alternative ways of applying isotonic regression to frontier estimation, analogous to corrected and modified ordinary least squares (COLS/MOLS) methods known in the parametric stream of frontier literature. We find that INLS is a useful extension to the toolbox of frontier estimation both in the deterministic and stochastic settings. In the absence of noise, the corrected INLS (CINLS) has a higher discriminating power than FDH. In the case of noisy data, we propose to apply the method of non-convex stochastic envelopment of data (non-convex StoNED), which disentangles inefficiency from noise based on the skewness of the INLS residuals. The proposed methods are illustrated by means of simulated examples.     

A New Method for Testing Leverage Effect

Leverage effect often arises in many fields,such as financial risk management, portfolio and option pricing. However,it still remains to be studied that whether there is leverage effect or not in real data. Based on local polynomial regression estimation and Kolmogorov-Smirnov nonparametric test, this paper introduces a new nonparametric test statistic for the leverage effect, and some asymptotic properties are also presented. Simulation studies show that the proposed method performs well. Finally, empirical studies on SP500 index and Microsoft data imply that leverage effect exists in the real data, which is consistent with the idea in finance.     

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??Leverage effect often arises in many fields,such as financial risk management, portfolio and option pricing. However,it still remains to be studied that whether there is leverage effect or not in real data. Based on local polynomial regression estimation and Kolmogorov-Smirnov nonparametric test, this paper introduces a new nonparametric test statistic for the leverage effect, and some asymptotic properties are also presented. Simulation studies show that the proposed method performs well. Finally, empirical studies on SP500 index and Microsoft data imply that leverage effect exists in the real data, which is consistent with the idea in finance.     

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??In the last few decades, longitudinal data was deeply research in statistics science and widely used in many field, such as finance, medical science, agriculture and so on. The characteristic of longitudinal data is that the values are independent from different samples but they are correlate from one sample. Many nonparametric estimation methods were applied into longitudinal data models with development of computer technology. Using Cholesky decomposition and Profile least squares estimation, we will propose a effective spline estimation method pointing at nonparametric model of longitudinal data with covariance matrix unknown in this paper. Finally, we point that the new proposed method is more superior than Naive spline estimation in the covariance matrix is unknown case by comparing the simulated results of one example.     

Mean estimation in the presence of change points

In this study we address the problem of the mean estimation of the IBEX-35 index stock quotes in the presence of change points. We rely on nonparametric regression methods for detecting and estimating changes points, and for estimating the discontinuous regression function. Model-assisted and model-based estimators and their jump-preserving counterparts are used for mean estimation and an empirical comparison between the methods is performed.     

Shrinkage estimator in normal mean vector estimation based on conditional maximum likelihood estimators

Estimation of normal mean vector has broad applications such as small area estimation, estimation of nonparametric functions and estimation of wavelet coefficients. In this paper, we propose a new shrinkage estimator based on conditional maximum likelihood estimator incorporating with Stein’s risk unbiased estimator (SURE) when data have the normality. We present some theoretical work and provide numerical studies to compare with some existing methods.     

Estimation of semi-varying coefficient model with surrogate data and validation sampling

In this paper, we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error. With the help of validation sampling, we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate. Data-driven bandwidth selection methods are also discussed. Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.     

无穷方差厚尾过程中非参数函数的小波估计

研究无穷方差厚尾过程中含有变点的非参数函数的估计问题。通过小波方法给出变点位置的估计值并得到其收敛速度。在已知变点估计值的基础上,将截尾方法与小波压缩方法相结合得到非参数函数的估计值。模拟研究结果说明对于无穷方差厚尾过程中的函数估计问题小波方法是有效的。     

基于非参数估计方法的沪铜期货价格研究

非参数估计方法是现代统计学的一个新发展方向,在各领域有重要的应用价值.本文针对非参数模型的三种估计方法,将其应用于沪铜期价与LME现价的相关关系分析,得到模型的拟合值和拟合曲线.最后,与最小二乘法的结果进行比较分析,证实了非参数估计在不同历史时期有预测精度高的优点.     

Oracle inequalities for the stochastic differential equations

This paper is a survey of recent results on the adaptive robust non parametric methods for the continuous time regression model with the semi-martingale noises with jumps. The noises are modeled by the Lévy processes, the Ornstein–Uhlenbeck processes and semi-Markov processes. We represent the general model selection method and the sharp oracle inequalities methods which provide the robust efficient estimation in the adaptive setting. Moreover, we present the recent results on the improved model selection methods for the nonparametric estimation problems.     

Sequential Monte Carlo Methods for Option Pricing

In this article, we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used successfully for a wide class of applications in engineering, statistics, physics, and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to-date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation.     

期权价格函数的局部多项式估计

本文直接从期权交易价格出发,利用非参数回归方法估计期权定价函数,首先给出期权价络函数的局部多项式估计,然后 Ｂｌａｃｋ－Ｓｃｈｏｌｅｓ公式讨论窗宽的确定,再给出期权价格函数的两步估计方法,最后对芝加哥商业交易所的英镑期货权作实际计算。     

纵向数据广义部分线性模型的惩罚GMM估计

对纵向数据的部分线性模型,通常的做法是用样条方法或者核方法逼近非参数部分,然后再用广义估计方程的估计方法去估计参数部分.本文使用P-样条拟合非参数函数,对不同的矩条件用不同的广义矩方法对模型的参数和非参数进行估计,并且给出了估计量的大样本性质;并用计算机模拟和实例证明了当模型中存在不同的矩条件时,采用不同的惩罚广义矩方法可以显著地提高估计精度.     

我国通货膨胀的非参数回归模型

本文首先讨论非参数回归模型的局部核权最小二乘估计 ,然后建立我国通货膨胀非参数回归模型 ,最后研究了反映出口与通货膨胀关系的弹性系数     

A two-stage approach to semilinear in-slide models

The semilinear in-slide models (SLIMs) have been shown to be effective methods for normalizing microarray data [J. Fan, P. Tam, G. Vande Woude, Y. Ren, Normalization and analysis of cDNA micro-arrays using within-array replications applied to neuroblastoma cell response to a cytokine, Proceedings of the National Academy of Science (2004) 1135-1140]. Using a backfitting method, [J. Fan, H. Peng, T. Huang, Semilinear high-dimensional model for normalization of microarray data: a theoretical analysis and partial consistency, Journal of American Statistical Association, 471, (2005) 781-798] proposed a profile least squares (PLS) estimation for the parametric and nonparametric components. The general asymptotic properties for their estimator is not developed. In this paper, we consider a new approach, two-stage estimation, which enables us to establish the asymptotic normalities for both of the parametric and nonparametric component estimators. We further propose a plug-in bandwidth selector using the asymptotic normality of the nonparametric component estimator. The proposed method allow for the modeling of the aggregated SLIMs case where we can explicitly show that taking the aggregated information into account can improve both of the parametric and nonparametric component estimator by the proposed two-stage approach. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedures.     

Adaptive local linear quantile regression

In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation (MSE) and mean absolute estimation (MAE) criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.     

Empirical likelihood for balanced ranked-set sampled data

Ranked-set sampling (RSS) often provides more efficient inference than simple random sampling (SRS). In this article, we propose a systematic nonparametric technique, RSS-EL, for hypothesis testing and interval estimation with balanced RSS data using empirical likelihood (EL). We detail the approach for interval estimation and hypothesis testing in one-sample and two-sample problems and general estimating equations. In all three cases, RSS is shown to provide more efficient inference than SRS of the same size. Moreover, the RSS-EL method does not require any easily violated assumptions needed by existing rank-based nonparametric methods for RSS data, such as perfect ranking, identical ranking scheme in two groups, and location shift between two population distributions. The merit of the RSS-EL method is also demonstrated through simulation studies. This work was supported by National Natural Science Foundation of China (Grant No. 10871037)