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Calibrating with a smile: A Mellin transform approach to volatility surface calibration 微笑校准:一种基于Mellin变换的挥发性面校准方法
IF 2.5 Q2 ECONOMICS Pub Date : 2025-10-01 DOI: 10.1016/j.ecosta.2022.05.004
M. Rodrigo , A. Lo
The implied volatility in the Black-Scholes framework is not a constant but a function of both the strike price (“smile/skew”) and the time to expiry. A popular approach to recovering the volatility surface is through the use of deterministic volatility function models via Dupire’s equation. A new method for volatility surface calibration based on the Mellin transform is proposed. An explicit formula for the volatility surface is obtained in terms of the Mellin transform of the call option price with respect to the strike price, and a numerical algorithm is provided. Results of numerical simulations are presented and the stability of the method is numerically verified. The proposed Mellin transform approach provides a simpler and more direct fitting of generalised forms of the volatility surface given previously in the literature.
布莱克-斯科尔斯框架中的隐含波动率不是一个常数,而是执行价格(“微笑/倾斜”)和到期时间的函数。一种流行的恢复波动面的方法是通过Dupire方程使用确定性波动函数模型。提出了一种基于Mellin变换的挥发性曲面标定方法。利用看涨期权价格相对于执行价格的梅林变换,给出了波动面的显式表达式,并给出了数值算法。给出了数值模拟结果,并对该方法的稳定性进行了数值验证。提出的Mellin变换方法提供了先前文献中给出的波动面广义形式的更简单和更直接的拟合。
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引用次数: 0
GMM Model Averaging Using Higher Order Approximations 使用高阶近似的GMM模型平均
IF 2.5 Q2 ECONOMICS Pub Date : 2025-10-01 DOI: 10.1016/j.ecosta.2022.09.004
Luis F. Martins , Vasco J. Gabriel
Moment conditions model averaging (MA) estimators in the GMM framework are considered. Under finite sample considerations, MA estimators with optimal weights are proposed, in the sense that weights minimize the corresponding higher-order asymptotic mean squared error (AMSE). It is shown that the higher-order AMSE objective function has a closed-form expression, which makes this procedure applicable in practice. In addition, and as an alternative, different averaging schemes based on moment selection criteria are considered, in which weights for averaging across GMM estimates can be obtained by direct smoothing or by numerical minimization of a specific criterion. Asymptotic properties assuming correctly specified models are derived and the performance of the proposed averaging approaches is contrasted with existing model selection alternatives i) analytically, for a simple IV example, and ii) by means of Monte Carlo experiments in a nonlinear setting, showing that MA compares favourably in many relevant setups. The usefulness of MA methods is illustrated by studying the effect of institutions on economic performance.
考虑了GMM框架下的矩条件模型平均估计。在有限样本的考虑下,提出了具有最优权值的MA估计量,即权值使相应的高阶渐近均方误差(AMSE)最小化。结果表明,高阶AMSE目标函数具有一个封闭的表达式,使该方法在实际应用中具有一定的适用性。此外,作为一种选择,考虑了基于矩选择准则的不同平均方案,其中通过直接平滑或通过特定准则的数值最小化来获得跨GMM估计的平均权值。在正确指定模型的前提下,推导了渐近性质,并将所提出的平均方法的性能与现有的模型选择方案进行了对比,i)分析,对于一个简单的IV示例,ii)通过非线性设置中的蒙特卡罗实验,表明MA在许多相关设置中比较有利。通过研究制度对经济绩效的影响,可以说明MA方法的有效性。
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引用次数: 0
Nonparametric estimation of copulas and copula densities by orthogonal projections 用正交投影估计联结体和联结体密度的非参数
IF 2.5 Q2 ECONOMICS Pub Date : 2025-10-01 DOI: 10.1016/j.ecosta.2023.04.002
Yves I. Ngounou Bakam , Denys Pommeret
A nonparametric copula density estimator based on Legendre orthogonal polynomials is proposed. A nonparametric copula estimator is then deduced by integration. Their asymptotic properties are reviewed. Both estimators are based on a sequence of moments that characterize the copulas and that we shall call the copula coefficients. A data-driven method is proposed to select the number of copula coefficients to use. An intensive simulation study shows the good performance of both copulas and copula densities estimators compared to a large panel of competitors. Two real datasets illustrate this approach.
提出了一种基于Legendre正交多项式的非参数联结密度估计。然后通过积分推导出非参数共轭估计量。讨论了它们的渐近性质。这两个估计量都是基于一串矩,这些矩描述了联结的特征,我们称之为联结系数。提出了一种数据驱动的方法来选择要使用的copula系数的数量。密集的模拟研究表明,与大型竞争对手相比,copula和copula密度估计器都具有良好的性能。两个真实的数据集说明了这种方法。
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引用次数: 0
Nearest neighbor matching: M-out-of-N bootstrapping without bias correction vs. the naive bootstrap 最近邻匹配:无偏差校正的m -of- n自举与朴素自举
IF 2.5 Q2 ECONOMICS Pub Date : 2025-10-01 DOI: 10.1016/j.ecosta.2023.04.005
Christopher Walsh , Carsten Jentsch
It is well known that the limiting variance of nearest neighbor matching estimators cannot be consistently estimated by a naive Efron-type bootstrap as the conditional variance of the bootstrap estimator does not generally converge to the correct limit in expectation. In essence this is caused by the fact that the bootstrap sample contains ties with positive probability even when the sample size becomes large. This negative result was originally derived in a simple setting by Abadie and Imbens (ECONOMETRICA, pp. 235–267, 76(6), 2008). A proof of concept for a direct M-out-of-N bootstrap on the data is provided in this setting. It is proven that in this setting the conditional variance of a direct M-out-of-N-type bootstrap estimator without bias-correction does converge to the correct limit in expectation. The key to the proof lies in the fact that asymptotically with probability one there are no ties in the bootstrap sample. The potential of the direct M-out-of-N-type bootstrap is investigated in simulations.
众所周知,最近邻匹配估计量的极限方差不能被朴素efron型自举一致估计,因为自举估计量的条件方差一般不会收敛到正确的期望极限。从本质上讲,这是由于即使样本量变大,bootstrap样本也包含正概率的联系。这个否定的结果最初是由Abadie和Imbens在一个简单的环境中得出的(ECONOMETRICA, pp. 235 - 267,76(6), 2008)。在此设置中,提供了对数据进行直接m -of- n自举的概念证明。证明了在这种情况下,无偏校正的直接m -of- n型自举估计量的条件方差收敛于期望的正确极限。证明的关键在于这样一个事实,即随着概率1的渐近,在自举样本中不存在联系。在仿真中研究了直接m -out- n型自举的潜力。
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引用次数: 0
The benefits of returns and options in the estimation of GARCH models. A Heston-Nandi GARCH insight GARCH模型估计中收益和期权的好处。Heston-Nandi GARCH的见解
IF 2.5 Q2 ECONOMICS Pub Date : 2025-10-01 DOI: 10.1016/j.ecosta.2022.12.001
Marcos Escobar-Anel , Lars Stentoft , Xize Ye
In a controlled, simulated setting, the questions of what the benefits are of including option prices in the estimation of GARCH models, the extent to which options can replace returns, and what the best type of options is for estimation, are addressed. The computational advantages of affine GARCH models for option pricing make these questions numerically tractable, therefore the experiments focus on the Heston-Nandi GARCH model. Three estimation methods, namely, returns-only estimation, options-only calibration and joint returns-options estimation-calibration are compared. The study reveals that, although the benefit is insignificant for the risk premium factor, adding options significantly reduces the standard errors of the GARCH dynamic parameters. This conclusion holds true under both linear and variance-dependent pricing kernels. The results suggest that, in a realistic setting, practitioners can use a large and recent sample of option prices to compensate for the lack of available return data. As a by-product, evidence also shows that out-of-the-money, short-maturity options are the best choice to improve the quality of the estimation.
在一个受控的、模拟的环境中,解决了在GARCH模型的估计中包括期权价格的好处是什么,期权可以取代收益的程度,以及用于估计的最佳期权类型是什么等问题。仿射GARCH模型在期权定价中的计算优势使得这些问题在数值上易于处理,因此实验集中在Heston-Nandi GARCH模型上。比较了纯收益估计、纯期权估计和联合收益-期权估计-校准三种估计方法。研究表明,虽然风险溢价因子的收益不显著,但增加期权显著降低了GARCH动态参数的标准误差。这个结论在线性和方差相关的定价核下都成立。结果表明,在现实环境中,从业者可以使用大量近期的期权价格样本来弥补可用收益数据的缺乏。作为副产品,证据还表明,现款外的短期期权是提高估计质量的最佳选择。
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引用次数: 0
Technical efficiency and inefficiency: Reliability of standard SFA models and a misspecification problem 技术效率和低效率:标准SFA模型的可靠性和错误规范问题
IF 2.5 Q2 ECONOMICS Pub Date : 2025-10-01 DOI: 10.1016/j.ecosta.2021.12.006
Subal C. Kumbhakar , A. Peresetsky , Y. Shchetynin , A. Zaytsev
It is formally proven that if inefficiency (u) is modelled through its variance, considered as a function of exogenous variables z, then the marginal effects of z on technical inefficiency (TI) and technical efficiency (TE) have opposite signs in the typical setup with a normally distributed random error and an exponentially or half-normally distributed u. This is true for both conditional and unconditional TI and TE. An example is provided to show that the signs of the marginal effects of z on TI and TE may coincide for some ranges of z. If the real data comes from a bimodal distribution of u, and a model is estimated with an exponential or half-normal distribution for u, the estimated efficiency and the marginal effect of z on TE could be wrong. Moreover, the rank correlations between the true and the estimated values of TE could be small and even negative for some subsamples of the data. This is a warning that in the case when the true (real life) distribution of the inefficiency is bimodal, commonly used standard SFA models could lead to wrong policy recommendations. The kernel density plot of the residuals is suggested as a diagnostic plot. The results are illustrated by simulations.
正式证明,如果效率低下(u)是通过其方差建模的,被认为是外生变量z的函数,那么z对技术效率低下(TI)和技术效率(TE)的边际效应在典型的正态分布随机误差和指数或半正态分布u的设置中具有相反的符号。这对于条件和无条件的TI和TE都是正确的。给出了一个例子,表明z对TI和TE的边际效应的符号可能在z的某些范围内重合。如果实际数据来自u的双峰分布,并且以u的指数或半正态分布估计模型,则估计的效率和z对TE的边际效应可能是错误的。此外,对于数据的某些子样本,TE的真实值和估计值之间的秩相关可能很小,甚至为负。这是一个警告,当低效率的真实(现实生活)分布是双峰的情况下,常用的标准SFA模型可能会导致错误的政策建议。残差的核密度图被建议作为诊断图。仿真结果说明了本文的研究结果。
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引用次数: 0
Variable Selection in Macroeconomic Forecasting with Many Predictors 多变量宏观经济预测中的变量选择
IF 2.5 Q2 ECONOMICS Pub Date : 2025-10-01 DOI: 10.1016/j.ecosta.2023.01.003
Zhenzhong Wang, Zhengyuan Zhu, Cindy Yu
In the data-rich environment, using many economic predictors to forecast a few key variables has become a new trend in econometrics. The commonly used approach is factor augment (FA) approach. This paper pursues another direction, variable selection (VS) approach, to handle high-dimensional predictors. VS is an active topic in statistics and computer science. However, it does not receive as much attention as FA in economics. This paper introduces several cutting-edge VS methods to economic forecasting, which includes: (1) classical greedy procedures; (2) l1 regularization; (3) false-discovery-rate control methods, (4) gradient descent with sparsification and (5) meta-heuristic algorithms. Comprehensive simulation studies are conducted to compare their variable selection accuracy and prediction performance under different scenarios. Among the reviewed methods, a meta-heuristic algorithm called sequential Monte Carlo algorithm performs the best. Surprisingly the classical forward selection is comparable to it and better than other more sophisticated algorithms. In addition, these VS methods are applied on economic forecasting and compared with the popular FA approach. It turns out for employment rate and CPI inflation, some VS methods can achieve considerable improvement over FA, and the selected predictors can be well explained by economic theories.
在数据丰富的环境下,利用多个经济预测因子对几个关键变量进行预测已成为计量经济学研究的新趋势。常用的方法是因子增强法(FA)。本文追求另一个方向,即变量选择(VS)方法来处理高维预测因子。VS是统计学和计算机科学中的一个活跃话题。然而,它并没有像经济学中的FA那样受到重视。本文介绍了几种前沿的VS经济预测方法,包括:(1)经典贪婪法;(2) l1正则化;(3)假发现率控制方法;(4)稀疏化梯度下降法;(5)元启发式算法。进行了全面的仿真研究,比较了它们在不同场景下的变量选择精度和预测性能。在回顾的方法中,一种称为顺序蒙特卡罗算法的元启发式算法表现最好。令人惊讶的是,经典的前向选择与它相当,并且优于其他更复杂的算法。此外,还将该方法应用于经济预测,并与流行的FA方法进行了比较。结果表明,对于就业率和CPI通胀,一些VS方法比FA方法有较大的改进,所选择的预测因子可以很好地用经济学理论解释。
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引用次数: 0
Approximation of BSDE with hidden forward equation and unknown volatility 隐含前向方程和未知波动率的BSDE逼近
IF 2.5 Q2 ECONOMICS Pub Date : 2025-10-01 DOI: 10.1016/j.ecosta.2023.01.002
Oleg V. Chernoyarov , Yury A. Kutoyants
The focus is on the approximation of the solution of BSDE in the case where the solution of forward equation is observed in the presence of small Gaussian noise. The volatility of the forward equation is considered to depend on some unknown parameter. This approximation is made in several steps. First a preliminary estimator of the unknown volatility is obtained, then using Kalman-Bucy filtration equations and Fisher-score device one-step MLE-process of this parameter is constructed. The solution of BSDE is approximated by means of the solution of PDE and the One-step MLE-process. The error of approximation is described in different metrics.
重点讨论了在存在小高斯噪声的情况下观察正演方程解的近似解。考虑前向方程的波动率依赖于某个未知参数。这种近似是通过几个步骤来实现的。首先得到未知波动率的初步估计量,然后利用Kalman-Bucy滤波方程和Fisher-score装置构造该参数的一步mle过程。利用PDE的解和一步mle过程逼近了BSDE的解。用不同的度量来描述近似误差。
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引用次数: 0
Joint Hypothesis Testing from Heterogeneous Samples under Cross-dependence 交叉依赖下异质性样本的联合假设检验
IF 2 Q2 ECONOMICS Pub Date : 2025-07-01 DOI: 10.1016/j.ecosta.2022.07.004
Uwe Hassler , Mehdi Hosseinkouchack
A testing principle is introduced that allows to combine evidence from N potentially correlated samples. It builds on a (weighted) sum of entities from the individual samples, which is fed into a self-normalizing variance ratio type statistic. Due to self-normalization the (autoco)variances within each sample as well as the cross-covariances between the samples melt into one scaling parameter that cancels from the ratios asymptotically. Tests constructed from this principle are hence robust with respect to cross-dependence without having to estimate any nuisance parameters. The weighting and the entities from the individual samples depend on the testing problem at hand. Two cases are discussed in detail. The first one are tests of restrictions on a parameter vector (e. g. testing restrictions on expected values), while the second one focusses on time series: panel integration tests (unit root as well as stationarity tests). The validity of the asymptotic theory in finite samples is established by means of simulation evidence.
介绍了一种测试原理,允许组合来自N个潜在相关样本的证据。它建立在来自单个样本的实体(加权)和的基础上,这些实体被馈送到一个自归一化方差比率类型的统计量中。由于自归一化,每个样本内的(自动)方差以及样本之间的交叉协方差融化成一个比例参数,该参数与比率渐近抵消。因此,根据这一原则构建的测试对于交叉依赖是鲁棒的,而不必估计任何讨厌的参数。权重和个体样本的实体取决于手头的测试问题。详细讨论了两个案例。第一个测试是对参数向量的限制的测试(例如对期望值的测试限制),而第二个测试侧重于时间序列:面板集成测试(单位根和平稳性测试)。通过仿真证明了该渐近理论在有限样本条件下的有效性。
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引用次数: 0
An Automatic Portmanteau Test For Nonlinear Dependence 非线性相关性的自动组合检验
IF 2 Q2 ECONOMICS Pub Date : 2025-07-01 DOI: 10.1016/j.ecosta.2022.12.003
Charisios Grivas
A data-driven version of a portmanteau test for detecting nonlinear types of statistical dependence is considered. An attractive feature of the proposed test is that it properly controls the type I error without being sensitive with respect to the number of autocorrelations used. In addition, the automatic test is found to have higher power in simulations when compared to the standard portmanteau test, for both raw data and residuals.
考虑了用于检测非线性统计依赖类型的组合测试的数据驱动版本。所提出的测试的一个吸引人的特点是,它适当地控制了I型误差,而对所使用的自相关的数量不敏感。此外,与标准组合测试相比,在模拟中发现自动测试在原始数据和残差方面都具有更高的功率。
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引用次数: 0
期刊
Econometrics and Statistics
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