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Three Non-Gaussian Models of Dependence in Returns 收益依赖的三种非高斯模型
Pub Date : 2015-06-19 DOI: 10.2139/ssrn.2635629
D. Madan
Three particular models of dependence in asset returns with non-Gaussian marginals are investigated on daily return data for sector exchange traded funds. The first model is a full rank Gaussian copula (FGC). The second models returns as a linear mixture of independent Levy processes (LML). The third correlates Gaussian components in a variance gamma representation (VGC). On a number of occasions all three models are comparable. More generally, in some by sectors, we get a superior performance from the LML model followed by VGC and FGC as measured by the proportion of portfolios with higher p-values. There are occasions when the VGC and FGC dominate. The concept of local correlation is introduced to help discriminate between the models and it is observed that the LML models display higher levels of local correlation especially in the tails when compared with either the VGC or FGC models.
本文以行业交易所交易基金的日收益数据为研究对象,研究了具有非高斯边际的资产收益相关性的三种特殊模型。第一个模型是一个全秩高斯copula (FGC)。第二个模型返回为独立Levy过程(LML)的线性混合。第三种方法将方差伽马表示(VGC)中的高斯分量关联起来。在许多情况下,这三种型号都具有可比性。更一般地说,在某些行业中,我们从LML模型中获得了更好的表现,其次是VGC和FGC,这是通过具有较高p值的投资组合的比例来衡量的。有时VGC和FGC占主导地位。引入了局部相关的概念来帮助区分模型,并且可以观察到,与VGC或FGC模型相比,LML模型显示出更高水平的局部相关,特别是在尾部。
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引用次数: 0
Better Investing Through Factors, Regimes and Sensitivity Analysis 通过因素、制度和敏感性分析提高投资效率
Pub Date : 2015-01-25 DOI: 10.2139/ssrn.2557236
Cristian Homescu
Recent periods of market turbulence and stress have created considerable interest in credible alternatives to traditional asset allocation methodologies. It would be preferred if portfolios can be decomposed into components that can be directly connected to independent risks and individually rewarded by the market for their level of risk. This can be achieved through factor-based investing, which relies on the observation that most return and risk characteristics for all asset classes can be well explained by particular building blocks, or factors.We describe main features of factors, factor investing and factor models, with emphasis placed on practical topics such as selection of significant factors associated to specific asset classes, differentiating between factors, anomalies or stylized facts, and preference for composite portfolios based on combining factors. We have also analyzed implementation details and the factor risk parity strategy.Then we consider improvements to factor-based investing through regime switching and sensitivity analysis. We present theoretical and practical frameworks for Markov switching models and for sensitivity analysis, and rely on representative examples to illustrate the benefits of efficiently incorporating regimes and sensitivity analysis into portfolio management.The final section describes features of good testing procedures for portfolio behavior and performance, in contrasts with possible testing pitfalls.
最近几段时间的市场动荡和压力,引发了人们对传统资产配置方法的可靠替代方案的极大兴趣。如果投资组合能够分解成与独立风险直接相关的组成部分,并根据各自的风险水平得到市场的单独奖励,那将是更好的选择。这可以通过基于因素的投资来实现,它依赖于这样一种观察,即所有资产类别的大多数回报和风险特征都可以用特定的构建块或因素来很好地解释。我们描述了因子、因子投资和因子模型的主要特征,重点放在实际主题上,如选择与特定资产类别相关的重要因素,区分因素、异常或程式化事实,以及基于组合因素的组合投资组合偏好。我们还分析了实施细节和因素风险平价策略。然后,我们考虑通过状态转换和敏感性分析来改进因子投资。我们提出了马尔可夫转换模型和敏感性分析的理论和实践框架,并依靠代表性的例子来说明有效地将制度和敏感性分析纳入投资组合管理的好处。最后一部分描述了投资组合行为和性能的良好测试过程的特征,与可能的测试缺陷进行对比。
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引用次数: 6
Correlation, Where are You? Where are We? Update on Correlation Modeling 相关性,你在哪里?我们在哪里?相关建模的最新进展
Pub Date : 2014-09-11 DOI: 10.2139/ssrn.2494939
Christian Kamtchueng
During the first decades following Black and Scholes, the quantitative finance have been focus mainly on the modeling of the volatility. Indeed, the expansion of derivatives product brought some liquidity regarding this parameter. The implied volatility is the reflect of market convention for the vanilla premium but are also an extension of the industry focus. If the volatility modelling is difficult, the correlation modelling stage at another level. In fact, many market participant portfolios were attached to correlation risk - market participants such as insurance companies and pension funds - therefore, banks innovated solutions which imply transfer of the risk. A huge range of products such as Dispersion, Correlation Swap, Basket Option, Best Of and Worst Of have been introduced and sold with more or less popularity. Banks were willing to take the risk but they needed more elaborate model in order to capture the correlation risk. If the business pressure was to trade and deal with the residual risk with conventional correlation framework (deterministic term structure), after the default of Lehman Brother, the Trading Desk had to transfer the pressure and challenge quants in order to have the ability to hedge their correlation exposure. In this paper, we enumerate industry innovations on correlation modeling and discuss some improvements and market understanding of it.
在布莱克和斯科尔斯之后的最初几十年里,量化金融主要集中在波动性的建模上。事实上,衍生产品的扩张为这一参数带来了一定的流动性。隐含波动率反映了市场对香草溢价的惯例,但也是行业焦点的延伸。如果波动性建模是困难的,相关性建模阶段在另一个层面。事实上,许多市场参与者的投资组合都与相关风险有关——保险公司和养老基金等市场参与者——因此,银行创新了意味着风险转移的解决方案。大量的产品,如分散,相关互换,篮子期权,最好的和最差的已经推出和销售或多或少受欢迎。银行愿意承担风险,但他们需要更复杂的模型来捕捉相关风险。如果业务压力是使用传统的相关框架(确定性期限结构)进行交易和处理剩余风险,那么在雷曼兄弟违约后,交易部门必须转移压力和挑战量化分析师,以便有能力对冲其相关敞口。本文列举了相关建模的行业创新,并讨论了相关建模的改进和市场理解。
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引用次数: 0
Model01: Quantifying the Risk of Incremental Model Changes 模型01:量化增量模型变更的风险
Pub Date : 2014-09-05 DOI: 10.2139/ssrn.2492256
D. Abasto, Mark P. Kust
DV01, the dollar value impact of a 1 basis point change in a yield curve is one of the most basic and widely used measures of market risk. Similar quantities and sensitivities have been defined for other parameters or “risk drivers” for a given, fixed model. In this present work we provide a meaningful and intuitive notion of Model01, which attempts to capture the analogue of a “1 basis point” bump in the space of models, beyond simple parametric changes. Importantly, our technique successfully calibrates each of these bumped models to the same set of liquid reference contracts. This turns out to be fundamental for a proper assessment of Model01 among exotic portfolios, and allows a meaningful comparison of the Model01 dollar value against the total reference price of a portfolio. Using the same procedure, it is possible to compute Model01 for single trades or portfolios of multiple trades, across different asset types and underliers, due to the flexibility of Weighted Monte Carlo techniques, on which it relies. The literature on quantification of model risk is limited. We will highlight the main features of R. Cont on model uncertainty and P. Glasserman and X. Xu on model risk, and compare Model01 against these approaches. The contributions from the present effort are manifold. We put forward the Hellinger distance as a more intuitive and genuine metric in the space of probability distributions, in contrast with relative entropy, which is more commonly used in the financial literature. We highlight connections between Model01 and an active area of research called information-geometry. This field applies the methods of differential geometry to the problem of statistical inference, and in particular, the problem of defining intuitive notions of distances across probability distributions. The problem at hand is strongly related, with a meaningful quantification of model uncertainty calling for a normalized measure of distances in the space of models. A fruitful connection and further explorations of these ideas should come then as no surprise. We motivate an interpretation of relative entropy as a distance squared. We employ this to analyze P. Glasserman and X. Xu techniques and cast them in rescaled units, revealing a linear dependence of their risk profiles which can be explained and proved. To the authors' best knowledge, these contributions represent novel undertakings in the financial literature, with the Hellinger distance, the interpretation of relative entropy and the introduction of information-geometry techniques being put forward in the context of model sensitivity for the first time in this present work. We apply the techniques of information geometry to shed light into relative entropy and the Hellinger distance, and reveal a natural Riemannian geometric structure in the parameter space of the alternative, bumped models used to compute Model01. The application of these concepts further enriches the interpretation of our results. Armed
DV01,即收益率曲线变化1个基点对美元价值的影响,是最基本、最广泛使用的市场风险指标之一。对于给定的固定模型,已经为其他参数或“风险驱动因素”定义了类似的数量和灵敏度。在目前的工作中,我们提供了一个有意义和直观的Model01概念,它试图捕捉模型空间中“1个基点”的碰撞的模拟,而不仅仅是简单的参数变化。重要的是,我们的技术成功地将这些碰撞模型校准为同一组液体参考合同。事实证明,这是在外来投资组合中对模型01进行适当评估的基础,并且允许对模型01的美元价值与投资组合的总参考价格进行有意义的比较。使用相同的过程,由于加权蒙特卡罗技术的灵活性,可以跨不同的资产类型和承保人计算单个交易或多个交易组合的Model01。关于模型风险量化的文献有限。我们将突出R. Cont关于模型不确定性和P. Glasserman和X. Xu关于模型风险的主要特征,并将Model01与这些方法进行比较。目前的努力的贡献是多方面的。与金融文献中更常用的相对熵相比,我们提出海灵格距离是概率分布空间中更直观、更真实的度量。我们强调了Model01与一个被称为信息几何的活跃研究领域之间的联系。该领域将微分几何的方法应用于统计推断问题,特别是定义跨概率分布距离的直观概念的问题。手头的问题与模型不确定性的有意义的量化密切相关,需要对模型空间中的距离进行标准化测量。因此,对这些思想的卓有成效的联系和进一步的探索应该不足为奇。我们将相对熵解释为距离的平方。我们利用这一点来分析P. Glasserman和X. Xu技术,并将它们投射到重新缩放的单位中,揭示了它们的风险概况的线性依赖关系,这可以解释和证明。据作者所知,这些贡献代表了金融文献中的新事业,在目前的工作中,海灵格距离、相对熵的解释和信息几何技术的引入首次在模型敏感性的背景下提出。我们运用信息几何技术揭示了相对熵和海灵格距离,并揭示了用于计算Model01的替代碰撞模型的参数空间中的自然黎曼几何结构。这些概念的应用进一步丰富了我们对结果的解释。有了这些技术,我们证明了Model01本质上依赖于一组用于模型校准的液体仪器和一组更奇特的产品之间的有效边际协方差。随着该投资组合的“异域性”或非流动性水平的增加,模型01也会增加。Model01代表了一个灵活的工具,可能适用于各种各样的金融工具,以统一的方式提供了对投资组合模型敏感性的一瞥。
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引用次数: 3
Model Uncertainty in Panel Vector Autoregressive Models 面板向量自回归模型中的模型不确定性
Pub Date : 2014-08-01 DOI: 10.2139/ssrn.2487540
G. Koop, Dimitris Korobilis
We develop methods for Bayesian model averaging (BMA) or selection (BMS) in Panel Vector Autoregressions (PVARs). Our approach allows us to select between or average over all possible combinations of restricted PVARs where the restrictions involve interdependencies between and heterogeneities across cross-sectional units. The resulting BMA framework can find a parsimonious PVAR specification, thus dealing with overparameterization concerns. We use these methods in an application involving the euro area sovereign debt crisis and show that our methods perform better than alternatives. Our findings contradict a simple view of the sovereign debt crisis which divides the euro zone into groups of core and peripheral countries and worries about financial contagion within the latter group.
我们开发了面板向量自回归(PVARs)中的贝叶斯模型平均(BMA)或选择(BMS)方法。我们的方法允许我们在限制性pvar的所有可能组合之间进行选择或平均,其中限制涉及到横断面单元之间的相互依赖性和异质性。由此产生的BMA框架可以找到一个简洁的PVAR规范,从而处理过度参数化问题。我们在一个涉及欧元区主权债务危机的应用中使用了这些方法,并表明我们的方法比其他方法表现得更好。我们的发现反驳了对主权债务危机的简单看法,即将欧元区划分为核心国家和外围国家,并担心后者内部的金融传染。
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引用次数: 77
Higher Order Realized Power Variations of Semi-Martingales with Applications 半鞅的高阶可实现幂变及其应用
Pub Date : 2014-05-19 DOI: 10.2139/ssrn.2438711
Yuta Koike, Zhi Liu
The realized power variations with even order of a discretely observed semi-martingale have been widely studied in literature, due to some important applications in finance, for example, estimating the integrated volatility and integrated quarticity. However, few works have paid attention to the realized power variations whose power indices are odd. In this paper, we derive some limit theorems for realized variations with odd functions of an Ito semi-martingale on the fixed time interval [0,T], observed discretely at a high frequency. In the continuous case, unlike the realized power variations of even order, for example the quadratic variation, they converge only in distribution (stably) after multiplied by some appropriate factors, which are related to the length of the sampling interval, and the limiting processes consist of centered Wiener integrals and Riemann integrals that play a role as asymptotic biases. The limit theorems for the general case containing jumps have also been derived. An important application of the result is to measure the realized skewness with high frequency data. Simulation studies for various models have been investigated. Finally, we provide some real applications.
由于在金融领域的一些重要应用,如估计综合波动率和综合质量,离散观测半鞅的已实现幂次偶阶变化已经得到了广泛的研究。然而,很少有研究关注已实现的功率变化,其功率指标是奇数的。本文给出了在固定时间区间[0,T]上离散观测到的Ito半鞅与奇函数的已实现变分的几个极限定理。在连续情况下,与偶阶的幂次变化(如二次变化)不同,它们只有在乘上一些与采样间隔长度有关的适当因子后才会在分布上(稳定地)收敛,并且极限过程由中心Wiener积分和Riemann积分组成,它们起渐近偏置的作用。还推导了一般情况下包含跳跃的极限定理。该结果的一个重要应用是测量高频数据的实现偏度。对各种模型进行了仿真研究。最后,我们提供了一些实际应用。
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引用次数: 0
Uniform Inference in Nonlinear Models with Mixed Identification Strength 混合识别强度非线性模型的一致推理
Pub Date : 2014-05-08 DOI: 10.2139/ssrn.2435179
Xu Cheng
The paper studies inference in nonlinear models where identification loss presents in multiple parts of the parameter space. For uniform inference, we develop a local limit theory that models mixed identification strength. Building on this non-standard asymptotic approximation, we suggest robust tests and confidence intervals in the presence of non-identified and weakly identified nuisance parameters. In particular, this covers applications where some nuisance parameters are non-identified under the null (Davies (1977, 1987)) and some nuisance parameters are subject to a full range of identification strength. The asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence. A sequential argument is used to peel the criterion function based on identification strength of the parameters. The robust test is uniformly valid and non-conservative.
本文研究了非线性模型中辨识损失分布在多个参数空间的推理问题。为了统一推理,我们建立了混合识别强度模型的局部极限理论。在这个非标准渐近近似的基础上,我们建议在存在未识别和弱识别的干扰参数时进行鲁棒检验和置信区间。特别是,这涵盖了在null (Davies(1977,1987))下未识别某些妨害参数的应用,以及一些妨害参数受制于全范围识别强度的应用。渐近结果包括依赖于局部化参数的不一致估计量和具有不同收敛速率的一致估计量。根据参数的识别强度,使用顺序参数剥离准则函数。稳健检验是一致有效和非保守的。
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引用次数: 11
A Likelihood Ratio and Markov Chain Based Method to Evaluate Density Forecasting 基于似然比和马尔可夫链的密度预测评估方法
Pub Date : 2014-03-25 DOI: 10.2139/ssrn.2416269
Yushu Li, Jonas Andersson
In this paper, we propose a likelihood ratio and Markov chain based method to evaluate density forecasting. This method can jointly evaluate the unconditional forecasted distribution and dependence of the outcomes. This method is an extension of the widely applied evaluation method for interval forecasting proposed by Christoffersen (1998). It is also a more refined approach than the pure contingency table based density forecasting method in Wallis (2003). We show that our method has very high power against incorrect forecasting distributions and dependence. Moreover, the straightforwardness and ease of application of this joint test provide a high potentiality for further applications in both financial and economical areas.
本文提出了一种基于似然比和马尔可夫链的密度预测方法。该方法可以综合评价结果的无条件预测分布和相关性。该方法是对Christoffersen(1998)提出的广泛应用的区间预测评价方法的扩展。它也是比Wallis(2003)中基于列联表的纯密度预测方法更精细的方法。我们证明了我们的方法对不正确的预测分布和依赖有很高的能力。此外,该联合测试的直接性和易用性为进一步在金融和经济领域的应用提供了很大的潜力。
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引用次数: 2
A Method to Find Diverse and Manageable Sets of Plausible Yet Severe Financial Scenarios 一种方法,以找到多样化和可管理的集似是而非严重的金融情景
Pub Date : 2014-01-14 DOI: 10.2139/ssrn.2379083
Craig Friedman, Yangyong Zhang
We introduce a new practical data-intensive method to generate/discover consistent finite representative collections of plausible yet severe macroprudential, microprudential, book-specific, and individual obligor/instrument scenarios. These scenarios are conditioned on current information (including current macroeconomic, index, industry and instrument/obligor-specific information), and can be conditioned on partial future scenario specifications as well (to accommodate regulatory stress testing requirements, for example, the CCAR requirements for banks, the projections of economists, or senior management). Our method is scalable, is designed to work with limited training data, can incorporate the fat-tailed and mutually dependent behavior that is characteristic of many financial quantities, and can reflect model misspecification risk.
我们引入了一种新的实用的数据密集型方法来生成/发现一致的有限代表性集合,这些集合是可信的但严格的宏观审慎、微观审慎、特定于书籍的和个人债务人/工具的场景。这些情景以当前信息(包括当前宏观经济、指数、行业和工具/债务人特定信息)为条件,也可以以部分未来情景规范为条件(以适应监管压力测试要求,例如银行的CCAR要求、经济学家或高级管理层的预测)。我们的方法是可扩展的,设计用于有限的训练数据,可以结合许多金融数量特征的肥尾和相互依赖的行为,并且可以反映模型错误规范的风险。
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引用次数: 0
Are European Sovereign Bonds Fairly Priced? The Role of Modeling Uncertainty 欧洲主权债券定价合理吗?建模不确定性的作用
Pub Date : 2013-11-06 DOI: 10.2139/ssrn.2350766
Leo J. de Haan, J. Hessel, Jan Willem van den End
This paper examines the extent to which large swings of sovereign yields in euro area countries during the sovereign debt crisis can be attributed to fundamentals. We focus on the inherent uncertainty in bond yield models, which is often overlooked in the literature. We show that the outcomes are strongly affected by modeling choices with regard to i) the confidence bands for the model prediction, ii) the assumption whether the model coefficients are similar across countries or not, iii) the sample selection, iv) the inclusion of financial variables and v) the choice of time-varying coefficients. These choices affect the explanatory power of macro fundamentals and the extent of mispricing. We find substantial misalignment compared to fundamentals for Greek yields, in most specifications also for Portugal and Ireland, but for the other EMU countries, including Spain and Italy, the evidence is less clear cut. This calls for modesty in interpreting bond yield models and for cautiousness when using them in policymaking.
本文考察了主权债务危机期间欧元区国家主权债券收益率的大幅波动在多大程度上可归因于基本面因素。我们关注的是债券收益率模型的内在不确定性,这在文献中经常被忽视。我们表明,在以下方面,建模选择对结果有很大影响:1)模型预测的置信区间,2)模型系数在各国之间是否相似的假设,3)样本选择,4)金融变量的包含,5)时变系数的选择。这些选择影响宏观基本面的解释力和错误定价的程度。我们发现,与希腊国债收益率的基本面相比,在大多数指标中,葡萄牙和爱尔兰也存在严重偏差,但对包括西班牙和意大利在内的其他欧洲货币联盟国家来说,证据就不那么明显了。这就要求我们在解释债券收益率模型时要谨慎,在制定政策时要谨慎。
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引用次数: 49
期刊
ERN: Other Econometrics: Econometric Model Construction
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