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Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model 小心帽子!赫斯顿随机波动模型中的约束投资组合优化
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-11-06 DOI: 10.1080/14697688.2023.2271223
M. Escobar-Anel, M. Kschonnek, R. Zagst
AbstractWe consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston's stochastic volatility model. We apply existing duality methods to obtain a closed-form expression for the optimal portfolio allocation. In doing so, we observe that allocation constraints impact the optimal constrained portfolio allocation in a fundamentally different way in Heston's stochastic volatility model than in the Black Scholes model. In particular, the optimal constrained portfolio may be different from the naive ‘capped’ portfolio, which caps off the optimal unconstrained portfolio at the boundaries of the constraints. Despite this difference, we illustrate by way of a numerical analysis that in most realistic scenarios the capped portfolio leads to slim annual wealth equivalent losses compared to the optimal constrained portfolio. During a financial crisis, however, a capped solution might lead to compelling annual wealth equivalent losses.Keywords: Portfolio optimisationAllocation constraintsDynamic programmingHeston's stochastic volatility modelIncomplete marketsJEL Classifications: G11C61 Disclosure statementNo potential conflict of interest was reported by the author(s).Supplemental dataSupplemental data for this article can be accessed online at http://dx.doi.org/10.1080/14697688.2023.2271223.Notes1 Note that obtaining and formally verifying the optimality of a candidate portfolio process requires more than just a solution to the associated HJB PDE, as pointed out by Korn and Kraft (Citation2004).2 As any π∈Λ can only take finite values L[0,T]⊗Q-a.s., we do not need to distinguish between (−∞,β] and [−∞,β] or [α,∞) and [α,∞] for any −∞≤α,β≤∞.3 Technically, one can formulate this assumption less restrictively by expressing ‘No Blow-Up’ in terms of the time spent in each of the zones Z−, Z0 and Z+. However, as this would significantly complicate the presentation without adding major additional insights, it is omitted here.4 If ρ=0 all of these transition times will be infinite.5 Using a similar separation with respect to the zones Z−, Z0 and Z+ and equation (B6), it is also possible to determine a closed-form expression for A from lemma 2.1.6 Equation (Equation18(18) b1−bη(κρσ+η2)<κ22σ2,(18) ) corresponds to part (i) of Assumption 2.4. In the setting of Kraft (Citation2005), part (ii) of Assumption 2.4 is also implied by (Equation18(18) b1−bη(κρσ+η2)<κ22σ2,(18) ) and so does not have to be mentioned explicitly.7 Note that this is different from classic mean-variance optimisation, where the variance of the terminal portfolio wealth Vv0,π(T) is constrained.8 Q.ai (Citation2022) reported that the average length of an S&P500 bear market (defined as a period with drawdown in excess of 20%) was 289 days.9 Since we exclusively work with power utility functions in this paper, we may without loss of generality assume that the WEL is independent of wealth.10 If π is deterministic and Jπ i
摘要在赫斯顿随机波动模型中,考虑效用最大化投资者的投资组合优化问题。利用已有的对偶方法,得到了投资组合最优配置的封闭表达式。在此过程中,我们观察到,在赫斯顿的随机波动率模型中,配置约束影响最优约束投资组合配置的方式与在布莱克·斯科尔斯模型中完全不同。特别是,最优约束投资组合可能不同于朴素的“封顶”投资组合,后者在约束的边界处封顶了最优无约束投资组合。尽管存在这种差异,但我们通过数值分析的方式说明,在大多数现实情况下,与最优约束投资组合相比,上限投资组合导致的年度财富当量损失较小。然而,在金融危机期间,有上限的解决方案可能会导致令人信服的年度财富等值损失。关键词:投资组合优化配置约束动态规划heston随机波动模型不完全市场jel分类:G11C61披露声明作者未报告潜在利益冲突请注意,正如Korn和Kraft (Citation2004)所指出的那样,获得并正式验证候选投资组合过程的最优性不仅仅需要相关HJB PDE的解决方案由于任意π∈Λ只能取有限值L[0,T]⊗Q-a.s。我们不需要区分(−∞,β]和[−∞,β]或[α,∞)和(α,∞)对于任何−∞≤α,β≤∞。3从技术上讲,我们可以通过在Z−,Z0和Z+区域中花费的时间来表示“没有爆炸”,从而不那么严格地表述这一假设。但是,由于这将使演示变得非常复杂,而不会增加主要的额外见解,因此在此省略如果ρ=0所有这些跃迁时间都是无穷大对Z−,Z0和Z+区域和方程(B6)使用类似的分离,也可以从引理2.1.6中确定a的封闭形式表达式(方程(Equation18(18) b1−bη(κρσ+η2)<κ22σ2,(18))对应于假设2.4的第(i)部分。在Kraft (Citation2005)的设定中,假设2.4的(ii)部分也隐含在(Equation18(18) b1−bη(κρσ+η2)<κ22σ2,(18))中,因此不必明确提及请注意,这与经典的均值-方差优化不同,其中终端投资组合财富v0,π(T)的方差是受约束的Q.ai (Citation2022)报告称,标准普尔500指数熊市(定义为跌幅超过20%的时期)的平均长度为289天由于我们在本文中专门研究功率效用函数,我们可以在不损失一般性的情况下假设WEL独立于财富如果π是确定性的,并且Jπ是Feynman-Kac PDE的唯一解,则可以使用指数仿射分析来描述Jπ在ode系统解方面的特征。如果给出了ODE的解,则WEL的Lπ(0,z0)是已知的封闭形式。我们在补充材料的引理B.6和推论B.7中提供了对这种方法的描述。在我们的研究中,我们用欧拉法近似了相应的ODE解要了解总体情况,请参考Escobar-Anel和Gschnaidtner (Citation2016)的表4。在这里,作者认为κ=3.5, σ=0.3, ρ= - 0.4的值是他们所回顾文献的“平均情况”。
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引用次数: 0
Islamic Banking and Finance, Second Edition Islamic Banking and Finance, Second Edition , by Zubair Hasan, Routledge (2023). Hardcover. ISBN 978-1-032-36064-5. E-book. ISBN 978-1-003-36697-3. 伊斯兰银行与金融,第二版伊斯兰银行与金融,第二版,祖拜尔·哈桑著,劳特利奇出版社(2023)。精装书。ISBN 978-1-032-36064-5。电子书。ISBN 978-1-003-36697-3。
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-11-03 DOI: 10.1080/14697688.2023.2270495
Muhammad Ash-Shiddiqy, None Mujtahid, None Khamim
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引用次数: 0
Dynamic core-satellite investing using higher order moments: an explicit solution 使用高阶矩的动态核心-卫星投资:一个显式解决方案
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-10-31 DOI: 10.1080/14697688.2023.2269987
Yanfeng Wang, Wanbo Lu, Kris Boudt
AbstractThe goal of core-satellite investing is to optimally balance the portfolio allocation between a core and satellite investment. This paper provides an explicit solution when the investor's optimality criterion is the third-order and fourth-order expansion of the expected utility function, respectively. Based on a numeric example, we document the sensitivity of the proposed weights to coskewness and cokurtosis components. Finally, we use ETFs to examine the portfolio performance of the core-satellite strategy with higher order moments. We document that integrating the higher order moment in core-satellite investing can improve the financial performance of a portfolio.Keywords: Higher order momentsExplicit solutionCore-satellite investingSensitivityJEL Classifications: G11C61 Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 For more convenient expression, we report the moments for the percentage log return in percentage point, but in the subsequent analysis, the moments of the log return are used.Additional informationFunding This work was partially supported by the Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University-Statistics) and the Collaborative Innovation Center of Statistical Data Engineering Technology & Application. National Natural Science Foundation of China [grant number 71771187, 72011530149, 72163029] and Fundamental Research Funds for the Central Universities in China [grant number JBK190602].
摘要核心-卫星投资的目标是使核心投资与卫星投资之间的投资组合配置达到最佳平衡。本文给出了当投资者的最优性准则分别是期望效用函数的三阶展开式和四阶展开式时的显式解。基于一个数值例子,我们记录了所提出的权重对余偏性和余峰度分量的敏感性。最后,我们用etf来检验具有高阶矩的核心-卫星策略的投资组合绩效。我们证明了在核心-卫星投资中整合高阶矩可以改善投资组合的财务绩效。关键词:高阶矩隐式解核心-卫星投资灵敏度jel分类:G11C61披露声明作者未报告潜在利益冲突。注1为了更方便地表达,我们以百分点为单位报告百分比对数回报的矩,但在随后的分析中,使用对数回报的矩。本工作得到浙江省重点建设高校特色优势学科(浙江工商大学-统计学)和统计数据工程技术与应用协同创新中心的部分支持。国家自然科学基金项目[批准号:71771187,72011530149,72163029]和中央高校基本科研业务费项目[批准号:JBK190602]。
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引用次数: 0
How does price (in)efficiency influence cryptocurrency portfolios performance? The role of multifractality 价格(in)效率如何影响加密货币投资组合的表现?多重分形的作用
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-10-24 DOI: 10.1080/14697688.2023.2266448
Eduardo Amorim Vilela de Salis, Leandro dos Santos Maciel
AbstractThis paper proposes a new investment strategy in the cryptocurrency market based on a two-step procedure. The first step is the computation of the asset's levels of efficiency in an universe of cryptocurrencies. Price returns efficiency degrees are measured by their corresponding levels of multifractality, obtained by the multifractal detrended fluctuation analysis method. The higher the multifractality, the higher the inefficiency in terms of the weak form of market efficiency. Cryptocurrencies are then ranked in terms of efficiency. The second step is the construction of portfolios under the Markowitz framework composed of the most/least efficient digital coins. Minimum variance, maximum Sharpe ratio, equally weighted and (in)efficient-based portfolios were considered. The former strategy is also proposed, where the weights are computed proportionally to the assets levels of (in)efficiency. The main findings are: cryptocurrency price returns are multifractal and their levels of (in)efficiency change over time; returns exhibit left-sided asymmetry, which implies that subsets of large fluctuations contribute substantially to the multifractal spectrum; in bull markets portfolios with the least efficiency assets provided a better risk–return relation; in periods of high volatility and high price depreciation (bear market) a better performance is associated with the portfolios composed by the more efficient cryptocurrencies.Keywords: Portfolio allocationCryptocurrencyMarket efficiencyMF-DFAMultifractalityJEL Classifications: G14G11 Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Markiel and Fama (Citation1970) and Titan (Citation2015) are surveys regarding the empirical analysis of the weak form of market efficiency.2 The Hurst exponent, referred to as the ‘index of dependence’ or ‘index of long-range dependence’, is used as a measure of long-term memory of time series. Originally developed in hydrology and commonly studied in fractal geometry, it relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases (Hurst Citation1951).3 Traditional nonlinear variance ratio tests or autocorrelation functions are not able to identify multifractal structures. Fractal properties are associated to time series that present heavy tails and long memory. As these features are commonly observed in financial asset price returns (stylized facts), the use of MF-DFA appears as a suitable technique to evaluate random walk properties in such series, as stated by the econophysics literature (Arshad et al. Citation2016, Ali et al. Citation2018, Tiwari et al. Citation2019).4 The works of Mensi et al. (Citation2018), Sukpitak and Hengpunya (Citation2016), Dewandaru et al. (Citation2015), Tiwari et al. (Citation2019), Shahzad et al. (Citation2017), Zhu and Zhang (Citation2018) and Rizvi and Arshad (Citation2017) are examples of using MF-DFA to evaluate th
摘要本文提出了一种新的基于两步法的加密货币市场投资策略。第一步是计算资产在加密货币世界中的效率水平。利用多重分形去趋势波动分析方法得到的多重分形对应的多重分形水平来衡量价格收益效率程度。多重分形越高,市场效率的弱形式效率越低。然后根据效率对加密货币进行排名。第二步是在Markowitz框架下构建由效率最高/最低的数字货币组成的投资组合。最小方差,最大夏普比率,等加权和(in)效率为基础的投资组合被考虑。还提出了前一种策略,其中权重与(in)效率的资产水平成比例计算。主要发现是:加密货币的价格回报是多重分形的,它们的效率水平随着时间的推移而变化;回报表现出左侧不对称,这意味着大波动的子集对多重分形谱有很大贡献;在牛市中,效率最低的资产组合提供了更好的风险收益关系;在高波动性和高价格贬值(熊市)时期,更好的表现与由更有效的加密货币组成的投资组合有关。关键词:投资组合配置加密货币市场效率ymf - dfam多分性jel分类:G14G11披露声明作者未报告潜在利益冲突。注1 Markiel and Fama (Citation1970)和Titan (Citation2015)是关于市场效率弱形式实证分析的调查赫斯特指数,又称“依赖指数”或“长期依赖指数”,用来衡量时间序列的长期记忆。它最初是在水文学中发展起来的,通常在分形几何中进行研究,它涉及时间序列的自相关性,以及这些自相关性随着值对之间的滞后增加而降低的速率(Hurst Citation1951)传统的非线性方差比检验或自相关函数不能识别多重分形结构。分形特性与呈现重尾和长记忆的时间序列有关。由于这些特征通常在金融资产价格回报(程式化事实)中观察到,正如经济物理学文献(Arshad等人)所述,使用MF-DFA似乎是评估此类序列中的随机游走特性的合适技术。Citation2016, Ali等。引文2018,Tiwari等人。Citation2019) 4。Mensi等人(Citation2018)、Sukpitak和Hengpunya (Citation2016)、Dewandaru等人(Citation2015)、Tiwari等人(Citation2019)、Shahzad等人(Citation2017)、Zhu和Zhang (Citation2018)以及Rizvi和Arshad (Citation2017)的作品都是使用MF-DFA来评估金融市场(主要是股票市场)中市场效率弱形式的例子Ozkan (Citation2021)、Diniz-Maganini等人(Citation2021)、mif等人(Citation2020)、Naeem等人(Citation2021)、Naeem等人(Citation2021)、Mensi等人(Citation2020)、Choi (Citation2021)和Mensi等人(Citation2021)也发现了COVID-19大流行对不同市场效率水平影响的证据Rizvi和Arshad (Citation2014)建议,标度范围假设smin=10, smax=(T/4),其中T为序列的观测次数可以使用更复杂的协方差矩阵估计方法,如EWMA和多元garch家族模型。然而,在投资组合选择中测试不同的协方差方法超出了本工作的主要目标可以考虑再平衡方案,但是,确定再平衡的时间以及考虑交易成本是复杂的任务,由于篇幅限制,被认为是今后的工作数据收集于https://finance.yahoo.com/.10,本工作中所有实验均使用R软件进行赫斯特指数,H(q),从q=−4到q=4,由于篇幅限制,这里没有给出,但可根据要求提供需要强调的是,2021年与熊市有关,这种行为可能与相应加密货币效率水平的下降有关。然而,多重分形的时间动力学分析超出了本文的研究范围。本研究由巴西国家科学技术发展委员会(CNPq)资助,基金编号304456/2020-9;Ripple Impact Fund是硅谷社区基金会的捐赠基金,在Grant 2018-196450(5855)下,作为大学区块链研究计划(UBRI)的一部分。
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引用次数: 0
Smiles in delta 三角洲的微笑
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-10-03 DOI: 10.1080/14697688.2023.2258932
Arianna Mingone
AbstractFukasawa introduced in Fukasawa [The normalizing transformation of the implied volatility smile. Math. Finance, 2012, 22(4), 753–762] two necessary conditions for no butterfly arbitrage on a given implied volatility smile which require that the functions d1 and d2 of the Black–Scholes formula have to be decreasing. In this article, we characterize the set of smiles satisfying these conditions, using the parametrization of the smile in delta. We obtain a parametrization of the set of such smiles via one real number and three positive functions, which can be used by practitioners to calibrate a weak arbitrage-free smile. We also show that such smiles and their symmetric smiles can be transformed into smiles in the strike space by a bijection. Our result motivates the study of the challenging question of characterizing the subset of butterfly arbitrage-free smiles using the parametrization in delta.Keywords: Implied volatilityVolatility smileDeltaButterfly arbitrageJEL Classification: G13C60C63 AcknowledgmentsI sincerely thank Zeliade Systems and especially Claude Martini for giving the opportunity to work with them and daily broaden my knowledge. The results in this paper have been achieved thanks to the concrete need of client CCPs of a volatility calibration in the sigma space which can be converted in the strike space. I thank Stefano De Marco for the precise reading of the article, and for the improvements suggested. I thank Antoine Jacquier who pointed out crucial refinements, and Vladimir Lucic who shared his fundamental knowledge with enthusiasm.Disclosure statementNo potential conflict of interest was reported by the author(s).
【摘要】Fukasawa引入了隐含波动率smile的归一化变换。数学。金融,2012,22(4),753-762]在给定的隐含波动率smile上不存在蝴蝶套利的两个必要条件,要求Black-Scholes公式的函数d1和d2必须递减。在本文中,我们利用delta中的smile参数化来表征满足这些条件的smile集合。我们通过一个实数和三个正函数得到了这种微笑集合的参数化,从业者可以使用它来校准弱无套利微笑。我们还证明了这样的微笑和它们的对称微笑可以通过双射转换成走向空间中的微笑。我们的结果激发了利用delta参数化来表征蝴蝶无套利微笑子集这一具有挑战性的问题的研究。关键词:隐含波动率波动率微笑edeltabutterfly套利el分类:G13C60C63致谢我衷心感谢Zeliade Systems,特别是Claude Martini给我与他们合作的机会,并每天拓宽我的知识。由于客户ccp需要在西格玛空间中进行波动率校准,从而可以在走向空间中进行转换,因此本文的结果得以实现。我感谢Stefano De Marco对这篇文章的准确阅读,以及提出的改进建议。我要感谢Antoine Jacquier,他指出了关键的改进,Vladimir Lucic热情地分享了他的基础知识。披露声明作者未报告潜在的利益冲突。
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引用次数: 0
Quantum-inspired variational algorithms for partial differential equations: application to financial derivative pricing 偏微分方程的量子启发变分算法:在金融衍生品定价中的应用
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-09-29 DOI: 10.1080/14697688.2023.2259954
Tianchen Zhao, Chuhao Sun, Asaf Cohen, James Stokes, Shravan Veerapaneni
AbstractVariational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schrödinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.Keywords: Variational quantum algorithmsVariational quantum Monte CarloMulti-asset Black-Scholes PDE AcknowledgmentsThe Authors thank the anonymous AE and the referees for their suggestions, which helped to improve our paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 VQAs for mult-asset financial derivative pricing have been subsequently explored in Kubo et al. (Citation2022).2 See appendix 1 for a derivation. Similiar ODEs have been introduced in the neural Galerkin method (Bruna et al. Citation2022).3 This can be considered as a special case of the complex-valued case (Hibat-Allah et al. Citation2020, Sharir et al. Citation2020).Additional informationFundingAuthors gratefully acknowledge support from NSF under grants DMS-2038030 and DMS-2006305. This research was supported in part through computational resources and services provided by the Advanced Research Computing (ARC) at the University of Michigan.
摘要变分量子蒙特卡罗(VMC)与神经网络量子态相结合,为解决一类特定偏微分方程(PDEs)的维数问题提供了一种新的攻角;即与时间相关的实数和虚数Schrödinger方程。在本文中,我们给出了适用于任意时变偏微分方程的VMC的简单推广,展示了基于许多相关标的资产的多资产Black-Scholes偏微分方程的欧洲期权定价技术。关键词:变分量子算法变分量子蒙特卡罗多资产Black-Scholes PDE致谢感谢匿名AE和审稿人的建议,他们帮助我们改进了论文。披露声明作者未报告潜在的利益冲突。注1 Kubo等人随后对多资产金融衍生品定价的vqa进行了探讨(Citation2022)参见附录1的推导。神经伽辽金方法(Bruna et al.)也引入了类似的ode。Citation2022)。3这可以看作是复值情况(Hibat-Allah et al.)的一个特例。引文2020,Sharir et al.。Citation2020)。作者感谢NSF在DMS-2038030和DMS-2006305项目下的支持。这项研究在一定程度上得到了密歇根大学高级研究计算(ARC)提供的计算资源和服务的支持。
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引用次数: 0
Household financial health: a machine learning approach for data-driven diagnosis and prescription 家庭财务健康:数据驱动诊断和处方的机器学习方法
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-09-28 DOI: 10.1080/14697688.2023.2254335
Kyeongbin Kim, Yoontae Hwang, Dongcheol Lim, Suhyeon Kim, Junghye Lee, Yongjae Lee
AbstractHousehold finances are being threatened by unprecedented social and economic upheavals, including an aging society and slow economic growth. Numerous researchers and practitioners have provided guidelines for improving the financial status of households; however, the challenge of handling heterogeneous households remains nontrivial. In this study, we propose a new data-driven framework for the financial health of households to address the needs for diagnosing and improving financial health. This research extends the concept of healthcare to household finance. We develop a novel deep learning-based diagnostic model for estimating household financial health risk scores from real-world household balance sheet data. The proposed model can successfully manage the heterogeneity of households by extracting useful latent representations of household balance sheet data while incorporating the risk information of each variable. That is, we guide the model to generate higher latent values for households with risky balance sheets. We also show that the gradient of the model can be utilized for prescribing recommendations for improving household financial health. The robustness and validity of the new framework are demonstrated using empirical analyses.Keywords: Household financeFinancial healthHeterogeneityRisk scoringDeep learning Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Note that Indicator 4 follows the opposite direction of the other indicators. For Indicators 1 to 3, having a large value would increase financial risk, while it is the opposite for Indicator 4. Hence, stochastic dominance in Indicator 4 should also be interpreted in the opposite way from the other indicators.2 In Appendix C, we used the Bonferroni post-hoc test to assess the significance of the difference in risk information for each of the input variables to RI-HAE.3 To be more precise, the reciprocal of shadow price represents the amount of money required to increase the financial risk score by one unit estimated under first-order approximation because shadow price is a slope of the linear function tangent to RI-HAE.Additional informationFundingThis work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. NRF-2022R1I1A4069163 and No. NRF-2020R1C1C1011063).
家庭财务正受到前所未有的社会和经济动荡的威胁,包括老龄化社会和缓慢的经济增长。许多研究人员和从业人员为改善家庭财务状况提供了指导方针;然而,处理异构家庭的挑战仍然不容忽视。在这项研究中,我们提出了一个新的数据驱动的家庭财务健康框架,以解决诊断和改善财务健康的需求。本研究将医疗保健的概念延伸至家庭财务。我们开发了一种新的基于深度学习的诊断模型,用于从现实世界的家庭资产负债表数据中估计家庭财务健康风险评分。该模型通过提取家庭资产负债表数据的有用潜在表示,同时结合每个变量的风险信息,成功地管理了家庭的异质性。也就是说,我们引导模型为具有风险资产负债表的家庭产生更高的潜在价值。我们还表明,该模型的梯度可以用于处方建议,以改善家庭财务健康。通过实证分析证明了新框架的鲁棒性和有效性。关键词:家庭财务财务健康异质性风险评分深度学习披露声明作者未报告潜在利益冲突。注1 4号指示灯与其他指示灯方向相反。指标1 ~ 3的数值越大,金融风险就越大;指标4的数值越大,金融风险就越大。因此,指标4中的随机优势也应该以与其他指标相反的方式来解释在附录C中,我们使用Bonferroni事后检验来评估ri - hae的每个输入变量的风险信息差异的显著性更准确地说,影子价格的倒数表示在一阶近似下估计将金融风险评分提高一个单位所需的资金数额,因为影子价格是与RI-HAE相切的线性函数的斜率。本研究由韩国国家研究基金会(NRF)资助,由韩国政府(MSIT)资助(No. 5)。NRF-2022R1I1A4069163nrf - 2020 r1c1c1011063)。
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引用次数: 0
On prices and returns in commercial prediction markets 关于商业预测市场的价格和回报
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-09-26 DOI: 10.1080/14697688.2023.2257756
Karl Whelan
The Commodity Futures Trading Commission (CFTC) has recently licensed a commercial prediction market to operate in the US. With regulatory restrictions lifted, these markets can now play the important role that has been often envisaged for them. For example, investors can use them to hedge various event-related risks directly rather than indirectly via portfolios expected to move a certain way if events occur. Commercial prediction markets charge fees, an element that has not been incorporated into previous theoretical work on these markets. We examine the impact of fees on prediction market prices and returns by introducing them to a model in which the market price equals the true probability when there are no fees. We find that existing fee models mean contract prices for low probability outcomes are below the true probability but the impact of fees means prediction markets feature a form of favorite-longshot bias: Post-fee loss rates depend negatively on the probability of the event being backed. We show this result holds even if prediction market operators set a fee structure that is more generous to contracts with a low probability of success.
美国商品期货交易委员会(CFTC)最近批准了一个商业预测市场在美国运营。随着监管限制的解除,这些市场现在可以发挥人们通常为它们设想的重要作用。例如,投资者可以利用它们直接对冲各种与事件相关的风险,而不是通过预期在事件发生时以某种方式移动的投资组合间接对冲。商业预测市场收取费用,这一因素没有被纳入之前关于这些市场的理论工作。我们通过引入一个模型来检验费用对预测市场价格和回报的影响,在这个模型中,当没有费用时,市场价格等于真实概率。我们发现,现有的收费模型意味着低概率结果的合约价格低于真实概率,但收费的影响意味着预测市场呈现出一种偏好长线偏好的形式:收费后的损失率与事件得到支持的概率呈负相关。我们证明,即使预测市场运营商设置了一个对成功概率较低的合同更慷慨的费用结构,这个结果也成立。
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引用次数: 0
A transform-based method for pricing Asian options under general two-dimensional models 一般二维模型下基于变换的亚洲期权定价方法
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-09-26 DOI: 10.1080/14697688.2023.2256358
Weinan Zhang, Pingping Zeng
AbstractWe propose a unified transform-based method, which we call the extended double spiral (EDS) method, for pricing arithmetic Asian options under general two-dimensional (2D) models that nest regime-switching Lévy models, stochastic volatility (SV) models with Lévy jumps, and time-changed Lévy models. We first construct a new single backward induction in the state space that relaxes the restriction of the independent increments of the log-asset price. Second, we build an exact and explicit double backward induction in the Fourier space based on this single backward induction, a combination of the 1D Fourier transform method and a key function characterizing the 2D model, and the double spiral method. Third, we develop a unified EDS algorithm to recursively implement this double backward induction via the fast Fourier transform (FFT), various quadrature rules, asymmetric truncation boundaries, and so on. Extensive numerical results across a broad class of 2D models, monitoring frequencies, option moneyness, and model parameters demonstrate that our method is remarkably accurate, efficient, robust, simple to implement, and widely applicable.Keywords: Arithmetic Asian optionsTwo-dimensional modelsExtended double spiral methodFast Fourier transformJEL Classifications: C00C63G13 Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 Here and subsequently, the state space and the Fourier space refer to the component Y.2 As a remark, in the continuous case, we need the transformation from ν′ to ln⁡nu′ to calculate (Equation17(17) Qh,M,M~(i)g(β,ν):=12π∫E(∑m=−M~MΓ¯(i)(β−mh)g(αi)(mh,ν′)h)×ΨΔ(−β+iα3−i;ν,ν′)dν′(17) ) when the left tail of the density function of the process v in the function Ψ grows rapidly.3 The derivations originate from a manuscript by Cai and Zeng (Citation2023).Additional informationFundingPingping Zeng would like to acknowledge the support from the National Natural Science Foundation of China (Grant Nos. 11701266 and 12171228), and the Philosophy and Social Science Planning Project of Guangdong Province, China (Grant No. GD20XGL31).
摘要针对一般二维(2D)模型下的亚洲期权定价算法,提出了一种基于统一变换的扩展双螺旋(EDS)方法,该方法包含了状态切换lsamsamy模型、具有lsamsamy跳变的随机波动率(SV)模型和时变lsamsamy模型。首先,我们在状态空间中构造了一个新的单一反向归纳,放宽了对数资产价格独立增量的限制。其次,在此基础上,结合一维傅里叶变换方法和表征二维模型的关键函数以及双螺旋方法,在傅里叶空间中建立了精确而显式的双逆向归纳。第三,我们开发了一种统一的EDS算法,通过快速傅里叶变换(FFT)、各种正交规则、不对称截断边界等递归地实现这种双重逆向归纳。广泛的二维模型、监测频率、期权金钱性和模型参数的数值结果表明,我们的方法非常准确、高效、鲁棒、易于实现,并且广泛适用。关键词:算术亚洲期权二维模型扩展双螺旋法快速傅立叶变换分类:C00C63G13披露声明作者未报告潜在利益冲突。注1这里及之后,状态空间和傅里叶空间都是指分量Y.2作为注释,在连续情况下,当函数Ψ中过程v的密度函数的左尾快速增长时,我们需要从ν '到ln '的变换来计算(方程17(17)Qh,M,M~(i)g(β,ν):=12π∫E(∑M = - M~MΓ¯(i)(β - mh)g(αi)(mh,ν ')h)×ΨΔ(- β+iα3 - i;ν,ν ')dν ' (17))衍生词来源于Cai和Zeng的一篇手稿(Citation2023)。基金资助:曾萍萍感谢国家自然科学基金项目(批准号:11701266和12171228)和广东省哲学社会科学规划项目(批准号:11701266和12171228)的支持。GD20XGL31)。
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引用次数: 1
Can volatility solve the naive portfolio puzzle? 波动性能解决幼稚的投资组合难题吗?
4区 经济学 Q1 Economics, Econometrics and Finance Pub Date : 2023-09-26 DOI: 10.1080/14697688.2023.2249996
Michael Curran, Ryan Zalla
AbstractWe investigate whether sophisticated volatility estimation improves the out-of-sample performance of mean-variance portfolio strategies relative to the naive 1/N strategy. The portfolio strategies rely solely upon second moments. Using a diverse group of portfolios and econometric models across multiple datasets, most models achieve higher Sharpe ratios and lower portfolio volatility that are statistically and economically significant relative to the naive rule, even after controlling for turnover costs. Our results suggest benefits to employing more sophisticated econometric models than the sample covariance matrix, and that mean-variance strategies often outperform the naive portfolio across multiple datasets and assessment criteria.Keywords: Mean-varianceNaive portfoliovolatilityJEL: G11G17 AcknowledgmentsWe thank Caitlin Dannhauser, Jesús Fernández-Villaverde, Alejandro Lopez-Lira, Rabih Moussawi, Michael Pagano, Nikolai Roussanov, Paul Scanlon, Frank Schorfheide, John Sedunov, Raman Uppal, and Raisa Velthuis for helpful comments. Christopher Antonello provided diligent research assistance.Disclosure statementNo potential conflict of interest was reported by the author(s).Supplemental dataSupplemental data for this article can be accessed online at http://dx.doi.org/10.1080/14697688.2023.2249996.Notes1 Instead of the portfolio strategy, our innovation explores a wide variety of econometric models. DeMiguel et al. (Citation2009b) find that the minimum-variance portfolio, though performing well relative to other portfolio strategies, significantly beats the 1/N strategy for only 1 in 7 of their datasets. Jagannathan and Ma (Citation2003) and Kirby and Ostdiek (Citation2012) innovate on the portfolio strategy, illustrating that short-sale constrained minimum-variance strategies and volatility-timing strategies enhance performance.2 We consider a wide range of mostly parametric econometric models. Non-parametric models using higher-frequency data (DeMiguel et al. Citation2013) and shrinkage approaches (Ledoit and Wolf Citation2017) also improve the accuracy of estimation. Daily frequency option-implied volatility reduces portfolio volatility, but never statistically significantly improves the Sharpe ratio relative to the 1/N strategy (DeMiguel et al. Citation2013). Although Johannes et al. (Citation2014) account for both estimation risk and time-varying volatility through eight variations of a similar class of constant and stochastic volatility models, we expand to more varied classes of volatility types with 14 econometric models. Initial investigations reveal our results to be at least as strong as Ledoit and Wolf (Citation2017).3 Our econometric estimation strategies yield improvements beyond the period and frequency differences.4 A portfolio strategy, whose covariance is estimated using a given econometric model, weakly dominates the naive benchmark if, for each performance criterion, the portfolio strategy performs at least as well a
在Ledoit和Wolf (Citation2004, Citation2017)之后,收缩协方差矩阵的使用与我们研究中较小的投资组合选择不太相关设w´表示我们对投资组合权重w的最优向量的估计,计量经济学的MSE偏差方差分解为MSE(w´)=Var(w´)+Bias2(w´,w),其中Bias(w´,w)=w´−w.12虽然我们试图涵盖广泛的计量经济模型类别,但我们的计量经济模型集并不详尽。例如,我们忽略了Hafner和Reznikova (Citation2012)和Ledoit和Wolf (Citation2003, Citation2017)的收缩估计量。虽然这些和其他计量经济模型很有趣,但我们的研究在计量经济模型的覆盖范围上是最广泛的详细的模型、实现和鲁棒性描述归到在线附录中有限样本的推断在预期收益波动方面也比预期平均收益更有信息量(Andersen和Teräsvirta Citation2009)不卖空所隐含的正则化保证了所得到的协方差矩阵的可逆性首先,我们的基准CP策略(Equation5(5) wt,jMVP,comv=argminw∈RN|w ' 1=1′wΣ´tcomvw ' .(5))的一个变体,对于每个策略(Equation2(2) wt,jMVP=argminw∈RN|w ' 1=1′wΣtj´w ' .(2)) - (Equation4(4) (wt,jVT)i=1/(Σ´tj)i,i∑i=1N1/(Σ´tj)i,ii=1,…,N.(4)),我们检查了相对于每个计量经济模型的13个投资组合中由naive投资给出的相应投资组合。更准确地说,考虑最小方差投资组合。我们形成了第14个投资组合策略wtMVP,com,该策略平均投资于13个真实最小方差投资组合的估计,即wtMVP,com=113∑j=113wt,jMVP。其次,对于每个计量经济模型,我们检查了三种策略(Equation2(2) wt,jMVP=argminw∈RN|w ' 1=1′wΣtj´w ' .(2)) - (Equation4(4) (wt,jVT)i=1/(Σ´tj)i,i∑i=1N1/(Σ´tj)i,ii=1,…,n(4))中由朴素投资给出的相应投资组合。更准确地说,考虑VAR计量经济模型。我们形成了第四个投资组合策略,wtVAR,comp,通过将VAR模型的波动率估计输入到策略(Equation2(2) wt,jMVP=argminw∈RN|w ' 1=1′wΣtj´w ' .(2)) - (Equation4(4) (wt,jVT)i=1/(Σ´tj)i,i∑i=1N1/(Σ´tj)i,ii=1,…,n(4))中,即wtVAR,comp=13∑k=13wt,VARk)。标准普尔于1962年建立了Compustat,以满足金融分析师的需求,并只向分析师认为最感兴趣的公司提供后台信息。结果表明,在1963年之前,对业绩良好的公司的选定样本的覆盖率明显较低无风险(RF)资产是Ibbotson Associates的一个月国库券利率,代表投资于货币市场的回报。我们将无风险利率从投资者的选择集中排除;因此,我们排除了超过无风险利率的收益我们还在稳健性检查中使用了等权重数据集2的行业组合在使用较旧的标准行业分类(SIC)方案和较长的数据的学者中很受欢迎,而更广泛的数据集3的行业组合使用较新的GICS代码在从业者中很受欢迎基于协方差的方法,如最小方差投资组合,相对于1/N的投资组合,可以降低方差,从而提高夏普比率。因此,我们也要考虑回报。虽然朴素策略在数据集1上表现良好,尽管在数据集6上优于朴素策略,但其他策略在数据集2到5上优于朴素策略。结果可应要求提供文献中的几篇论文认为交易成本为10或50个基点(Kirby and Ostdiek Citation2012, DeMiguel et al.)。Citation2014)和其他人考虑交易成本因股票规模和时间而异(Brandt等人)。Citation2009)。在高周转率的情况下,保守地假设50个基点的交易成本会使我们的模型偏离1/N策略预测误差定义为使用估计的投资组合权重的预期收益与平均收益之间的差值。测试背后的损失差分着眼于预测误差的平方之差,我们计算自相关的损失差分校正我们只报告价值加权数据的结果在线附录中的表S2.1-3报告了三种投资组合方差策略之间的两两比较。对于大多数计量经济模型和数据集的每个评估标准,最小方差策略表现最好,波动率定时策略表现最差。 27为了解释数据集1和3较差的性能,首先,文献一致发现Fama-French数据集的性能较差(DeMiguel等人)。Citation2009b);其次,6个数据集的简单相关矩阵显示,数据集3是唯一与其他数据集负相关的数据集配置可能会发生变化,即使对于幼稚的投资组合,也需要重新平衡周转。考虑到营业额,预期收益不会更大,但标准差可能更小,也可能更大澄清一下,“✓”= 1,“✓*”= 2/3,“(空白)= 0,=−1“×”。我们通过只赋值2/3而不是1来贴现在10%水平上显著的结果。
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Quantitative Finance
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