Pub Date : 2023-11-06DOI: 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
{"title":"Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model","authors":"M. Escobar-Anel, M. Kschonnek, R. Zagst","doi":"10.1080/14697688.2023.2271223","DOIUrl":"https://doi.org/10.1080/14697688.2023.2271223","url":null,"abstract":"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","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135679626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1080/14697688.2023.2270495
Muhammad Ash-Shiddiqy, None Mujtahid, None Khamim
{"title":"Islamic Banking and Finance, Second Edition <b>Islamic Banking and Finance, Second Edition</b> , by Zubair Hasan, Routledge (2023). Hardcover. ISBN 978-1-032-36064-5. E-book. ISBN 978-1-003-36697-3.","authors":"Muhammad Ash-Shiddiqy, None Mujtahid, None Khamim","doi":"10.1080/14697688.2023.2270495","DOIUrl":"https://doi.org/10.1080/14697688.2023.2270495","url":null,"abstract":"","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 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].
{"title":"Dynamic core-satellite investing using higher order moments: an explicit solution","authors":"Yanfeng Wang, Wanbo Lu, Kris Boudt","doi":"10.1080/14697688.2023.2269987","DOIUrl":"https://doi.org/10.1080/14697688.2023.2269987","url":null,"abstract":"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].","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135863982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-24DOI: 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
{"title":"How does price (in)efficiency influence cryptocurrency portfolios performance? The role of multifractality","authors":"Eduardo Amorim Vilela de Salis, Leandro dos Santos Maciel","doi":"10.1080/14697688.2023.2266448","DOIUrl":"https://doi.org/10.1080/14697688.2023.2266448","url":null,"abstract":"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","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-03DOI: 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。
{"title":"Smiles in delta","authors":"Arianna Mingone","doi":"10.1080/14697688.2023.2258932","DOIUrl":"https://doi.org/10.1080/14697688.2023.2258932","url":null,"abstract":"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).","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 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。
{"title":"Quantum-inspired variational algorithms for partial differential equations: application to financial derivative pricing","authors":"Tianchen Zhao, Chuhao Sun, Asaf Cohen, James Stokes, Shravan Veerapaneni","doi":"10.1080/14697688.2023.2259954","DOIUrl":"https://doi.org/10.1080/14697688.2023.2259954","url":null,"abstract":"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.","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135198920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-28DOI: 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).
{"title":"Household financial health: a machine learning approach for data-driven diagnosis and prescription","authors":"Kyeongbin Kim, Yoontae Hwang, Dongcheol Lim, Suhyeon Kim, Junghye Lee, Yongjae Lee","doi":"10.1080/14697688.2023.2254335","DOIUrl":"https://doi.org/10.1080/14697688.2023.2254335","url":null,"abstract":"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).","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135345246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-26DOI: 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.
{"title":"On prices and returns in commercial prediction markets","authors":"Karl Whelan","doi":"10.1080/14697688.2023.2257756","DOIUrl":"https://doi.org/10.1080/14697688.2023.2257756","url":null,"abstract":"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.","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134885820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-26DOI: 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 lnnu′ 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).
{"title":"A transform-based method for pricing Asian options under general two-dimensional models","authors":"Weinan Zhang, Pingping Zeng","doi":"10.1080/14697688.2023.2256358","DOIUrl":"https://doi.org/10.1080/14697688.2023.2256358","url":null,"abstract":"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 lnnu′ 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).","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134885956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-26DOI: 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
{"title":"Can volatility solve the naive portfolio puzzle?","authors":"Michael Curran, Ryan Zalla","doi":"10.1080/14697688.2023.2249996","DOIUrl":"https://doi.org/10.1080/14697688.2023.2249996","url":null,"abstract":"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","PeriodicalId":20747,"journal":{"name":"Quantitative Finance","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134903424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}