In this article, we aim to provide a detailed econometric analysis of the realized volatility in international stock markets of Brazil, China, Europe, India, the United Kingdom, and the United States, which represent a mix of large developing, and developed markets. For our purpose, we use the functional data analysis (FDA) framework, whence discrete volatility data were first transformed into continuous functions, and thereafter, derivatives of the continuous functions were investigated, and kinetic and potential energy associated is the volatility system were extracted. Results revealed that COVID-19 indeed had a significant effect on international financial market volatility for all the countries, with the exception of China. The realized volatility of the international financial markets did return to their pre-COVID levels in May 2020, and this recovery time was significantly faster than the 2008 financial crisis recovery period. Within the FDA framework, we further investigated the role of uncertainty on the realized volatility, specifically from an outbreak of an infectious disease (such as COVID-19) and a daily newspaper-based infectious disease index as the predictor. The regression analysis showed that the volatility of financial markets can be accurately modeled by this infectious disease index, but only for periods experiencing an epidemic or pandemic.
{"title":"Comparing risk profiles of international stock markets as functional data: COVID-19 versus the global financial crisis","authors":"Ryan Liam Shackleton, Sonali Das, Rangan Gupta","doi":"10.1002/asmb.2879","DOIUrl":"10.1002/asmb.2879","url":null,"abstract":"<p>In this article, we aim to provide a detailed econometric analysis of the realized volatility in international stock markets of Brazil, China, Europe, India, the United Kingdom, and the United States, which represent a mix of large developing, and developed markets. For our purpose, we use the functional data analysis (FDA) framework, whence discrete volatility data were first transformed into continuous functions, and thereafter, derivatives of the continuous functions were investigated, and kinetic and potential energy associated is the volatility system were extracted. Results revealed that COVID-19 indeed had a significant effect on international financial market volatility for all the countries, with the exception of China. The realized volatility of the international financial markets did return to their pre-COVID levels in May 2020, and this recovery time was significantly faster than the 2008 financial crisis recovery period. Within the FDA framework, we further investigated the role of uncertainty on the realized volatility, specifically from an outbreak of an infectious disease (such as COVID-19) and a daily newspaper-based infectious disease index as the predictor. The regression analysis showed that the volatility of financial markets can be accurately modeled by this infectious disease index, but only for periods experiencing an epidemic or pandemic.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.2879","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Accelerated degradation tests (ADTs) are widely used for assessing the reliability of long-life products. During an ADT, accelerated stresses not only expedite the degradation of test products but also increase the likelihood of encountering traumatic shocks. Moreover, it is important to acknowledge that measurement errors can be inevitable during the observation process of an ADT. Unfortunately, these errors are often overlooked in the optimal design of the ADT, especially when multiple competing failure modes are present. In this article, we propose a new approach to design ADTs when measurement errors exist and test products suffer from degradation failures and random shock failures. We utilize the Wiener process to model the degradation path, incorporating normally distributed measurement errors, and an exponential distribution to fit the time between random shock failures. Given the number of test products and the termination time, we optimize the ADT plans under three common design criteria. The equivalence theorem is used to verify the optimality of the optimal ADT plans. A real-life example and sensitivity analysis are provided to illustrate our proposed method. The results demonstrate that when competing failure modes are present, the optimal ADT plans, which account for measurement errors, differ significantly from those that do not consider such errors.
{"title":"Optimal designs of accelerated degradation tests with random shock failures and measurement errors","authors":"Lin Wu, Xiao-Dong Zhou, Rong-Xian Yue","doi":"10.1002/asmb.2878","DOIUrl":"https://doi.org/10.1002/asmb.2878","url":null,"abstract":"<p>Accelerated degradation tests (ADTs) are widely used for assessing the reliability of long-life products. During an ADT, accelerated stresses not only expedite the degradation of test products but also increase the likelihood of encountering traumatic shocks. Moreover, it is important to acknowledge that measurement errors can be inevitable during the observation process of an ADT. Unfortunately, these errors are often overlooked in the optimal design of the ADT, especially when multiple competing failure modes are present. In this article, we propose a new approach to design ADTs when measurement errors exist and test products suffer from degradation failures and random shock failures. We utilize the Wiener process to model the degradation path, incorporating normally distributed measurement errors, and an exponential distribution to fit the time between random shock failures. Given the number of test products and the termination time, we optimize the ADT plans under three common design criteria. The equivalence theorem is used to verify the optimality of the optimal ADT plans. A real-life example and sensitivity analysis are provided to illustrate our proposed method. The results demonstrate that when competing failure modes are present, the optimal ADT plans, which account for measurement errors, differ significantly from those that do not consider such errors.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141991738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Value at risk (VaR) is a quantitative measure used to evaluate the risk linked to the potential loss of investment or capital. Estimation of the VaR entails the quantification of prospective losses in a portfolio of investments, using a certain likelihood, under normal market conditions within a specific time period. The objective of this article is to construct a model and estimate the VaR for a diversified portfolio consisting of multiple cash commodity positions driven by standard Brownian motions and jump processes. Subsequently, a thorough analytical estimation of the VaR is conducted for the proposed model. The results are then applied to two distinct commodities—corn and soybean—enabling a comprehensive comparison of the VaR values in the presence and absence of jumps.
{"title":"Estimation of VaR with jump process: Application in corn and soybean markets","authors":"Minglian Lin, Indranil SenGupta, William Wilson","doi":"10.1002/asmb.2880","DOIUrl":"https://doi.org/10.1002/asmb.2880","url":null,"abstract":"<p>Value at risk (VaR) is a quantitative measure used to evaluate the risk linked to the potential loss of investment or capital. Estimation of the VaR entails the quantification of prospective losses in a portfolio of investments, using a certain likelihood, under normal market conditions within a specific time period. The objective of this article is to construct a model and estimate the VaR for a diversified portfolio consisting of multiple cash commodity positions driven by standard Brownian motions and jump processes. Subsequently, a thorough analytical estimation of the VaR is conducted for the proposed model. The results are then applied to two distinct commodities—corn and soybean—enabling a comprehensive comparison of the VaR values in the presence and absence of jumps.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we introduce and study an extreme shock model in which the distribution of magnitude of shocks can change due to environmental effects. A new decision parameter is used to model the change point, and the non‐homogeneous Poisson process is employed to model the arrival of shocks. We derive the reliability function and mean time to system failure for the defined model. Furthermore, we propose an optimal age replacement policy. The results are illustrated when the change point follows the Erlang distribution.
{"title":"Extreme shock model with change point based on the Poisson process of shocks","authors":"Dheeraj Goyal, Min Xie","doi":"10.1002/asmb.2881","DOIUrl":"https://doi.org/10.1002/asmb.2881","url":null,"abstract":"In this article, we introduce and study an extreme shock model in which the distribution of magnitude of shocks can change due to environmental effects. A new decision parameter is used to model the change point, and the non‐homogeneous Poisson process is employed to model the arrival of shocks. We derive the reliability function and mean time to system failure for the defined model. Furthermore, we propose an optimal age replacement policy. The results are illustrated when the change point follows the Erlang distribution.","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141337044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Emissions trading systems (ETS) constitute a widely used tool to control greenhouse gas emissions and thus are vital to the global efforts to mitigate climate change. As most ETS' are divided into separate phases, this raises the policy question whether emissions allowances can be banked, that is, transferred to subsequent phases for later use. We provide a continuous‐time stochastic ETS model in a multiperiod setting that can allow for banking across phases. In particular, we are able to represent the influence of emissions development on the value of banked allowances. We introduce two distinct approaches to the multiperiod model: A basic approach delivers a model that is analytically more tractable and computationally less costly, while our more complex two‐dimensional approach entails a more realistic representation of the system. Numerical results show that banking decreases the mean emissions and increases allowance prices; at the same time, it increases the probability of complying with the emissions cap. In combination with the current penalty of the EU ETS at 100 Euro per ton, banking essentially guarantees compliance. We therefore conclude that banking is a crucial policy choice to improve the effectiveness and the reliability of an ETS.
{"title":"A multiperiod model of an emissions trading system","authors":"Ricarda Rosemann, Jörn Sass","doi":"10.1002/asmb.2867","DOIUrl":"https://doi.org/10.1002/asmb.2867","url":null,"abstract":"Emissions trading systems (ETS) constitute a widely used tool to control greenhouse gas emissions and thus are vital to the global efforts to mitigate climate change. As most ETS' are divided into separate phases, this raises the policy question whether emissions allowances can be banked, that is, transferred to subsequent phases for later use. We provide a continuous‐time stochastic ETS model in a multiperiod setting that can allow for banking across phases. In particular, we are able to represent the influence of emissions development on the value of banked allowances. We introduce two distinct approaches to the multiperiod model: A basic approach delivers a model that is analytically more tractable and computationally less costly, while our more complex two‐dimensional approach entails a more realistic representation of the system. Numerical results show that banking decreases the mean emissions and increases allowance prices; at the same time, it increases the probability of complying with the emissions cap. In combination with the current penalty of the EU ETS at 100 Euro per ton, banking essentially guarantees compliance. We therefore conclude that banking is a crucial policy choice to improve the effectiveness and the reliability of an ETS.","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141353693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Giovanna Apicella, Enrico De Giorgi, Emilia Di Lorenzo, Marilena Sibillo
Longevity crucially affects demand for pensions, insurance products and annuities. Consistent empirical evidence shows that women have historically experienced lower mortality rates than men. In this article, we study a measure of the gender gap in mortality rates, we call “Gender Gap Ratio”, across a wide range of ages and for four countries: France, Italy, Sweden, and USA. We show the stylized facts that characterize the trend of the Gender Gap Ratio, both in its historical evolution and future projection. Focusing on an example temporary life annuity contract, we give a monetary consistency to the Gender Gap Ratio. We show evidence that a Gender Gap Ratio that ranges between 1.5 and 2.5, depending on age, translates into a significant reduction of up to 23% in the benefits from a temporary life annuity contract for women with respect to men, against the same amount invested in the life annuity. The empirical evidence discussed in this article documents the crucial importance of working toward a more widespread demographic literacy, for example, a range of tools and strategies to raise longevity consciousness among individuals and policy-makers, in the framework of gender equality policies.
{"title":"Gender-inclusive financial and demographic literacy: Monetizing the gender mortality gap","authors":"Giovanna Apicella, Enrico De Giorgi, Emilia Di Lorenzo, Marilena Sibillo","doi":"10.1002/asmb.2876","DOIUrl":"10.1002/asmb.2876","url":null,"abstract":"<p>Longevity crucially affects demand for pensions, insurance products and annuities. Consistent empirical evidence shows that women have historically experienced lower mortality rates than men. In this article, we study a measure of the gender gap in mortality rates, we call “Gender Gap Ratio”, across a wide range of ages and for four countries: France, Italy, Sweden, and USA. We show the stylized facts that characterize the trend of the Gender Gap Ratio, both in its historical evolution and future projection. Focusing on an example temporary life annuity contract, we give a monetary consistency to the Gender Gap Ratio. We show evidence that a Gender Gap Ratio that ranges between 1.5 and 2.5, depending on age, translates into a significant reduction of up to 23% in the benefits from a temporary life annuity contract for women with respect to men, against the same amount invested in the life annuity. The empirical evidence discussed in this article documents the crucial importance of working toward a more widespread demographic literacy, for example, a range of tools and strategies to raise longevity consciousness among individuals and policy-makers, in the framework of gender equality policies.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.2876","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141363719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Allan Jonathan da Silva, Jack Baczynski, José V. M. Vicente
Interest rate derivative pricing is a critical aspect of fixed-income markets, where efficient methods are essential. This study introduces a novel approach to pricing path-dependent interest rate derivatives within a broad class of affine jumps. The study's particular setting is the Fourier-cosine series (COS) method adaptation, which offers an accurate and computationally efficient method for pricing interest rate derivatives. The Fourier-cosine series approach can be used to compute probability density functions and option pricing with a linear computing complexity and exponential convergence rate. The lack of a quick and precise pricing technique for Asian interest rate options in diverse fixed-income market scenarios is a research gap that is being addressed. This approach closes this gap by providing quasi-closed and closed-form equations for a range of density and characteristic functions, resulting in precise pricing. The results demonstrate the versatility of the COS method in interest rate markets. Similar to what has been previously reported for stock options, the numerical findings demonstrate the extreme precision and computing speed of the pricing and hedging estimations provided here. This method is an innovative approach to interest rate derivative pricing, offering researchers and practitioners a powerful tool for efficiently calculating prices and calibrating options across strikes and maturities.
利率衍生品定价是固定收益市场的一个重要方面,高效的定价方法至关重要。本研究介绍了一种新方法,用于在仿射跃迁的大类中对路径依赖利率衍生品进行定价。该研究的特定环境是傅立叶-余弦数列(COS)方法适应性,它为利率衍生品定价提供了一种精确且计算效率高的方法。傅立叶-余弦数列方法可用于计算概率密度函数和期权定价,计算复杂度为线性,收敛速度为指数。在各种固定收入市场情况下,亚洲利率期权缺乏快速精确的定价技术,这是一个正在解决的研究空白。这种方法为一系列密度和特征函数提供了准封闭和封闭式方程,从而实现了精确定价,填补了这一空白。研究结果证明了 COS 方法在利率市场中的多功能性。与之前关于股票期权的报告类似,数值结果表明本文提供的定价和对冲估算极其精确,计算速度极快。该方法是利率衍生品定价的一种创新方法,为研究人员和从业人员提供了一种有效计算价格和校准不同行权价和期限期权的强大工具。
{"title":"Efficient pricing of path-dependent interest rate derivatives","authors":"Allan Jonathan da Silva, Jack Baczynski, José V. M. Vicente","doi":"10.1002/asmb.2877","DOIUrl":"10.1002/asmb.2877","url":null,"abstract":"<p>Interest rate derivative pricing is a critical aspect of fixed-income markets, where efficient methods are essential. This study introduces a novel approach to pricing path-dependent interest rate derivatives within a broad class of affine jumps. The study's particular setting is the Fourier-cosine series (COS) method adaptation, which offers an accurate and computationally efficient method for pricing interest rate derivatives. The Fourier-cosine series approach can be used to compute probability density functions and option pricing with a linear computing complexity and exponential convergence rate. The lack of a quick and precise pricing technique for Asian interest rate options in diverse fixed-income market scenarios is a research gap that is being addressed. This approach closes this gap by providing quasi-closed and closed-form equations for a range of density and characteristic functions, resulting in precise pricing. The results demonstrate the versatility of the COS method in interest rate markets. Similar to what has been previously reported for stock options, the numerical findings demonstrate the extreme precision and computing speed of the pricing and hedging estimations provided here. This method is an innovative approach to interest rate derivative pricing, offering researchers and practitioners a powerful tool for efficiently calculating prices and calibrating options across strikes and maturities.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}