Negative probabilities arise primarily in physics, statistical quantum mechanics, and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link between these two viewpoints. Bartlett provides a definition of negative probabilities based on extraordinary random variables and properties of their characteristic function. A version of the Bayes rule is given with negative mixing weights. The classic half-coin distribution and Polya-Gamma mixing are discussed. Heisenberg's principle of uncertainty and the duality of scale mixtures of Normals is also discussed. A number of examples of dual densities with negative mixing measures are provided including the Linnik and Wigner distributions. Finally, we conclude with directions for future research.
{"title":"Negative Probability","authors":"Nick Polson, Vadim Sokolov","doi":"10.1002/asmb.2910","DOIUrl":"https://doi.org/10.1002/asmb.2910","url":null,"abstract":"<p>Negative probabilities arise primarily in physics, statistical quantum mechanics, and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link between these two viewpoints. Bartlett provides a definition of negative probabilities based on extraordinary random variables and properties of their characteristic function. A version of the Bayes rule is given with negative mixing weights. The classic half-coin distribution and Polya-Gamma mixing are discussed. Heisenberg's principle of uncertainty and the duality of scale mixtures of Normals is also discussed. A number of examples of dual densities with negative mixing measures are provided including the Linnik and Wigner distributions. Finally, we conclude with directions for future research.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.2910","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120639","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}
We consider several survival models in heterogeneous settings. Heterogeneity in the failure rates of subpopulations results (as a specific case) in the famous failure rate paradox when the failure rate of a mixture of items with constant failure rates is decreasing. Random failure rate that is due to a point process that increases it at random times on fixed values also results in the “bending down” of the population failure rate. Similar effect is observed while analyzing the extreme shock models with shock processes that possess memory. Finally, another paradox when, due to heterogeneity in a vital parameter of a model, a terminating point process with decreasing rate after “mixing” becomes a non-terminating one with increasing rate is described. Those are the impacts of heterogeneity that are discussed from the unified perspective that employs the “principle”: the weaker subpopulations are dying out first.
{"title":"Heterogeneity in Populations and the Paradoxes of Survival: A Tribute to Nozer Singpurwalla","authors":"Maxim Finkelstein, Ji Hwan Cha","doi":"10.1002/asmb.2919","DOIUrl":"https://doi.org/10.1002/asmb.2919","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider several survival models in heterogeneous settings. Heterogeneity in the failure rates of subpopulations results (as a specific case) in the famous failure rate paradox when the failure rate of a mixture of items with constant failure rates is decreasing. Random failure rate that is due to a point process that increases it at random times on fixed values also results in the “bending down” of the population failure rate. Similar effect is observed while analyzing the extreme shock models with shock processes that possess memory. Finally, another paradox when, due to heterogeneity in a vital parameter of a model, a terminating point process with decreasing rate after “mixing” becomes a non-terminating one with increasing rate is described. Those are the impacts of heterogeneity that are discussed from the unified perspective that employs the “principle”: the weaker subpopulations are dying out first.</p>\u0000 </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120642","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}
Since Lotfi Zadeh introduced fuzzy logic and fuzzy sets, this theory characterizing the uncertainty of classification has a proven record in fields of computation and engineering. These successful applications, however, have been falsely interpreted as competition or replacement of probability theory by those in many statistical and mathematical communities. Such misconceptions are the result of a lack of understanding about types of uncertainties, and anchored attitudes clinging to the past. Nozer Singpurwalla, among other statisticians, came to the realization that probability and fuzzy set theory can and should work in concert (i.e., not in competition) to accommodate two different types of uncertainty present within a problem or system. The authors had the honor to collaborate with Nozer; those works are featured as successful applications of the probability measure of fuzzy sets in reliability where respective uncertainties of the outcome of events and of classification exist. This paper features those works which embody the use of Bayesian analysis and the subjective interpretation of probability.
{"title":"Probability and Fuzzy Working in Concert—Honoring the Reliability Contributions of Nozer D. Singpurwalla","authors":"Kimberly F. Sellers, Jane M. Booker","doi":"10.1002/asmb.2918","DOIUrl":"https://doi.org/10.1002/asmb.2918","url":null,"abstract":"<div>\u0000 \u0000 <p>Since Lotfi Zadeh introduced fuzzy logic and fuzzy sets, this theory characterizing the uncertainty of classification has a proven record in fields of computation and engineering. These successful applications, however, have been falsely interpreted as competition or replacement of probability theory by those in many statistical and mathematical communities. Such misconceptions are the result of a lack of understanding about types of uncertainties, and anchored attitudes clinging to the past. Nozer Singpurwalla, among other statisticians, came to the realization that probability and fuzzy set theory can and should work in concert (i.e., not in competition) to accommodate two different types of uncertainty present within a problem or system. The authors had the honor to collaborate with Nozer; those works are featured as successful applications of the probability measure of fuzzy sets in reliability where respective uncertainties of the outcome of events and of classification exist. This paper features those works which embody the use of Bayesian analysis and the subjective interpretation of probability.</p>\u0000 </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120640","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}
Peng Liu, Yili Hong, Luis A. Escobar, William Q. Meeker
Fatigue data arise in many research and applied areas, and there have been statistical methods developed to model and analyze such data. The distributions of fatigue life and fatigue strength are often of interest to engineers designing products that might fail due to fatigue from cyclic-stress loading. Based on a specified statistical model and the maximum likelihood method, the cumulative distribution function (cdf) and quantile function (qf) can be estimated for the fatigue-life and fatigue-strength distributions. Likelihood-based confidence bands can then be obtained for the cdf and qf. This paper provides equivalence results for confidence bands for fatigue-life and fatigue-strength models. These results are useful for data analysis and computing implementation. We show (a) the equivalence of the confidence bands for the fatigue-life cdf and the fatigue-life qf, (b) the equivalence of confidence bands for the fatigue-strength cdf and the fatigue-strength qf, and (c) the equivalence of confidence bands for the fatigue-life qf and the fatigue-strength qf. Then we illustrate the usefulness of those equivalence results with two examples using experimental fatigue data.
{"title":"On the Equivalence of Likelihood-Based Confidence Bands for Fatigue-Life and Fatigue-Strength Distributions","authors":"Peng Liu, Yili Hong, Luis A. Escobar, William Q. Meeker","doi":"10.1002/asmb.2911","DOIUrl":"https://doi.org/10.1002/asmb.2911","url":null,"abstract":"<p>Fatigue data arise in many research and applied areas, and there have been statistical methods developed to model and analyze such data. The distributions of fatigue life and fatigue strength are often of interest to engineers designing products that might fail due to fatigue from cyclic-stress loading. Based on a specified statistical model and the maximum likelihood method, the cumulative distribution function (cdf) and quantile function (qf) can be estimated for the fatigue-life and fatigue-strength distributions. Likelihood-based confidence bands can then be obtained for the cdf and qf. This paper provides equivalence results for confidence bands for fatigue-life and fatigue-strength models. These results are useful for data analysis and computing implementation. We show (a) the equivalence of the confidence bands for the fatigue-life cdf and the fatigue-life qf, (b) the equivalence of confidence bands for the fatigue-strength cdf and the fatigue-strength qf, and (c) the equivalence of confidence bands for the fatigue-life qf and the fatigue-strength qf. Then we illustrate the usefulness of those equivalence results with two examples using experimental fatigue data.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.2911","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144085167","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}
Balancing consumer's and producer's risk is an important consideration when planning tests. Instead of focusing on finding a single best test plan, we introduce a general framework to systematically identify a set of binomial test plans by leveraging the inverse relationship between the two risks. The framework is applied to compare a variety of assurance testing frameworks, including classical tests, and Bayesian reliability assurance tests such as the Bayesian assurance test, the assurance reliability demonstration test, and the coverage criterion test. Efficient algorithms are presented to compute the set of test plans, providing practitioners with a comprehensive range of options to choose from. In addition, we include a comparison to the sequential probability ratio test. We also provide formal proofs for the inverse relationship between consumer's and producer's risk in Bayesian reliability assurance tests that underlie our algorithms. A case study is presented to illustrate the framework's application and compare the risks associated with different test plans.
{"title":"Comparing Risks for Binomial Reliability Assurance Test Planning","authors":"Hyoshin Kim, Alyson G. Wilson","doi":"10.1002/asmb.2912","DOIUrl":"https://doi.org/10.1002/asmb.2912","url":null,"abstract":"<p>Balancing consumer's and producer's risk is an important consideration when planning tests. Instead of focusing on finding a single best test plan, we introduce a general framework to systematically identify a set of binomial test plans by leveraging the inverse relationship between the two risks. The framework is applied to compare a variety of assurance testing frameworks, including classical tests, and Bayesian reliability assurance tests such as the Bayesian assurance test, the assurance reliability demonstration test, and the coverage criterion test. Efficient algorithms are presented to compute the set of test plans, providing practitioners with a comprehensive range of options to choose from. In addition, we include a comparison to the sequential probability ratio test. We also provide formal proofs for the inverse relationship between consumer's and producer's risk in Bayesian reliability assurance tests that underlie our algorithms. A case study is presented to illustrate the framework's application and compare the risks associated with different test plans.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.2912","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144085173","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}
Roberto Baviera, Carlo Sgarra, Tiziano Vargiolu, Rituparna Sen
{"title":"Foreword to the Special Issue on Energy Finance and Climate Change","authors":"Roberto Baviera, Carlo Sgarra, Tiziano Vargiolu, Rituparna Sen","doi":"10.1002/asmb.2909","DOIUrl":"https://doi.org/10.1002/asmb.2909","url":null,"abstract":"","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"40 6","pages":"1470-1471"},"PeriodicalIF":1.3,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868033","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 paper, we are the first to consider the combination of the minimal repair with the defined better than minimal repair. With a given probability, each failure of a repairable system is minimally repaired and with complementary probability it is better than minimally repaired. The latter can be interpreted in terms of a reliability growth model when a defect of a system is eliminated on each failure. It turns out that the better than minimal repair can be even better than a perfect one if a perfect repair is understood as a replacement of the whole system or stochastically equivalent operation. We provide stochastic description of the failure/repair process by introducing and describing the corresponding bivariate point process via the concept of stochastic intensity. Distributions for the number of failures for the pooled and marginal processes are derived along with their expected values. The latter can describe the process of reliability growth in applications. Some meaningful special cases are discussed.
{"title":"On a New Point Process Approach to Reliability Improvement Modeling for Repairable Systems","authors":"Maxim Finkelstein, Ji Hwan Cha","doi":"10.1002/asmb.2906","DOIUrl":"https://doi.org/10.1002/asmb.2906","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we are the first to consider the combination of the minimal repair with the defined better than minimal repair. With a given probability, each failure of a repairable system is minimally repaired and with complementary probability it is better than minimally repaired. The latter can be interpreted in terms of a reliability growth model when a defect of a system is eliminated on each failure. It turns out that the better than minimal repair can be even better than a perfect one if a perfect repair is understood as a replacement of the whole system or stochastically equivalent operation. We provide stochastic description of the failure/repair process by introducing and describing the corresponding bivariate point process via the concept of stochastic intensity. Distributions for the number of failures for the pooled and marginal processes are derived along with their expected values. The latter can describe the process of reliability growth in applications. Some meaningful special cases are discussed.</p>\u0000 </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144085168","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}
Kevin Li, Graham Tierney, Christoph Hellmayr, Mike West
Theoretical developments in sequential Bayesian analysis of multivariate dynamic models underlie new methodology for counterfactual prediction. This extends the utility of existing models with computationally efficient methodology, enabling routine exploration of post-intervention analyses with multiple time series in putatively casual studies. Methodological contributions also define the concept of outcome adaptive modelling to monitor and respond to changes in experimental time series following interventions. The benefits of sequential analyses with time-varying parameter models for such investigations are inherited in this broader setting. A case study in forecasting retail revenue following marketing interventions highlights the methodological advances.
{"title":"Compositional Dynamic Modelling for Counterfactual Prediction in Multivariate Time Series","authors":"Kevin Li, Graham Tierney, Christoph Hellmayr, Mike West","doi":"10.1002/asmb.2908","DOIUrl":"https://doi.org/10.1002/asmb.2908","url":null,"abstract":"<div>\u0000 \u0000 <p>Theoretical developments in sequential Bayesian analysis of multivariate dynamic models underlie new methodology for counterfactual prediction. This extends the utility of existing models with computationally efficient methodology, enabling routine exploration of post-intervention analyses with multiple time series in putatively casual studies. Methodological contributions also define the concept of outcome adaptive modelling to monitor and respond to changes in experimental time series following interventions. The benefits of sequential analyses with time-varying parameter models for such investigations are inherited in this broader setting. A case study in forecasting retail revenue following marketing interventions highlights the methodological advances.</p>\u0000 </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144085169","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}
<div> <p>Consider a job that normally requires <span></span><math> <mrow> <mi>a</mi> </mrow></math> units of time to complete. A higher authority comes and interrupts the service. The inter-arrival times of the interrupts are <span></span><math> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mi>⋯</mi> </mrow></math>, which are the actual available service times to work on the job. Thus, if the first available service time <span></span><math> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow></math> is larger than <span></span><math> <mrow> <mi>a</mi> </mrow></math>, the job gets completed, and the remaining service time <span></span><math> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>−</mo> <mi>a</mi> </mrow></math> is the first available service time for the next job. If not, the previous service is lost and service on the job starts from scratch using <span></span><math> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow></math> the next available service time. As before, if <span></span><math> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>≥</mo> <mi>a</mi> </mrow></math>, the job gets completed and the remaining service time <span></span><math> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>−</mo> <mi>a</mi> </mrow></math> is the first available service time for the next job. If not, the service is lost, and <span></s
{"title":"Start Over After Pre-Empt (SOAP) Protocol","authors":"Jayaram Sethuraman","doi":"10.1002/asmb.2902","DOIUrl":"https://doi.org/10.1002/asmb.2902","url":null,"abstract":"<div>\u0000 \u0000 <p>Consider a job that normally requires <span></span><math>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 </mrow></math> units of time to complete. A higher authority comes and interrupts the service. The inter-arrival times of the interrupts are <span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mi>⋯</mi>\u0000 </mrow></math>, which are the actual available service times to work on the job. Thus, if the first available service time <span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math> is larger than <span></span><math>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 </mrow></math>, the job gets completed, and the remaining service time <span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>−</mo>\u0000 <mi>a</mi>\u0000 </mrow></math> is the first available service time for the next job. If not, the previous service is lost and service on the job starts from scratch using <span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math> the next available service time. As before, if <span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>≥</mo>\u0000 <mi>a</mi>\u0000 </mrow></math>, the job gets completed and the remaining service time <span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>−</mo>\u0000 <mi>a</mi>\u0000 </mrow></math> is the first available service time for the next job. If not, the service is lost, and <span></s","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144085404","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}
Monroe (1978) demonstrates that any local semimartingale can be represented as a time-changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time-change are independent? We prove that a local semimartingale is not equivalent to a BM with a time-change that is independent from the BM. Our result is obtained utilizing a class of additive processes: the additive normal tempered stable (ATS). This class of processes exhibits an exceptional ability to calibrate the equity volatility surface accurately. We notice that the sub-class of additive processes that can be obtained with an independent additive subordination is incompatible with market data and shows significantly worse calibration performances than the ATS, especially on short time maturities. These results have been observed every business day in a semester on a dataset of S&P 500 and EURO STOXX 50 options.
{"title":"Is (Independent) Subordination Relevant in Equity Derivatives?","authors":"Michele Azzone, Roberto Baviera","doi":"10.1002/asmb.2904","DOIUrl":"10.1002/asmb.2904","url":null,"abstract":"<p>Monroe (1978) demonstrates that any local semimartingale can be represented as a time-changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time-change are independent? We prove that a local semimartingale is not equivalent to a BM with a time-change that is independent from the BM. Our result is obtained utilizing a class of additive processes: the additive normal tempered stable (ATS). This class of processes exhibits an exceptional ability to calibrate the equity volatility surface accurately. We notice that the sub-class of additive processes that can be obtained with an independent additive subordination is incompatible with market data and shows significantly worse calibration performances than the ATS, especially on short time maturities. These results have been observed every business day in a semester on a dataset of S&P 500 and EURO STOXX 50 options.</p>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.2904","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142665589","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}
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