{"title":"Pricing Basket Spread Option Under the Correlated Skew Brownian Motions","authors":"Qifeng Zhong, Xingye Yue, Jing Yao","doi":"10.1002/asmb.70040","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this article, we propose synthetic analytical approximate pricing formulas for basket and basket spread options within a multidimensional correlated skew Brownian motion framework. For basket options, we derive two analytical approximate pricing formulas by utilizing the partial exact approximation, the moment matching method and convex bounds approximation together and achieve accurate and analytical approximations. For basket spread options, we derive a lower bound approximation using the Bjerksund–Stensland-type approach. Numerical examples demonstrate superior performance with consistent robustness and high precision of our formulas, remarkably maintaining excellent performance for high-dimensional options. We also note that these approximate pricing formulas can serve as powerful control variates for the variance reduction of Monte Carlo simulations.</p>\n </div>","PeriodicalId":55495,"journal":{"name":"Applied Stochastic Models in Business and Industry","volume":"41 5","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2025-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Stochastic Models in Business and Industry","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/asmb.70040","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we propose synthetic analytical approximate pricing formulas for basket and basket spread options within a multidimensional correlated skew Brownian motion framework. For basket options, we derive two analytical approximate pricing formulas by utilizing the partial exact approximation, the moment matching method and convex bounds approximation together and achieve accurate and analytical approximations. For basket spread options, we derive a lower bound approximation using the Bjerksund–Stensland-type approach. Numerical examples demonstrate superior performance with consistent robustness and high precision of our formulas, remarkably maintaining excellent performance for high-dimensional options. We also note that these approximate pricing formulas can serve as powerful control variates for the variance reduction of Monte Carlo simulations.
期刊介绍：
ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process.
The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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