{"title":"Geometric Asian power option pricing with transaction cost under the geometric fractional Brownian motion with w sources of risk in fuzzy environment","authors":"","doi":"10.1016/j.cam.2024.116165","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we obtain an explicit formula to calculate the geometric Asian power option price with floating strike price and transaction cost under the fractional geometric Brownian motion model with w sources of risk and fuzzy parameters. First, by considering the Leland and Kabanov theorems, we derive a non-linear PDE with the transaction cost formula to obtain the option price. Then, using the Green function find a closed form solution for the PDE and achieve the price of the option under different amounts of the model and option parameters. Next, we consider the model’s parameters as fuzzy numbers and acquire a general formula to obtain intervals for the option price under different belief degrees and power option parameter amounts.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037704272400414X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we obtain an explicit formula to calculate the geometric Asian power option price with floating strike price and transaction cost under the fractional geometric Brownian motion model with w sources of risk and fuzzy parameters. First, by considering the Leland and Kabanov theorems, we derive a non-linear PDE with the transaction cost formula to obtain the option price. Then, using the Green function find a closed form solution for the PDE and achieve the price of the option under different amounts of the model and option parameters. Next, we consider the model’s parameters as fuzzy numbers and acquire a general formula to obtain intervals for the option price under different belief degrees and power option parameter amounts.
期刊介绍:
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
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