{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T17:12:29Z","timestamp":1732727549141,"version":"3.29.0"},"reference-count":32,"publisher":"SAGE Publications","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,3,2]]},"abstract":"As an economic lever in financial market, interest rate option is not only the function of facilitating the bank to adjust the market fund supply and demand relation indirectly, but also provides the guarantee for investors to choose whether to exercise the right at the maturity date, thereby locking in the interest rate risk. This paper mainly studies the price of the interest rate ceiling as well as floor under the uncertain environment. Firstly, from the perspective of expert reliability, rather than relying on a large amount of historical financial data, to consider interest rate trends, and further assume that the dynamic change of the interest rate conforms to the uncertain process. Secondly, since uncertain fractional-order differential equations (UFDEs) have non-locality features to reflect memory and hereditary characteristics for the asset price changes, thus is more suitable to model the real financial market. We construct the mean-reverting interest rate model based on the UFDE in Caputo type. Then, the pricing formula of the interest rate ceiling and floor are provided separately. Finally, corresponding numerical examples and algorithms are given by using the predictor-corrector method, which support the validity of the proposed model.<\/jats:p>","DOI":"10.3233\/jifs-201930","type":"journal-article","created":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T16:03:47Z","timestamp":1609257827000},"page":"5197-5206","source":"Crossref","is-referenced-by-count":0,"title":["Valuation of interest rate ceiling and floor based on the uncertain fractional differential equation in Caputo sense"],"prefix":"10.1177","volume":"40","author":[{"given":"Ting","family":"Jin","sequence":"first","affiliation":[{"name":"School of Science, Nanjing Forestry University, Nanjing, Jiangsu, China"}]},{"given":"Hui","family":"Ding","sequence":"additional","affiliation":[{"name":"College of Economics and Management, Nanjing Forestry University, Nanjing, Jiangsu, China"}]},{"given":"Bo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, China"}]},{"given":"Hongxuan","family":"Xia","sequence":"additional","affiliation":[{"name":"College of International Education, Nanjing Forestry University, Nanjing, Jiangsu, China"}]},{"given":"Chenxi","family":"Xue","sequence":"additional","affiliation":[{"name":"School of Science, Nanjing Forestry University, Nanjing, Jiangsu, China"}]}],"member":"179","reference":[{"issue":"1-2","key":"10.3233\/JIFS-201930_ref1","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/0304-405X(76)90022-2","article-title":"Option pricing when underlying stock returns are discontinuous","volume":"3","author":"Merton","year":"1976","journal-title":"Journal of Financial Economics"},{"issue":"5","key":"10.3233\/JIFS-201930_ref2","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.1111\/j.1540-6261.1986.tb02528.x","article-title":"Term structure movements and pricing interest rate contingent claims","volume":"41","author":"Ho","year":"1986","journal-title":"Journal of Finance"},{"issue":"4","key":"10.3233\/JIFS-201930_ref3","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1093\/rfs\/3.4.573","article-title":"Pricing interest-ratederivative securities","volume":"3","author":"Hull","year":"1990","journal-title":"Review of Financial Studies"},{"issue":"2","key":"10.3233\/JIFS-201930_ref4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0304-405X(77)90016-2","article-title":"An equilibrium characterization of the term structure","volume":"5","author":"Vasicek","year":"1977","journal-title":"Journal of Financial Economics"},{"issue":"3","key":"10.3233\/JIFS-201930_ref5","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/S0378-4266(04)00054-8","article-title":"Pricing and hedging interest rate options: Evidence from cap-floor markets","volume":"29","author":"Gupta","year":"2005","journal-title":"Journal of Banking and Finance"},{"issue":"2","key":"10.3233\/JIFS-201930_ref6","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10588-008-9049-8","article-title":"Firmnet: the scope of firms and the allocation of task in a knowledge-based economy","volume":"15","author":"Mollona","year":"2009","journal-title":"Computational and Mathematical Organization Theory"},{"issue":"9","key":"10.3233\/JIFS-201930_ref7","doi-asserted-by":"crossref","first-page":"5217","DOI":"10.1016\/j.amc.2011.11.004","article-title":"Numerical solution of a pde model for a ratchet-cap pricing with bgm interest rate dynamics","volume":"218","author":"Su\u00e1rez-Taboada","year":"2012","journal-title":"Applied Mathematics and Computation"},{"issue":"2","key":"10.3233\/JIFS-201930_ref8","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1109\/TNNLS.2018.2846646","article-title":"Dendritic neural model with effective learning algorithms for classification, approximation, and prediction","volume":"30","author":"Gao","year":"2019","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"issue":"3","key":"10.3233\/JIFS-201930_ref10","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1504\/IJBIC.2020.10033314","article-title":"An effective improved co-evolution ant colony optimization algorithm with multi-strategies and its application","volume":"16","author":"Deng","year":"2020","journal-title":"International Journal of Bio-Inspired Computation"},{"doi-asserted-by":"publisher","key":"10.3233\/JIFS-201930_ref11","DOI":"10.1016\/j.asoc.2020.106724"},{"issue":"1","key":"10.3233\/JIFS-201930_ref12","first-page":"3","article-title":"Fuzzy process, hybrid process and uncertain process","volume":"2","author":"Liu","year":"2008","journal-title":"Journal of Uncertain Systems"},{"key":"10.3233\/JIFS-201930_ref13","first-page":"3","article-title":"Some research problems in uncertainy theory","volume":"3","author":"Liu","year":"2009","journal-title":"Journal of Uncertain Systems"},{"key":"10.3233\/JIFS-201930_ref14","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s10700-010-9073-2","article-title":"Existence and uniqueness theorem for uncertain differential equations","volume":"9","author":"Chen","year":"2010","journal-title":"Fuzzy Optimization and Decision Making"},{"issue":"1","key":"10.3233\/JIFS-201930_ref15","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10700-012-9139-4","article-title":"Some stability theorems of uncertain differential equation","volume":"12","author":"Yao","year":"2013","journal-title":"Fuzzy Optimization and Decision Making"},{"doi-asserted-by":"crossref","unstructured":"Yao K. and Chen X. , A numerical method for solving uncertain differential equations, Journal of Intelligent and Fuzzy Systems 25 01 (2013).","key":"10.3233\/JIFS-201930_ref16","DOI":"10.3233\/IFS-120688"},{"key":"10.3233\/JIFS-201930_ref17","doi-asserted-by":"crossref","first-page":"385","DOI":"10.2307\/1911242","article-title":"A theory of the term structure of interest rates","volume":"53","author":"Cox","year":"1985","journal-title":"Econometrica"},{"key":"10.3233\/JIFS-201930_ref18","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.matcom.2019.04.009","article-title":"Barrier option pricing of mean-reverting stock model in uncertain environment","volume":"166","author":"Tian","year":"2019","journal-title":"Mathematics and Computers in Simulation"},{"key":"10.3233\/JIFS-201930_ref19","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.chaos.2019.03.037","article-title":"Asian-barrier option pricing formulas of uncertain financial market","volume":"123","author":"Yang","year":"2019","journal-title":"Chaos, Solitons & Fractals"},{"key":"10.3233\/JIFS-201930_ref21","doi-asserted-by":"crossref","first-page":"110026","DOI":"10.1016\/j.chaos.2020.110026","article-title":"Parameter estimation of uncertain differential equation with application to financial market","volume":"139","author":"Yang","year":"2020","journal-title":"Chaos Solitons & Fractals"},{"key":"10.3233\/JIFS-201930_ref22","doi-asserted-by":"crossref","first-page":"125724","DOI":"10.1016\/j.amc.2020.125724","article-title":"Generalized moment estimation for uncertain differential equations","volume":"392","author":"Liu","year":"2020","journal-title":"Applied Mathematics and Computation"},{"issue":"4","key":"10.3233\/JIFS-201930_ref23","doi-asserted-by":"crossref","first-page":"2317","DOI":"10.3233\/JIFS-17354","article-title":"An uncertain differential equation for sis epidemic model","volume":"33","author":"Li","year":"2017","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"4","key":"10.3233\/JIFS-201930_ref24","doi-asserted-by":"crossref","first-page":"2417","DOI":"10.1007\/s00500-018-03678-6","article-title":"Uncertain population model","volume":"24","author":"Zhang","year":"2020","journal-title":"Soft Computing"},{"issue":"15","key":"10.3233\/JIFS-201930_ref25","doi-asserted-by":"crossref","first-page":"3359","DOI":"10.1002\/mma.3335","article-title":"Uncertain fractional differential equations and an interest rate model","volume":"38","author":"Zhu","year":"2015","journal-title":"Mathematical Methods in the Applied Sciences"},{"issue":"1","key":"10.3233\/JIFS-201930_ref26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40467-015-0028-6","article-title":"Existence and uniqueness of the solution to uncertain fractional differential equation","volume":"3","author":"Zhu","year":"2015","journal-title":"Journal of Uncertainty Analysis and Applications"},{"issue":"2","key":"10.3233\/JIFS-201930_ref27","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s10700-018-9293-4","article-title":"European option pricing model based on uncertain fractional differential equation","volume":"18","author":"Lu","year":"2019","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"10.3233\/JIFS-201930_ref28","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.amc.2018.09.044","article-title":"Numerical approach for solution to an uncertain fractional differential equation","volume":"343","author":"Lu","year":"2019","journal-title":"Applied Mathematics and Computation"},{"key":"10.3233\/JIFS-201930_ref29","doi-asserted-by":"crossref","first-page":"122357","DOI":"10.1016\/j.physa.2019.122357","article-title":"Extreme values for solution to uncertain fractional differential equation and application to american option pricing model","volume":"534","author":"Jin","year":"2019","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"10.3233\/JIFS-201930_ref30","doi-asserted-by":"crossref","first-page":"124991","DOI":"10.1016\/j.amc.2019.124991","article-title":"Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model","volume":"372","author":"Jin","year":"2020","journal-title":"Applied Mathematics and Computation"},{"key":"10.3233\/JIFS-201930_ref31","doi-asserted-by":"crossref","first-page":"109836","DOI":"10.1016\/j.chaos.2020.109836","article-title":"First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model","volume":"137","author":"Jin","year":"2020","journal-title":"Chaos Solitons & Fractals"},{"issue":"4","key":"10.3233\/JIFS-201930_ref32","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1023\/A:1016601312158","article-title":"The numerical solution of fractional differential equations: speed versus accuracy","volume":"26","author":"Ford","year":"2001","journal-title":"Numerical Algorithms"},{"issue":"1-4","key":"10.3233\/JIFS-201930_ref33","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1023\/A:1016592219341","article-title":"A predictorcorrector approach for the numerical solution of fractional differential equations","volume":"29","author":"Diethelm","year":"2002","journal-title":"Nonlinear Dynamics"},{"doi-asserted-by":"crossref","unstructured":"Chen X. and Gao J. , Uncertain term structure model of interest rate, Soft Computing 17 04 (2013).","key":"10.3233\/JIFS-201930_ref35","DOI":"10.1007\/s00500-012-0927-0"}],"container-title":["Journal of Intelligent & Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-201930","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,26]],"date-time":"2024-11-26T13:51:27Z","timestamp":1732629087000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospress&doi=10.3233\/JIFS-201930"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,2]]},"references-count":32,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.3233\/jifs-201930","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"type":"print","value":"1064-1246"},{"type":"electronic","value":"1875-8967"}],"subject":[],"published":{"date-parts":[[2021,3,2]]}}}