{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:08:18Z","timestamp":1778717298341,"version":"3.51.4"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s11075-025-02178-7","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T08:07:13Z","timestamp":1753258033000},"page":"1317-1353","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stability and error estimates of operator-splitting methods for pricing American option under regime-switching model with jumps"],"prefix":"10.1007","volume":"102","author":[{"given":"Pradeep Kumar","family":"Sahu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kuldip Singh","family":"Patel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muddun","family":"Bhuruth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,23]]},"reference":[{"key":"2178_CR1","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1086\/260062","volume":"81","author":"F Black","year":"1973","unstructured":"Black, F., Scholes, M.: Pricing of options and corporate liabilities. J. Political Econ. 81, 637\u2013654 (1973)","journal-title":"J. Political Econ."},{"key":"2178_CR2","doi-asserted-by":"crossref","unstructured":"Merton, R.\u00a0C.: Theory of rational option pricing. Bell J. Econ. Manag. Sci. pp. 141\u2013183 (1973)","DOI":"10.2307\/3003143"},{"issue":"8","key":"2178_CR3","doi-asserted-by":"publisher","first-page":"1086","DOI":"10.1287\/mnsc.48.8.1086.166","volume":"48","author":"SG Kou","year":"2002","unstructured":"Kou, S.G.: A jump-diffusion model for option pricing. Manag. Sci. 48(8), 1086\u20131101 (2002)","journal-title":"Manag. Sci."},{"issue":"2","key":"2178_CR4","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1093\/rfs\/6.2.327","volume":"6","author":"SL Heston","year":"1993","unstructured":"Heston, S.L.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6(2), 327\u2013343 (1993)","journal-title":"Rev. Financ. Stud."},{"key":"2178_CR5","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/s11075-016-0138-3","volume":"74","author":"MN Koleva","year":"2017","unstructured":"Koleva, M.N., Mudzimbabwe, W., Vulkov, L.G.: Fourth-order compact schemes for a parabolic-ordinary system of European option pricing liquidity shocks model. Numer. Algorithms 74, 59\u201375 (2017)","journal-title":"Numer. Algorithms"},{"issue":"5","key":"2178_CR6","doi-asserted-by":"publisher","first-page":"2144","DOI":"10.1137\/110820920","volume":"33","author":"Y Huang","year":"2011","unstructured":"Huang, Y., Forsyth, P.A., Labahn, G.: Methods for pricing American options under regime switching. SIAM. Sci. Comput. 33(5), 2144\u20132168 (2011)","journal-title":"SIAM. Sci. Comput."},{"key":"2178_CR7","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.apnum.2012.10.005","volume":"65","author":"AF Bastani","year":"2013","unstructured":"Bastani, A.F., Ahmadi, Z., Damircheli, D.: A radial basis collocation method for pricing American options under regime-switching jump-diffusion models. Appl. Numer. Math. 65, 79\u201390 (2013)","journal-title":"Appl. Numer. Math."},{"issue":"4","key":"2178_CR8","doi-asserted-by":"publisher","first-page":"69","DOI":"10.21314\/JCF.2002.084","volume":"5","author":"BF Nielsen","year":"2002","unstructured":"Nielsen, B.F., Skavhaug, O., Tveito, A.: Penalty and front-fixing methods for the numerical solution of American option problems. J. Comput. Financ. 5(4), 69\u201398 (2002)","journal-title":"J. Comput. Financ."},{"issue":"1","key":"2178_CR9","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.cam.2007.10.044","volume":"222","author":"D Tangman","year":"2008","unstructured":"Tangman, D., Gopaul, A., Bhuruth, M.: A fast high-order finite difference algorithm for pricing American options. J. Comput. Appl. Math. 222(1), 17\u201329 (2008)","journal-title":"J. Comput. Appl. Math."},{"issue":"7","key":"2178_CR10","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1016\/j.aml.2004.06.010","volume":"17","author":"S Ikonen","year":"2004","unstructured":"Ikonen, S., Toivanen, J.: Operator splitting methods for American option pricing. Appl. Math. Lett. 17(7), 809\u2013814 (2004)","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"2178_CR11","doi-asserted-by":"publisher","first-page":"1949","DOI":"10.1137\/060674697","volume":"30","author":"J Toivanen","year":"2008","unstructured":"Toivanen, J.: Numerical valuation of European and American options under Kou\u2019s jump-diffusion model. SIAM J. Sci. Comput. 30(4), 1949\u20131970 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"2178_CR12","doi-asserted-by":"publisher","first-page":"1860","DOI":"10.1137\/100806552","volume":"33","author":"Y Kwon","year":"2011","unstructured":"Kwon, Y., Lee, Y.: A second-order tridiagonal method for American options under jump-diffusion models. SIAM J. Sci. Comput. 33(4), 1860\u20131872 (2011)","journal-title":"SIAM J. Sci. Comput."},{"issue":"10","key":"2178_CR13","doi-asserted-by":"publisher","first-page":"2434","DOI":"10.1016\/j.camwa.2018.08.040","volume":"76","author":"M Haghi","year":"2018","unstructured":"Haghi, M., Mollapourasl, R., Vanmaele, M.: An RBF-FD method for pricing American options under jump-diffusion models. Comput. Math. Appl. 76(10), 2434\u20132459 (2018)","journal-title":"Comput. Math. Appl."},{"issue":"7","key":"2178_CR14","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1016\/j.apnum.2011.02.002","volume":"61","author":"S Salmi","year":"2011","unstructured":"Salmi, S., Toivanen, J.: An iterative method for pricing American options under jump-diffusion models. Appl. Numer. Math. 61(7), 821\u2013831 (2011)","journal-title":"Appl. Numer. Math."},{"key":"2178_CR15","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.matcom.2020.07.015","volume":"189","author":"R Company","year":"2021","unstructured":"Company, R., Egorova, V.N., J\u00f3dar, L.: A front-fixing ETD numerical method for solving jump-diffusion American option pricing problems. Math. Comput. Simul. 189, 69\u201384 (2021)","journal-title":"Math. Comput. Simul."},{"key":"2178_CR16","doi-asserted-by":"crossref","unstructured":"Ikonen, S., Toivanen, J.: Efficient numerical methods for pricing American options under stochastic volatility. Numer. Methods Partial Differential Equations: Int. J. 24(1), 104\u2013126 (2008)","DOI":"10.1002\/num.20239"},{"key":"2178_CR17","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/s00211-009-0227-5","volume":"113","author":"S Ikonen","year":"2009","unstructured":"Ikonen, S., Toivanen, J.: Operator splitting methods for pricing American options under stochastic volatility. Numer. Math. 113, 299\u2013324 (2009)","journal-title":"Numer. Math."},{"issue":"3","key":"2178_CR18","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1016\/j.camwa.2014.06.015","volume":"68","author":"Y Lee","year":"2014","unstructured":"Lee, Y.: Financial options pricing with regime-switching jump-diffusions. Comput. Math. Appl. 68(3), 392\u2013404 (2014)","journal-title":"Comput. Math. Appl."},{"key":"2178_CR19","doi-asserted-by":"crossref","unstructured":"Lee, S., Lee, Y.: Stability of numerical methods under the regime-switching jump-diffusion model with variable coefficients. ESAIM: Math. Model. Num. Anal. 53(5), 1741\u20131762 (2019)","DOI":"10.1051\/m2an\/2019035"},{"key":"2178_CR20","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.apnum.2018.07.008","volume":"134","author":"R Mollapourasl","year":"2018","unstructured":"Mollapourasl, R., Haghi, M., Liu, R.: Localized kernel-based approximation for pricing financial options under regime switching jump diffusion model. Appl. Numer. Math. 134, 81\u2013104 (2018)","journal-title":"Appl. Numer. Math."},{"issue":"2","key":"2178_CR21","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1007\/s11075-023-01719-2","volume":"97","author":"R Yadav","year":"2024","unstructured":"Yadav, R., Yadav, D.K., Kumar, A.: RBF-FD based some implicit-explicit methods for pricing option under regime-switching jump-diffusion model with variable coefficients. Numer. Algorithms 97(2), 645\u2013685 (2024)","journal-title":"Numer. Algorithms"},{"issue":"8","key":"2178_CR22","doi-asserted-by":"publisher","first-page":"2646","DOI":"10.1002\/mma.5539","volume":"42","author":"Y Chen","year":"2019","unstructured":"Chen, Y., Xiao, A., Wang, W.: An IMEX-BDF2 compact scheme for pricing options under regime-switching jump-diffusion models. Math. Methods Appl. Sci. 42(8), 2646\u20132663 (2019)","journal-title":"Math. Methods Appl. Sci."},{"issue":"6","key":"2178_CR23","doi-asserted-by":"publisher","first-page":"1137","DOI":"10.1080\/00207160.2018.1446526","volume":"96","author":"K Kazmi","year":"2019","unstructured":"Kazmi, K.: An IMEX predictor-corrector method for pricing options under regime-switching jump-diffusion models. Int. J. Comput. Math. 96(6), 1137\u20131157 (2019)","journal-title":"Int. J. Comput. Math."},{"key":"2178_CR24","doi-asserted-by":"publisher","first-page":"112919","DOI":"10.1016\/j.chaos.2022.112919","volume":"166","author":"M Shirzadi","year":"2023","unstructured":"Shirzadi, M., Rostami, M., Dehghan, M., Li, X.: American options pricing under regime-switching jump-diffusion models with meshfree finite point method. Chaos, Solitons & Fractals 166, 112919 (2023)","journal-title":"Chaos, Solitons & Fractals"},{"key":"2178_CR25","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.cam.2015.12.019","volume":"300","author":"N Rambeerich","year":"2016","unstructured":"Rambeerich, N., Pantelous, A.A.: A high order finite element scheme for pricing options under regime switching jump diffusion processes. J. Comput. Appl. Math. 300, 83\u201396 (2016)","journal-title":"J. Comput. Appl. Math."},{"issue":"8","key":"2178_CR26","doi-asserted-by":"publisher","first-page":"2989","DOI":"10.1016\/j.camwa.2018.01.026","volume":"75","author":"M Yousuf","year":"2018","unstructured":"Yousuf, M., Khaliq, A., Alrabeei, S.: Solving complex PIDE systems for pricing American option under multi-state regime-switching jump-diffusion model. Comput. Math. Appl. 75(8), 2989\u20133001 (2018)","journal-title":"Comput. Math. Appl."},{"key":"2178_CR27","doi-asserted-by":"publisher","first-page":"3691","DOI":"10.1007\/s40314-017-0540-z","volume":"37","author":"S Heidari","year":"2018","unstructured":"Heidari, S., Azari, H.: A front-fixing finite element method for pricing American options under regime-switching jump-diffusion models. Comput. Appl. Math. 37, 3691\u20133707 (2018)","journal-title":"Comput. Appl. Math."},{"key":"2178_CR28","doi-asserted-by":"publisher","first-page":"115484","DOI":"10.1016\/j.cam.2023.115484","volume":"437","author":"C Huang","year":"2024","unstructured":"Huang, C., Song, H., Yang, J., Zhou, B.: Error analysis of finite difference scheme for American option pricing under regime-switching with jumps. J. Comput. Appl. Math. 437, 115484 (2024)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"2178_CR29","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s10915-020-01137-9","volume":"82","author":"F Chen","year":"2020","unstructured":"Chen, F., Shen, J.: Stability and error analysis of operator splitting methods for American options under the Black-Scholes model. J. Sci. Comput. 82(2), 33 (2020)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"2178_CR30","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1007\/s40314-023-02510-8","volume":"43","author":"DK Yadav","year":"2024","unstructured":"Yadav, D.K., Bhardwaj, A., Kumar, A.: Errors in the IMEX-BDF-OS methods for pricing American style options under the jump-diffusion model. Comput. Appl. Math. 43(1), 6 (2024)","journal-title":"Comput. Appl. Math."},{"issue":"9","key":"2178_CR31","doi-asserted-by":"publisher","first-page":"1112","DOI":"10.1080\/00207160.2012.669475","volume":"89","author":"S Salmi","year":"2012","unstructured":"Salmi, S., Toivanen, J.: Comparison and survey of finite difference methods for pricing American options under finite activity jump-diffusion models. Int. J. Comput. Math. 89(9), 1112\u20131134 (2012)","journal-title":"Int. J. Comput. Math."},{"key":"2178_CR32","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.apnum.2014.05.007","volume":"84","author":"S Salmi","year":"2014","unstructured":"Salmi, S., Toivanen, J.: IMEX schemes for pricing options under jump-diffusion models. Appl. Num. Math. 84, 3\u201345 (2014)","journal-title":"Appl. Num. Math."},{"key":"2178_CR33","unstructured":"Elliott, R.\u00a0J., Aggoun, L., Moore, J.\u00a0B.: Hidden Markov models: Estimation and control. Vol.\u00a029, Springer Science & Business Media, (2008)"},{"key":"2178_CR34","doi-asserted-by":"crossref","unstructured":"Achdou, Y., Pironneau, O.: Computational methods for option pricing, SIAM, (2005)","DOI":"10.1137\/1.9780898717495"},{"key":"2178_CR35","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/BF02935787","volume":"19","author":"E Emmrich","year":"2005","unstructured":"Emmrich, E.: Stability and error of the variable two-step BDF for semilinear parabolic problems. J. Appl. Math. Comput. 19, 33\u201355 (2005)","journal-title":"J. Appl. Math. Comput."},{"key":"2178_CR36","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/BF00047211","volume":"21","author":"P Jaillet","year":"1990","unstructured":"Jaillet, P., Lamberton, D., Lapeyre, B.: Variational inequalities and the pricing of American options. Acta Appl. Math. 21, 263\u2013289 (1990)","journal-title":"Acta Appl. Math."},{"issue":"3","key":"2178_CR37","doi-asserted-by":"publisher","first-page":"1289","DOI":"10.1137\/18M1194328","volume":"57","author":"W Wang","year":"2019","unstructured":"Wang, W., Chen, Y., Fang, H.: On the variable two-step IMEX BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance. SIAM J. Numer. Anal. 57(3), 1289\u20131317 (2019)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-025-02178-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-025-02178-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-025-02178-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T23:12:36Z","timestamp":1778713956000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-025-02178-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,23]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["2178"],"URL":"https:\/\/doi.org\/10.1007\/s11075-025-02178-7","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,23]]},"assertion":[{"value":"3 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"The authors declare that they have no conflict of interest.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}