{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T02:36:53Z","timestamp":1773801413230,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["23-21-00474"],"award-info":[{"award-number":["23-21-00474"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Manag Sci"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s10287-024-00519-w","type":"journal-article","created":{"date-parts":[[2024,6,9]],"date-time":"2024-06-09T16:01:23Z","timestamp":1717948883000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A simplified Wiener\u2013Hopf factorization method for pricing double barrier options under L\u00e9vy processes"],"prefix":"10.1007","volume":"21","author":[{"given":"Oleg","family":"Kudryavtsev","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,9]]},"reference":[{"key":"519_CR1","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1287\/ijoc.1050.0137","volume":"18","author":"J Abate","year":"2006","unstructured":"Abate J, Whitt W (2006) A unified framework for numerically inverting Laplace transforms. INFORMS J Comput 18:408\u2013421. https:\/\/doi.org\/10.1287\/ijoc.1050.0137","journal-title":"INFORMS J Comput"},{"issue":"1","key":"519_CR2","doi-asserted-by":"publisher","first-page":"79","DOI":"10.21314\/JCF.2007.164","volume":"11","author":"S Asmussen","year":"2007","unstructured":"Asmussen S et al (2007) Pricing equity default swaps under an approximation to the CGMY L\u00e9vy model. J Comput Financ 11(1):79\u201393","journal-title":"J Comput Financ"},{"key":"519_CR3","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s10287-021-00394-9","volume":"18","author":"LV Ballestra","year":"2021","unstructured":"Ballestra LV (2021) Enhancing finite difference approximations for double barrier options: mesh optimization and repeated Richardson extrapolation. Comput Manag Sci 18:239\u2013263. https:\/\/doi.org\/10.1007\/s10287-021-00394-9","journal-title":"Comput Manag Sci"},{"key":"519_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2023.106592","volume":"130","author":"M Bosupeng","year":"2024","unstructured":"Bosupeng M et al (2024) Does exchange rate volatility affect the impact of appreciation and depreciation on the trade balance? A nonlinear bivariate approach. Econ Modell 130:106592","journal-title":"Econ Modell"},{"key":"519_CR5","doi-asserted-by":"crossref","unstructured":"B\u00f6ttcher A, Karlovich YI, Spitkovsky IM (2002) Convolution operators and factorization of almost periodic matrix functions. In: Operator Theory: Advances and Applications, 131. Birkh\u00e4user Verlag","DOI":"10.1007\/978-3-0348-8152-4_8"},{"issue":"3","key":"519_CR6","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1111\/j.1467-9965.2010.00469.x","volume":"22","author":"M Boyarchenko","year":"2011","unstructured":"Boyarchenko M, Levendorski\u01d0 S (2011) Valuation of continuously monitored double barrier options and related securities. Math Financ 22(3):419\u2013444. https:\/\/doi.org\/10.1111\/j.1467-9965.2010.00469.x","journal-title":"Math Financ"},{"key":"519_CR7","doi-asserted-by":"crossref","unstructured":"Boyarchenko SI, Levendorski\u01d0 SZ (2002) Non-Gaussian Merton-Black-Scholes Theory. Advanced Series on Statistical Science & Applied Probability, 9, World Scientific Publishing Co., Singapore","DOI":"10.1142\/9789812777485"},{"key":"519_CR8","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s10436-004-0010-7","volume":"1","author":"SI Boyarchenko","year":"2005","unstructured":"Boyarchenko SI, Levendorski\u01d0 SZ (2005) American options: the EPV pricing model. Ann Financ 1:267\u2013292. https:\/\/doi.org\/10.1007\/s10436-004-0010-7","journal-title":"Ann Financ"},{"issue":"2","key":"519_CR9","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1086\/338705","volume":"75","author":"Carr","year":"2002","unstructured":"Carr et al (2002) The fine structure of asset returns: an empirical investigation. J Bus 75(2):305\u2013332. https:\/\/doi.org\/10.1086\/338705","journal-title":"J Bus"},{"key":"519_CR10","volume-title":"Financial modelling with jump processes","author":"R Cont","year":"2008","unstructured":"Cont R, Tankov P (2008) Financial modelling with jump processes, 2nd edn. Chapman & Hall\/CRC, Boca Raton","edition":"2"},{"issue":"4","key":"519_CR11","doi-asserted-by":"publisher","first-page":"1596","DOI":"10.1137\/S0036142903436186","volume":"43","author":"R Cont","year":"2005","unstructured":"Cont R, Voltchkova E (2005) A finite difference scheme for option pricing in jump diffusion and exponential L\u00e9vy models. SIAM J Numer Anal 43(4):1596\u20131626","journal-title":"SIAM J Numer Anal"},{"issue":"1","key":"519_CR12","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1142\/S0219024910005681","volume":"13","author":"J Crosby","year":"2010","unstructured":"Crosby J et al (2010) Approximating L\u00e9vy processes with a view to option pricing. Int J Theor Appl Financ 13(1):63\u201391. https:\/\/doi.org\/10.1142\/S0219024910005681","journal-title":"Int J Theor Appl Financ"},{"key":"519_CR13","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF02551274","volume":"2","author":"G Cybenko","year":"1989","unstructured":"Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst 2:303\u2013314. https:\/\/doi.org\/10.1007\/BF02551274","journal-title":"Math Control Signals Syst"},{"key":"519_CR14","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/978-1-4614-7248-3_3","volume-title":"Quantitative energy finance","author":"E Eberlein","year":"2014","unstructured":"Eberlein E (2014) Fourier-based valuation methods in mathematical finance. In: Benth F, Kholodnyi V, Laurence P (eds) Quantitative energy finance. Springer, New York, pp 85\u2013114"},{"key":"519_CR15","doi-asserted-by":"crossref","unstructured":"Gil A, Segura J, Temme NM (2007) Numerical methods for special functions. SIAM, Philadelphia","DOI":"10.1137\/1.9780898717822"},{"key":"519_CR16","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s11147-017-9139-1","volume":"21","author":"P Hieber","year":"2018","unstructured":"Hieber P (2018) Pricing exotic options in a regime switching economy: a Fourier transform method. Rev Deriv Res 21:231\u2013252","journal-title":"Rev Deriv Res"},{"issue":"2","key":"519_CR17","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","volume":"4","author":"K Hornik","year":"1991","unstructured":"Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4(2):251\u2013257","journal-title":"Neural Netw"},{"key":"519_CR18","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/j.econmod.2012.09.017","volume":"34","author":"O Holtem\u00f6ller","year":"2013","unstructured":"Holtem\u00f6ller O, Mallick S (2013) Exchange rate regime, real misalignment and currency crises. Econ Model 34:5\u201314","journal-title":"Econ Model"},{"key":"519_CR19","doi-asserted-by":"crossref","unstructured":"Itkin A (2017) Pricing derivatives under L\u00e9vy models. In: Pseudo-differential operators, 12. Birkh\u00e4user New York","DOI":"10.1007\/978-1-4939-6792-6"},{"key":"519_CR20","doi-asserted-by":"publisher","first-page":"1086","DOI":"10.1287\/mnsc.48.8.1086.166","volume":"48","author":"SG Kou","year":"2002","unstructured":"Kou SG (2002) A jump-diffusion model for option pricing. Manage Sci 48:1086\u20131101","journal-title":"Manage Sci"},{"key":"519_CR21","doi-asserted-by":"publisher","first-page":"61","DOI":"10.21314\/JCF.2017.332","volume":"21","author":"JL Kirkby","year":"2017","unstructured":"Kirkby JL (2017) Robust option pricing with characteristic functions and the B-spline order of density projection. J Comput Financ 21:61\u2013100. https:\/\/doi.org\/10.21314\/JCF.2017.332","journal-title":"J Comput Financ"},{"key":"519_CR22","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1134\/S2070048211060068","volume":"3","author":"O Kudryavtsev","year":"2011","unstructured":"Kudryavtsev O (2011) An efficient numerical method to solve a special class of integro-differential equations relating to the Levy models. Math Models Comput Simul 3:706\u2013711. https:\/\/doi.org\/10.1134\/S2070048211060068","journal-title":"Math Models Comput Simul"},{"key":"519_CR23","doi-asserted-by":"crossref","unstructured":"Kudryavtsev O (2013) Finite difference methods for option pricing under L\u00e9vy processes: Wiener\u2013Hopf factorization approach. Sci World J 963625","DOI":"10.1155\/2013\/963625"},{"issue":"2","key":"519_CR24","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1137\/S0040585X97T989441","volume":"64","author":"OE Kudryavtsev","year":"2019","unstructured":"Kudryavtsev OE (2019) Approximate Wiener\u2013Hopf factorization and Monte Carlo methods for ley processes. Theory Probab Appl 64(2):186\u2013208. https:\/\/doi.org\/10.1137\/S0040585X97T989441","journal-title":"Theory Probab Appl"},{"key":"519_CR25","doi-asserted-by":"publisher","unstructured":"Kudryavtsev O (2021) A simple Wiener\u2013Hopf factorization approach for pricing double-barrier options. In: Karapetyants AN, Pavlov IV, Shiryaev AN (eds) Operator theory and harmonic analysis. OTHA 2020. Springer Proceedings in Mathematics & Statistics, 358. Springer, Cham, pp 273\u2013291. https:\/\/doi.org\/10.1007\/978-3-030-76829-4_15","DOI":"10.1007\/978-3-030-76829-4_15"},{"key":"519_CR26","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/s00780-009-0103-2","volume":"13","author":"O Kudryavtsev","year":"2009","unstructured":"Kudryavtsev O, Levendorski\u01d0 S (2009) Fast and accurate pricing of barrier options under L\u00e9vy processes. Financ Stoch 13:531\u2013562. https:\/\/doi.org\/10.1007\/s00780-009-0103-2","journal-title":"Financ Stoch"},{"issue":"4","key":"519_CR27","first-page":"1310","volume":"28","author":"O Kudryavtsev","year":"2020","unstructured":"Kudryavtsev O, Luzhetskaya P (2020) The Wiener\u2013Hopf factorization for pricing options made easy. Eng Lett 28(4):1310\u20131317","journal-title":"Eng Lett"},{"key":"519_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.econmod.2021.105524","volume":"101","author":"A Kumar","year":"2021","unstructured":"Kumar A, Mallick S, Sinha A (2021) Is uncertainty the same everywhere? Advanced versus emerging economies. Econ Modell 101:105524","journal-title":"Econ Modell"},{"key":"519_CR29","volume-title":"Introductory lectures on fluctuations of L\u00e9vy processes with applications","author":"AE Kyprianou","year":"2006","unstructured":"Kyprianou AE (2006) Introductory lectures on fluctuations of L\u00e9vy processes with applications. Springer, Berlin"},{"key":"519_CR30","unstructured":"Lelong J (2017) PNL: A free scientific library. https:\/\/pnlnum.github.io\/pnl\/"},{"issue":"2","key":"519_CR31","doi-asserted-by":"publisher","first-page":"69","DOI":"10.21314\/JCF.2005.157","volume":"9","author":"S Levendorski\u01d0","year":"2006","unstructured":"Levendorski\u01d0 S, Kudryavtsev O, Zherder V (2006) The relative efficiency of numerical methods for pricing American options under L\u00e9vy processes. J Comput Financ 9(2):69\u201397","journal-title":"J Comput Financ"},{"key":"519_CR32","unstructured":"Saux NL (2008) Approximating L\u00e9vy processes by a hyperexponential jump-diffusion process with a view to option pricing. M.Sc Dissertation, Imperial College London. http:\/\/www.john-crosby.co.uk"},{"issue":"1","key":"519_CR33","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/j.ejor.2018.04.016","volume":"271","author":"CE Phelan","year":"2018","unstructured":"Phelan CE et al (2018) Fluctuation identities with continuous monitoring and their application to price barrier options. Eur J Oper Res 271(1):210\u2013223. https:\/\/doi.org\/10.1016\/j.ejor.2018.04.016","journal-title":"Eur J Oper Res"},{"key":"519_CR34","volume-title":"Numerical recipes in C: the art of scientific computing","author":"W Press","year":"2007","unstructured":"Press W et al (2007) Numerical recipes in C: the art of scientific computing, 3rd edn. Cambridge Univ. Press, Cambridge","edition":"3"},{"key":"519_CR35","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s10690-007-9048-7","volume":"13","author":"J Poirot","year":"2006","unstructured":"Poirot J, Tankov P (2006) Monte Carlo option pricing for tempered stable (CGMY) processes. Asia-Pacific Finan Mark 13:327\u2013344","journal-title":"Asia-Pacific Finan Mark"},{"key":"519_CR36","volume-title":"L\u00e9vy processes and infinitely divisible distributions","author":"K Sato","year":"2013","unstructured":"Sato K (2013) L\u00e9vy processes and infinitely divisible distributions, 2nd edn. Cambridge University Press, Cambridge","edition":"2"},{"issue":"4","key":"519_CR37","doi-asserted-by":"publisher","first-page":"31","DOI":"10.21314\/JCF.2007.169","volume":"10","author":"I Wang","year":"2007","unstructured":"Wang I, Wan J, Forsyth P (2007) Robust numerical valuation of European and American options under the CGMY process. J Comput Financ 10(4):31\u201370","journal-title":"J Comput Financ"}],"container-title":["Computational Management Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-024-00519-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10287-024-00519-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10287-024-00519-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T12:15:50Z","timestamp":1719058550000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10287-024-00519-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["519"],"URL":"https:\/\/doi.org\/10.1007\/s10287-024-00519-w","relation":{},"ISSN":["1619-697X","1619-6988"],"issn-type":[{"value":"1619-697X","type":"print"},{"value":"1619-6988","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6]]},"assertion":[{"value":"17 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author states that there is no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}],"article-number":"37"}}