{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:25:14Z","timestamp":1787336714576,"version":"build-2736575974"},"reference-count":58,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p>This paper considers pricing European options in a large class of one-dimensional Markovian jump processes known as subordinate diffusions, which are obtained by time changing a diffusion process with an independent L\u00e9vy or additive random clock. These jump processes are non-L\u00e9vy in general, and they can be viewed as a natural generalization of many popular L\u00e9vy processes used in finance. Subordinate diffusions offer richer jump behavior than L\u00e9vy processes and they have found a variety of applications in financial modeling. The pricing problem for these processes presents unique challenges, as existing numerical PIDE schemes fail to be efficient and the applicability of transform methods to many subordinate diffusions is unclear. We develop a novel method based on a finite difference approximation of spatial derivatives and matrix eigendecomposition, and it can deal with diffusions that exhibit various types of boundary behavior. Since financial payoffs are typically not smooth, we apply a smoothing technique and use extrapolation to speed up convergence. We provide convergence and error analysis and perform various numerical experiments to show that the proposed method is fast and accurate. Extension to pricing path-dependent options will be investigated in a followup paper.<\/jats:p>","DOI":"10.1137\/15m1048926","type":"journal-article","created":{"date-parts":[[2016,7,12]],"date-time":"2016-07-12T10:57:14Z","timestamp":1468321034000},"page":"B539-B569","source":"Crossref","is-referenced-by-count":26,"title":["Option Pricing in Some Non-L\u00e9vy Jump Models"],"prefix":"10.1137","volume":"38","author":[{"given":"Lingfei","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gongqiu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2016,7,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011354913068"},{"key":"atypb2","first-page":"41","volume":"2","author":"O.","year":"1998","journal-title":"Finance Stoch."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1088\/1469-7688\/1\/3\/303"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8163-0"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2007.00314.x"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1142\/4955"},{"key":"atypb7","volume-title":"J. Comput. Finance","author":"Boyarchenko S.","year":"2013"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/9.4.1211"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1969-0258291-7"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-006-0012-6"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.1999.043"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/10.3.525"},{"key":"atypb13","volume-title":"Financial Modeling with Jump Processes","author":"Cont R.","year":"2004"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903436186"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-005-0153-z"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drh011"},{"key":"atypb17","unstructured":"I. S. Dhillon,\n                      A new $O(n^2)$ Algorithm for the Symmetric Tridiagonal Eigenvalue\/Eigenvector Problem\n                      , Ph.D. thesis, The University of California at Berkeley, 1997."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830176"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1214\/10-AAP698"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/080718061"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-009-0252-4"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2008.00338.x"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1070.0419"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-009-0096-x"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1994.1429"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1974-0356524-1"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00080"},{"key":"atypb28","volume-title":"A Second Course in Stochastic Processes","author":"Karlin S.","year":"1981"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/018"},{"key":"atypb30","volume-title":"Linear and quasi-linear equations of parabolic type","volume":"23","author":"Ladyzhenskai\u00cd\u00a1a O. A.","year":"1988"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14390-8_41"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-016-0300-8"},{"key":"atypb33","volume-title":"Pure jump models for pricing and hedging VIX derivatives, working paper","author":"Li J.","year":"2015"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2013.1167"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2013.11.017"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1111\/mafi.12003"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-015-0271-1"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2013.06.010"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1080\/14697688.2015.1125521"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2015.08.010"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2012.06.002"},{"key":"atypb42","volume-title":"Handbook of Financial Engineering, Handbooks in Operations Research and Management Sciences","author":"Linetsky V.","year":"2008"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1137\/070683878"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.2008.181"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1956-0087012-3"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2010.00411.x"},{"key":"atypb47","volume-title":"Math. Finance","author":"Mendoza-Arriaga R.","year":"2014"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1214\/13-AAP936"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-8965-1"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1007\/978-88-470-1781-8"},{"key":"atypb51","doi-asserted-by":"publisher","DOI":"10.21314\/JCF.2003.101"},{"key":"atypb52","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(96)00120-2"},{"key":"atypb53","volume-title":"L\u00e9vy Processes and Infinitely Divisible Distributions","author":"Sato K.","year":"1999"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1515\/9783110269338"},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1974-0341889-7"},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2010.08342"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(79)90039-9"},{"key":"atypb58","first-page":"210","volume":"5","author":"Yueh W.-C.","year":"2005","journal-title":"Appl. Math. E-Notes"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/15M1048926","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:27:56Z","timestamp":1787333276000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/15M1048926"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1]]},"references-count":58,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["10.1137\/15M1048926"],"URL":"https:\/\/doi.org\/10.1137\/15m1048926","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1]]}}}