{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T11:12:41Z","timestamp":1759921961780,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,15]],"date-time":"2025-01-15T00:00:00Z","timestamp":1736899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003336","name":"BNSF","doi-asserted-by":"publisher","award":["KP-06-M62\/1","BG-RRP-2.013-0001-C01"],"award-info":[{"award-number":["KP-06-M62\/1","BG-RRP-2.013-0001-C01"]}],"id":[{"id":"10.13039\/501100003336","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Union\u2013NextGenerationEU","award":["KP-06-M62\/1","BG-RRP-2.013-0001-C01"],"award-info":[{"award-number":["KP-06-M62\/1","BG-RRP-2.013-0001-C01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Volatility recovery is of paramount importance in contemporary finance. Volatility levels are heavily used in risk and portfolio management. We employ the Hull\u2013White one- and two-factor models to describe the market condition. We computationally recover the volatility term structure as a piecewise-linear function of time. For every maturity, a cost functional, defined as the squared differences between theoretical and market prices, is minimized and the respective linear part is reconstructed. On the last time steps, before each maturity, the derivative price is decomposed in order to make the minimization problem analytically solvable. The procedure works fast since only scalar values are obtained on each minimization. However, the predictor\u2013corrector nature of the algorithm allows for the precise recovery of very complex volatility functions. An implicit scheme is used to solve the PDEs on bounded domains. The computational simulations with artificial and real data show that the proposed algorithm is stable, accurate and efficient.<\/jats:p>","DOI":"10.3390\/computation13010016","type":"journal-article","created":{"date-parts":[[2025,1,15]],"date-time":"2025-01-15T04:42:08Z","timestamp":1736916128000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computational Reconstruction of the Volatility Term Structure in the General Hull\u2013White Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9826-9603","authenticated-orcid":false,"given":"Slavi G.","family":"Georgiev","sequence":"first","affiliation":[{"name":"Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev Str., 1113 Sofia, Bulgaria"},{"name":"Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0684-8574","authenticated-orcid":false,"given":"Lubin G.","family":"Vulkov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1093\/rfs\/3.4.573","article-title":"Pricing interest-rate-derivative securities","volume":"3","author":"Hull","year":"1990","journal-title":"Rev. Fin. 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