{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:34:52Z","timestamp":1772296492309,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,10,30]],"date-time":"2008-10-30T00:00:00Z","timestamp":1225324800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Finance Stoch"],"published-print":{"date-parts":[[2009,1]]},"DOI":"10.1007\/s00780-008-0078-4","type":"journal-article","created":{"date-parts":[[2008,10,29]],"date-time":"2008-10-29T01:52:57Z","timestamp":1225245177000},"page":"1-48","source":"Crossref","is-referenced-by-count":49,"title":["Local volatility dynamic models"],"prefix":"10.1007","volume":"13","author":[{"given":"Ren\u00e9","family":"Carmona","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergey","family":"Nadtochiy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,10,30]]},"reference":[{"key":"78_CR1","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717495","volume-title":"Computational Methods for Option Pricing","author":"Y. Achdou","year":"2005","unstructured":"Achdou, Y., Pironneau, O.: Computational Methods for Option Pricing. SIAM, Philadelphia (2005)"},{"key":"78_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0060286","volume-title":"Konvergenz von Differenzenverfahren f\u00fcr lineare und nichtlineare Anfangswertaufgaben","author":"R. Ansorge","year":"1970","unstructured":"Ansorge, R., Hass, R.: Konvergenz von Differenzenverfahren f\u00fcr lineare und nichtlineare Anfangswertaufgaben. Springer, Berlin (1970)"},{"issue":"4","key":"78_CR3","first-page":"607","volume":"22","author":"D.G. Aronson","year":"1968","unstructured":"Aronson, D.G.: Non-negative solutions to linear parabolic equations. Ann. Sc. Norm. Super. Pisa Cl. Sci. 22(4), 607\u2013694 (1968)","journal-title":"Ann. Sc. Norm. Super. Pisa Cl. Sci."},{"key":"78_CR4","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1088\/1469-7688\/2\/1\/305","volume":"2","author":"H. Berestycki","year":"2002","unstructured":"Berestycki, H., Busca, J., Florent, I.: Asymptotics and calibration of local volatility models. Quant. Finance 2, 61\u201369 (2002)","journal-title":"Quant. Finance"},{"key":"78_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/cpa.20039","volume":"57","author":"H. Berestycki","year":"2004","unstructured":"Berestycki, H., Busca, J., Florent, I.: Computing the implied volatility in stochastic volatility models. Commun. Pure Appl. Math. 57, 1\u201322 (2004)","journal-title":"Commun. Pure Appl. Math."},{"key":"78_CR6","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1214\/aoms\/1177729032","volume":"24","author":"D. Blackwell","year":"1953","unstructured":"Blackwell, D.: Equivalent comparisons of experiments. Ann. Math. Stat. 24, 265\u2013272 (1953)","journal-title":"Ann. Math. Stat."},{"key":"78_CR7","first-page":"151","volume-title":"Mathematical Finance\u2014Bachelier Congress","author":"D. Brigo","year":"2001","unstructured":"Brigo, D., Mercurio, F.: Displaced and mixture diffusions for analytically tractable smile models. In: Geman, H., Madan, D., Pliska, St.R., Vorst, T. (eds.) Mathematical Finance\u2014Bachelier Congress, 2000, pp. 151\u2013174. Springer, Berlin (2001)"},{"key":"78_CR8","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1142\/S0219024902001511","volume":"5","author":"D. Brigo","year":"2002","unstructured":"Brigo, D., Mercurio, F.: Lognormal-mixture dynamics and calibration to market volatility smiles. Int. J. Theor. Appl. Finance 5, 427\u2013446 (2002)","journal-title":"Int. J. Theor. Appl. Finance"},{"key":"78_CR9","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1080\/14697680600668071","volume":"6","author":"H. Buehler","year":"2006","unstructured":"Buehler, H.: Expensive martingales. Quant. Finance 6, 207\u2013218 (2006)","journal-title":"Quant. Finance"},{"key":"78_CR10","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-540-73327-0","volume-title":"Paris\u2013Princeton Lectures in Mathematical Finance","author":"R. Carmona","year":"2007","unstructured":"Carmona, R.: HJM: A unified approach to dynamic models for fixed income, credit and equity markets. In: Carmona, R., et al. (eds.) Paris\u2013Princeton Lectures in Mathematical Finance, 2005. Lecture Notes in Mathematics, vol. 1919, pp. 3\u201345. Springer, Berlin (2007)"},{"key":"78_CR11","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1017\/CBO9780511569708.013","volume-title":"Option Pricing, Interest Rates and Risk Management","author":"P. Carr","year":"2001","unstructured":"Carr, P., Madan, D.: Toward a theory of volatility trading. In: Cvitani\u0107, J., Jouini, E., Musiela, M. (eds.) Option Pricing, Interest Rates and Risk Management, pp. 458\u2013476. Cambridge University Press, Cambridge (2001)"},{"issue":"2","key":"78_CR12","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1111\/1468-0300.00090","volume":"31","author":"R. Cont","year":"2002","unstructured":"Cont, R., da Fonseca, I., Durrleman, V.: Stochastic models of implied volatility surfaces. Econ. Notes 31(2), 361\u2013377 (2002)","journal-title":"Econ. Notes"},{"key":"78_CR13","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1088\/1469-7688\/2\/1\/304","volume":"2","author":"R. Cont","year":"2002","unstructured":"Cont, R., da Fonseca, J.: Dynamics of implied volatility surfaces. Quant. Finance 2, 45\u201360 (2002)","journal-title":"Quant. Finance"},{"key":"78_CR14","doi-asserted-by":"crossref","unstructured":"Cousot, L.: When can given European call prices be met by a martingale? An answer based on the building of a Markov chain model, June 2005, http:\/\/ssrn.com\/abstract=754544","DOI":"10.2139\/ssrn.754544"},{"key":"78_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1467-9965.2007.00291.x","volume":"17","author":"M.H.A. Davis","year":"2007","unstructured":"Davis, M.H.A., Hobson, D.G.: The range of traded option prices. Math. Finance 17, 1\u201314 (2007)","journal-title":"Math. Finance"},{"key":"78_CR16","unstructured":"Derman, E., Kani, I.: The volatility smile and its implied tree. Technical Report, Quantitative Research Notes, Goldman Sachs (1994)"},{"key":"78_CR17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1142\/S0219024998000059","volume":"1","author":"E. Derman","year":"1998","unstructured":"Derman, E., Kani, I.: Stochastic implied trees: Arbitrage pricing with stochastic term and strike structure of volatility. Int. J. Theor. Appl. Finance 1, 61\u2013110 (1998)","journal-title":"Int. J. Theor. Appl. Finance"},{"key":"78_CR18","first-page":"32","volume":"7","author":"B. Dupire","year":"1994","unstructured":"Dupire, B.: Pricing with a smile. Risk 7, 32\u201339 (1994)","journal-title":"Risk"},{"key":"78_CR19","unstructured":"Durrleman, V.: From implied to spot volatility. Technical Report, Stanford University, April 2005, http:\/\/ssrn.com\/abstract=1162425"},{"key":"78_CR20","doi-asserted-by":"crossref","unstructured":"Durrleman, V., El Karoui, N.: Coupling smiles. Technical Report, Stanford University, November 2006, http:\/\/ssrn.com\/abstract=1005332","DOI":"10.2139\/ssrn.1005332"},{"key":"78_CR21","volume-title":"Semiparametric Modeling of Implied Volatility","author":"M.R. Fengler","year":"2008","unstructured":"Fengler, M.R.: Semiparametric Modeling of Implied Volatility. Springer, Berlin (2008)"},{"key":"78_CR22","series-title":"Lecture Notes in Mathematics","volume-title":"Consistency Problems for Heath\u2013Jarrow\u2013Morton Interest Rate Models","author":"D. Filipovi\u0107","year":"2002","unstructured":"Filipovi\u0107, D.: Consistency Problems for Heath\u2013Jarrow\u2013Morton Interest Rate Models. Lecture Notes in Mathematics, vol.\u00a01760. Springer, Berlin (2002)"},{"key":"78_CR23","volume-title":"Partial Differential Equations of Parabolic Type","author":"A. Friedman","year":"1964","unstructured":"Friedman, A.: Partial Differential Equations of Parabolic Type. Prentice Hall, Englewood Cliffs (1964)"},{"key":"78_CR24","unstructured":"Labord\u00e8re, P.-H.: A general asymptotic implied volatility in stochastic volatility models. Preprint, arXiv:cond-mat\/0504317v2 [cond-mat.other], April 2005"},{"key":"78_CR25","unstructured":"Jacod, J., Protter, P.: Risk neutral compatibility with option prices. Technical Report, Universit\u00e9 de Paris VI and Cornell University, April 2006, http:\/\/people.orie.cornell.edu\/~protter\/WebPapers\/JP-OptionPrice.pdf"},{"key":"78_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9333-7","volume-title":"Partial Differential Equations","author":"F. John","year":"1982","unstructured":"John, F.: Partial Differential Equations. Springer, Berlin (1982)"},{"key":"78_CR27","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF01432281","volume":"198","author":"H. Kellerer","year":"1972","unstructured":"Kellerer, H.: Markov-Komposition und eine Anwendung auf Martingale. Math. Ann. 198, 99\u2013122 (1972)","journal-title":"Math. Ann."},{"key":"78_CR28","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1006\/jdeq.1996.3244","volume":"136","author":"M.A. Kouritzin","year":"1997","unstructured":"Kouritzin, M.A.: Averaging for fundamental solutions of parabolic equations. J. Differ. Equ. 136, 35\u201375 (1997)","journal-title":"J. Differ. Equ."},{"key":"78_CR29","volume-title":"Stochastic Flows and Stochastic Differential Equations","author":"H. Kunita","year":"1990","unstructured":"Kunita, H.: Stochastic Flows and Stochastic Differential Equations. Cambridge University Press, Cambridge (1990)"},{"key":"78_CR30","first-page":"216","volume-title":"Collected papers of the New York University Mathematical Finance Seminar, vol.\u00a0II","author":"J.P. Laurent","year":"2000","unstructured":"Laurent, J.P., Leisen, D.: Building a consistent pricing model from observed option prices. In: Avellaneda, M. (ed.) Collected papers of the New York University Mathematical Finance Seminar, vol.\u00a0II, pp. 216\u2013238. World Scientific, Singapore (2000)"},{"key":"78_CR31","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1142\/S0219024901000870","volume":"4","author":"R. Lee","year":"2001","unstructured":"Lee, R.: Implied volatility: Statics, dynamics, and probabilistic interpretation. Int. J. Theor. Appl. Finance 4, 45\u201389 (2001)","journal-title":"Int. J. Theor. Appl. Finance"},{"key":"78_CR32","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1111\/j.0960-1627.2004.00200.x","volume":"14","author":"R. Lee","year":"2004","unstructured":"Lee, R.: The moment formula for implied volatility at extreme strikes. Math. Finance 14, 469\u2013480 (2004)","journal-title":"Math. Finance"},{"key":"78_CR33","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5885-8","volume-title":"Numerical Solutions to Partial Differential Equations","author":"T. Meis","year":"1981","unstructured":"Meis, T., Marcowitz, U.: Numerical Solutions to Partial Differential Equations. Springer, Berlin (1981)"},{"key":"78_CR34","volume-title":"Stochastic Integration and Differential Equations","author":"P. Protter","year":"2004","unstructured":"Protter, P.: Stochastic Integration and Differential Equations, 2nd edn. Springer, Berlin (2004)","edition":"2"},{"key":"78_CR35","doi-asserted-by":"crossref","first-page":"2071","DOI":"10.1098\/rsta.1999.0418","volume":"357","author":"P. Sch\u00f6nbucher","year":"1999","unstructured":"Sch\u00f6nbucher, P.: A market model for stochastic implied volatility. Phil. Trans. R. Soc. Ser. A 357, 2071\u20132092 (1999)","journal-title":"Phil. Trans. R. Soc. Ser. A"},{"key":"78_CR36","unstructured":"Sch\u00f6nbucher, P.: Portfolio losses and the term structure of loss transition rates: a new methodology for the pricing of portfolio credit derivatives. Technical Report, ETH Z\u00fcrich, December 2005, http:\/\/www.schonbucher.de\/papers\/cdo_loss_transition_rates.pdf"},{"key":"78_CR37","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1111\/j.1467-9965.2007.00323.x","volume":"18","author":"M. Schweizer","year":"2008","unstructured":"Schweizer, M., Wissel, J.: Term structures of implied volatilities: Absence of arbitrage and existence results. Math. Finance 18, 77\u2013114 (2008)","journal-title":"Math. Finance"},{"key":"78_CR38","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/s00780-008-0068-6","volume":"12","author":"M. Schweizer","year":"2008","unstructured":"Schweizer, M., Wissel, J.: Arbitrage-free market models for option prices: The multi-strike case. Finance Stoch. 12, 469\u2013505 (2008)","journal-title":"Finance Stoch."},{"key":"78_CR39","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1073\/pnas.37.12.826","volume":"37","author":"S. Sherman","year":"1951","unstructured":"Sherman, S.: On a theorem of Hardy, Littlewood, P\u00f3lya and Blackwell. Proc. Natl. Acad. Sci. USA 37, 826\u2013831 (1951)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"78_CR40","unstructured":"Stein, C.: Notes on the comparison of experiments. Technical Report, University of Chicago (1951)"},{"key":"78_CR41","doi-asserted-by":"crossref","unstructured":"Torresetti, R., Brigo, D., Pallavicini, A.: Implied expected tranche loss surface from CDO data. Technical Report, Banca IMI, March 2007, http:\/\/www.damianobrigo.it\/impliedetl.pdf","DOI":"10.2139\/ssrn.933291"},{"key":"78_CR42","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1002\/cpa.3160200210","volume":"20","author":"S.R.S. Varadhan","year":"1967","unstructured":"Varadhan, S.R.S.: On the behavior of the fundamental solution of the heat equation with variable coefficients. Commun. Pure Appl. Math. 20, 431\u2013455 (1967)","journal-title":"Commun. Pure Appl. Math."}],"container-title":["Finance and Stochastics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00780-008-0078-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00780-008-0078-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00780-008-0078-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,9]],"date-time":"2020-05-09T16:25:40Z","timestamp":1589041540000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00780-008-0078-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,10,30]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["78"],"URL":"https:\/\/doi.org\/10.1007\/s00780-008-0078-4","relation":{},"ISSN":["0949-2984","1432-1122"],"issn-type":[{"value":"0949-2984","type":"print"},{"value":"1432-1122","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,10,30]]}}}