LEADER 04833nam 22006255 450 001 9910254287303321 005 20220329220231.0 010 $a1-4939-6792-4 024 7 $a10.1007/978-1-4939-6792-6 035 $a(CKB)3710000001079870 035 $a(DE-He213)978-1-4939-6792-6 035 $a(MiAaPQ)EBC4813329 035 $a(PPN)198866143 035 $a(EXLCZ)993710000001079870 100 $a20170227d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPricing derivatives under Lévy models $emodern finite-difference and pseudo-differential operators approach /$fby Andrey Itkin 205 $a1st ed. 2017. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (XX, 308 p. 64 illus., 62 illus. in color.) 225 1 $aPseudo-Differential Operators, Theory and Applications,$x2297-0355 ;$v12 311 $a1-4939-6790-8 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aBasics of a finite-difference method -- Modern finite-difference approach -- An M-matrix theory and FD -- Brief Introduction into Lévy processes -- Pseudo-parabolic and fractional equations of option pricing -- Pseudo-parabolic equations for various Lévy models -- High-order splitting methods for forward PDEs and PIDEs -- Multi-dimensional structural default models and correlated jumps -- LSV models with stochastic interest rates and correlated jumps -- Stochastic skew model -- Glossary -- References -- Index. 330 $aThis monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance. 410 0$aPseudo-Differential Operators, Theory and Applications,$x2297-0355 ;$v12 606 $aEconomics, Mathematical  606 $aMathematical models 606 $aComputer mathematics 606 $aPartial differential equations 606 $aQuantitative Finance$3https://scigraph.springernature.com/ontologies/product-market-codes/M13062 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aEconomics, Mathematical . 615 0$aMathematical models. 615 0$aComputer mathematics. 615 0$aPartial differential equations. 615 14$aQuantitative Finance. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aComputational Science and Engineering. 615 24$aPartial Differential Equations. 676 $a515.7242 700 $aItkin$b Andrey$4aut$4http://id.loc.gov/vocabulary/relators/aut$0766804 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254287303321 996 $aPricing Derivatives Under Lévy Models$91560525 997 $aUNINA