Isogeometric Analysis for the Pricing of Financial Derivatives with Nonlinear Models: Convertible Bonds and Options
Kazbek R. Erlangga Y. Amanbek Y. Wei D.
2026Springer
Computational Economics
2026
Computational efficiency is essential for enhancing the accuracy and practicality of pricing complex financial derivatives. In this paper, we discuss Isogeometric Analysis (IGA) for valuing financial derivatives, modeled by two nonlinear Black-Scholes PDEs: the Leland model for European options with transaction costs and the AFV model for convertible bonds with default options. We compare the solutions of IGA with finite difference methods (FDM) and finite element methods (FEM). In particular, very accurate solutions can be numerically calculated on far less mesh (knots) than FDM or FEM, by using non-uniform knots and weighted cubic NURBS, which in turn reduces the computational time significantly.
Convertible bonds , Greeks , Isogeometric analysis , NURBS , Options , Transaction costs
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Department of Computation and Data Science, Astana IT University, Mangilik El C1, Astana, Kazakhstan
Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Kabanbay Batyr 53, Astana, Kazakhstan
Department of Mathematics and Statistics, Zayed University, Abu Dhabi Campus, P.O. Box 144534, Abu Dhabi, United Arab Emirates
Department of Computation and Data Science
Department of Mathematics
Department of Mathematics and Statistics
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026