Isogeometric Analysis for the Pricing of Financial Derivatives with Nonlinear Models: Convertible Bonds and Options

Author First name, Last name, Institution

Rakhymzhan Kazbek, Astana IT University
Yogi Erlangga, Zayed University
Yerlan Amanbek, Nazarbayev University
Dongming Wei, Nazarbayev University

Document Type

Article

Source of Publication

Computational Economics

Publication Date

2-25-2026

Abstract

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.

DOI Link

10.1007/s10614-025-11235-1

ISSN

0927-7099

Publisher

Springer Science and Business Media LLC

Disciplines

Physical Sciences and Mathematics

Keywords

Convertible bonds, Greeks, Isogeometric analysis, NURBS, Options, Transaction costs

Scopus ID

105031157796

Recommended Citation

Kazbek, Rakhymzhan; Erlangga, Yogi; Amanbek, Yerlan; and Wei, Dongming, "Isogeometric Analysis for the Pricing of Financial Derivatives with Nonlinear Models: Convertible Bonds and Options" (2026). All Works. 7829.
https://zuscholars.zu.ac.ae/works/7829

Indexed in Scopus

yes

Open Access

no