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

TL;DR

This paper explores the use of Isogeometric Analysis (IGA) to efficiently price complex financial derivatives modeled by nonlinear PDEs, demonstrating superior accuracy and reduced computational time compared to traditional methods.

Contribution

It introduces IGA as a novel approach for pricing nonlinear financial derivatives, showing improved accuracy and efficiency over FDM and FEM.

Findings

IGA achieves high accuracy with fewer mesh points.

IGA reduces computational time significantly.

IGA outperforms FDM and FEM in pricing complex derivatives.

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 call 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.