Isogeometric analysis in option pricing

TL;DR

This paper demonstrates how isogeometric analysis using NURBS surfaces can efficiently solve option pricing models, especially for complex derivatives lacking closed-form solutions.

Contribution

It introduces a novel application of isogeometric analysis to option pricing, enabling accurate solutions with minimal discretization steps.

Findings

Efficient numerical solutions for option pricing models.

Small number of discretization steps yields accurate results.

Applicable to derivatives without closed-form solutions.

Abstract

Isogeometric analysis is a recently developed computational approach that integrates finite element analysis directly into design described by non-uniform rational B-splines (NURBS). In this paper we show that price surfaces that occur in option pricing can be easily described by NURBS surfaces. For a class of stochastic volatility models, we develop a methodology for solving corresponding pricing partial integro-differential equations numerically by isogeometric analysis tools and show that a very small number of space discretization steps can be used to obtain sufficiently accurate results. Presented solution by finite element method is especially useful for practitioners dealing with derivatives where closed-form solution is not available.