标题： 基于非线性模型的金融衍生品定价的等几何分析：可转换债券和期权 显示英文标题

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

摘要： 计算效率对于提高复杂金融衍生品定价的准确性和实用性至关重要。 在本文中，我们讨论用于定价金融衍生品的等几何分析（IGA），这些衍生品由两个非线性Black-Scholes偏微分方程建模：带有交易成本的欧式看涨期权的Leland模型和带有违约期权的可转换债券的AFV模型。 我们将IGA的解与有限差分方法（FDM）和有限元方法（FEM）的解进行了比较。 特别是，通过使用非均匀节点和加权三次NURBS，可以在远少于FDM或FEM的网格（节点）上数值计算出非常精确的解，从而显著减少计算时间。 显示英文摘要

摘要： 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.