A Reduced Basis Method for Parabolic Partial Differential Equations with Parameter Functions and Application to Option Pricing

IF 0.8 4区经济学 Q4 BUSINESS, FINANCE

Journal of Computational Finance Pub Date : 2014-08-12 DOI:10.21314/JCF.2016.323

A. Mayerhofer, K. Urban

引用次数: 11

Abstract

We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients (for calibration) and enables us to choose the initial condition (for option pricing) as a parameter function. A corresponding discretization in space and time for the initial condition are introduced. Finally, we present a novel reduced basis method that is able to use the initial condition of the parabolic partial differential equation as a parameter (function). The corresponding numerical results are shown.

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带参数函数的抛物型偏微分方程的约基法及其在期权定价中的应用

我们考虑Heston模型作为参数化抛物型偏微分方程的一个例子。我们推导出一个时空变分公式，允许在系数中加入参数(用于校准)，并使我们能够选择初始条件(用于期权定价)作为参数函数。对初始条件进行了相应的时间和空间离散化处理。最后，我们提出了一种新的简化基方法，该方法能够使用抛物型偏微分方程的初始条件作为参数(函数)。给出了相应的数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Finance BUSINESS, FINANCE-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： The Journal of Computational Finance is an international peer-reviewed journal dedicated to advancing knowledge in the area of financial mathematics. The journal is focused on the measurement, management and analysis of financial risk, and provides detailed insight into numerical and computational techniques in the pricing, hedging and risk management of financial instruments. The journal welcomes papers dealing with innovative computational techniques in the following areas: Numerical solutions of pricing equations: finite differences, finite elements, and spectral techniques in one and multiple dimensions. Simulation approaches in pricing and risk management: advances in Monte Carlo and quasi-Monte Carlo methodologies; new strategies for market factors simulation. Optimization techniques in hedging and risk management. Fundamental numerical analysis relevant to finance: effect of boundary treatments on accuracy; new discretization of time-series analysis. Developments in free-boundary problems in finance: alternative ways and numerical implications in American option pricing.