A reduced basis method for parabolic partial differential equations with parameter functions and application to option pricing

被引：4
|
作者：
Mayerhofer, Antonia [1 ]
Urban, Karsten [1 ]
机构：
[1] Univ Ulm, Inst Numer Math, Helmholtzstr 22, D-89069 Ulm, Germany
来源：
JOURNAL OF COMPUTATIONAL FINANCE | 2017年 / 20卷 / 04期
关键词：
option pricing; parabolic problems; reduced basis method (RBM); error estimates; Heston model; BASIS APPROXIMATION; GREEDY ALGORITHMS; DISCRETIZATION;
D O I：
10.21314/JCF.2016.323
中图分类号：
F8 [财政、金融];
学科分类号：
0202 ;
摘要：
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.
引用
收藏
页码：71 / 106
页数：36
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