A DG Approach to the Numerical Solution of the Stein-Stein Stochastic Volatility Option Pricing Model

被引:3
作者
Hozman, J. [1 ]
Tichy, T. [2 ]
机构
[1] Tech Univ Liberec, Fac Sci Humanities & Educ, Liberec 46117, Czech Republic
[2] VSB Tech Univ Ostrava, Fac Econ, Ostrava 70121, Czech Republic
来源
PROCEEDINGS OF THE 43RD INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'17) | 2017年 / 1910卷
关键词
BLACK;
D O I
10.1063/1.5013965
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.
引用
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页数:7
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