A Simulation of the Heston Model with Stochastic Volatility Using the Finite Difference Method

Date Received: Feb 25, 2020

Date Published: Sep 29, 2020

DOI: https://doi.org/10.31817/vjas.2020.3.1.07

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Issue: Vol. 3 No. 1 (2020): Vietnam Journal of Agricultural Sciences

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ENGINEERING AND TECHNOLOGY

How to Cite:

Giang, V., Hai, N., Hang, N., Hanh, N., & Huyen, N. (2020). A Simulation of the Heston Model with Stochastic Volatility Using the Finite Difference Method. Vietnam Journal of Agricultural Sciences, 3(1), 541–554. https://doi.org/10.31817/vjas.2020.3.1.07

A Simulation of the Heston Model with Stochastic Volatility Using the Finite Difference Method

Vu Thi Thu Giang (*) 1 , Nguyen Huu Hai 1 , Nguyen Thuy Hang 1 , Nguyen Van Hanh 1   , Nguyen Thi Huyen 1

  • Corresponding author: vtgiang@vnua.edu.vn
  • 1 Faculty of Information Technology, Vietnam National University of Agriculture, Hanoi 131000, Vietnam

    • Keywords

    Heston model, European options, Stochastic Volatility, Finite difference method

    Abstract


    In this study, we investigated one of the most popular stochastic volatility pricing models, the Heston model, for European options. This paper deals with the implementation of a finite difference scheme to solve a two-dimensional partial differential equation form of the Heston model. We explain in detail the explicit scheme for the Heston model, especially on the boundaries. Some simple ideas to modify the treatment on the boundaries, which leads to a lower computational cost, are also stated. The paper also covers comparisons between the explicit solution and the semi-analytical solution.