Application of the Heston Stochastic Volatility Model for Borsa Istanbul Using Impression Matrix Norm

A. Duran and B. İzgi, Application of the Heston stochastic volatility model for Borsa Istanbul using impression matrix norm, Journal of Computational and Applied Mathematics, 281, 2015, pp. 126-134, DOI 10.1016/j.cam.2014.12.020

Posted: 23 May 2018

See all articles by Ahmet Duran

Ahmet Duran

Istanbul Technical University, Department of Mathematical Engineering; University of Michigan at Ann Arbor

Burhaneddin İzgi

Istanbul Technical University - Department of Mathematical Engineering

Date Written: April 7, 2014

Abstract

We study the behavior of solutions for stochastic differential equations such as the Heston stochastic volatility model. We examine the numerical solutions using Euler–Maruyama, Milstein and stochastic Runge–Kutta methods to investigate whether there is a role of the methods for different volatility cases or not, related to the impact of cumulative errors on this application. We perform simulations for different stock market conditions by using the large data set from Borsa Istanbul-100 (BIST-100) between 04.01.2007 and 31.12.2012. We use volatilities in terms of extreme values at the overlapping case when we examine initial and long term volatilities for the application of the Heston model. We also apply unit volatility based on extreme values to approximate volatilities in our analysis. We ex-amine the advantages and limitations of the model. Moreover, we introduce 3-dimensional matrix norms. Furthermore, we define market impression matrix norm as an application to the 3 dimensional matrix norms. We can benefit from it to quantify market impression approximately by means of the numerical solutions for the stochastic differential equations. Finally, we analyze the simulation results for various parameters.

Suggested Citation

Duran, Ahmet and İzgi, Burhaneddin, Application of the Heston Stochastic Volatility Model for Borsa Istanbul Using Impression Matrix Norm (April 7, 2014). A. Duran and B. İzgi, Application of the Heston stochastic volatility model for Borsa Istanbul using impression matrix norm, Journal of Computational and Applied Mathematics, 281, 2015, pp. 126-134, DOI 10.1016/j.cam.2014.12.020. Available at SSRN: https://ssrn.com/abstract=3169317

Ahmet Duran (Contact Author)

Istanbul Technical University, Department of Mathematical Engineering ( email )

Ayazaga Kampusu
Fen Edebiyat Fakultesi
İstanbul
Turkey

HOME PAGE: http://web.itu.edu.tr/aduran

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

Burhaneddin İzgi

Istanbul Technical University - Department of Mathematical Engineering ( email )

Ayazaga Kampusu
Fen Edebiyat Fakultesi
İstanbul
Turkey

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