A Comparative Analysis of the Black-Scholes- Merton Model and the Heston Stochastic Volatility Model

Authors

  • Tahmid Tamrin Suki Department of Applied Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
  • ABM Shahadat Hossain Department of Applied Mathematics, University of Dhaka, Dhaka-1000, Bangladesh

DOI:

https://doi.org/10.3329/ganit.v39i0.44168

Keywords:

Stochastic volatility, Heston model, Black-Scholes-Merton model, Skewness and kurtosis, Affecting factors, Greeks.

Abstract

This paper compares the performance of two different option pricing models, namely, the Black-Scholes-Merton (B-S-M) model and the Heston Stochastic Volatility (H-S-V) model. It is known that the most popular B-S-M Model makes the assumption that volatility of an asset is constant while the H-S-V model considers it to be random. We examine the behavior of both B-S-M and H-S-V formulae with the change of different affecting factors by graphical representations and hence assimilate them. We also compare the behavior of some of the Greeks computed by both of these models with changing stock prices and hence constitute 3D plots of these Greeks. All the numerical computations and graphical illustrations are generated by a powerful Computer Algebra System (CAS), MATLAB.

GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 127-140

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Published

2019-11-19

How to Cite

Suki, T. T., & Hossain, A. S. (2019). A Comparative Analysis of the Black-Scholes- Merton Model and the Heston Stochastic Volatility Model. GANIT: Journal of Bangladesh Mathematical Society, 39, 127–140. https://doi.org/10.3329/ganit.v39i0.44168

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