On Modified Heston Model for Forecasting Stock Market Prices

Naiga Babra Charlotte; Joseph Mung’atu; Nafiu Lukman Abiodun; Mark Adjei

doi:https://doi.org/10.14445/22315373/IJMTT-V68I1P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 1 | Year 2022 | Article Id. IJMTT-V68I1P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I1P513

On Modified Heston Model for Forecasting Stock Market Prices

Naiga Babra Charlotte, Joseph Mung’atu, Nafiu Lukman Abiodun, Mark Adjei

Citation :

Naiga Babra Charlotte, Joseph Mung’atu, Nafiu Lukman Abiodun, Mark Adjei, "On Modified Heston Model for Forecasting Stock Market Prices," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 1, pp. 115-129, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I1P513

Abstract

Heston stochastic volatility model is the most popular stochastic volatility model used in pricing options despite its inefficiencies with Short term maturities. In this paper, we improved the Heston Model by incorporating the log-normal jump diffusions in the model. The derivation of the closed form solution of the Heston model and the full derivation of the Heston Model with jump are presented. We applied the models to National Association of Securities Dealers Automatic Quotation System(NASDAQ April 2021) stock data and back-tested them against the Black Scholes model since it predicts better option prices in short term maturities as compared to the Heston Model. Using Mean Squared Error, Heston Model with jump performs better than the Black scholes Model by 47.3% and Heston model by 58.08% error reduction.

Keywords

Heston stochastic volatility model; Heston Model with jump; Black scholes Model; PDE; Mean Squared Error.

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