Improve Stock Price Model-Based Stochastic Pantograph Differential Equation
Although the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This work considers the stock price...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-07-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/7/1358 |
| _version_ | 1797415414265806848 |
|---|---|
| author | Mahmoud A. Eissa M. Elsayed |
| author_facet | Mahmoud A. Eissa M. Elsayed |
| author_sort | Mahmoud A. Eissa |
| collection | DOAJ |
| description | Although the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This work considers the stock price of European options with a new class of the non-constant delay model. The stochastic pantograph differential equation (SPDE) with a variable delay is provided in order to overcome the weaknesses of using stochastic models with constant delay. The proposed model is constructed to improve the evaluation process and prediction accuracy for stock prices. The feasibility of the proposed model is introduced under relatively weak conditions imposed on its volatility function. Furthermore, the sensitivity of time lag is discussed. The robust stochastic theta Milstein (STM) method is combined with the Monte Carlo simulation to compute asset prices within the proposed model. In addition, we prove that the numerical solution can preserve the non-negativity of the solution of the model. Numerical experiments using real financial data indicate that there is an increasing possibility of prediction accuracy for the proposed model with a variable delay compared to non-linear models with constant delay and the classical Black and Scholes model. |
| first_indexed | 2024-03-09T05:48:17Z |
| format | Article |
| id | doaj.art-91f2ae6a918f4867959ac168aedb4455 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:48:17Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-91f2ae6a918f4867959ac168aedb44552023-12-03T12:19:33ZengMDPI AGSymmetry2073-89942022-07-01147135810.3390/sym14071358Improve Stock Price Model-Based Stochastic Pantograph Differential EquationMahmoud A. Eissa0M. Elsayed1Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Kom 32511, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Kom 32511, EgyptAlthough the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This work considers the stock price of European options with a new class of the non-constant delay model. The stochastic pantograph differential equation (SPDE) with a variable delay is provided in order to overcome the weaknesses of using stochastic models with constant delay. The proposed model is constructed to improve the evaluation process and prediction accuracy for stock prices. The feasibility of the proposed model is introduced under relatively weak conditions imposed on its volatility function. Furthermore, the sensitivity of time lag is discussed. The robust stochastic theta Milstein (STM) method is combined with the Monte Carlo simulation to compute asset prices within the proposed model. In addition, we prove that the numerical solution can preserve the non-negativity of the solution of the model. Numerical experiments using real financial data indicate that there is an increasing possibility of prediction accuracy for the proposed model with a variable delay compared to non-linear models with constant delay and the classical Black and Scholes model.https://www.mdpi.com/2073-8994/14/7/1358stochastic pantograph differential equationsstock price modelingnumerical techniquespositivityprediction |
| spellingShingle | Mahmoud A. Eissa M. Elsayed Improve Stock Price Model-Based Stochastic Pantograph Differential Equation Symmetry stochastic pantograph differential equations stock price modeling numerical techniques positivity prediction |
| title | Improve Stock Price Model-Based Stochastic Pantograph Differential Equation |
| title_full | Improve Stock Price Model-Based Stochastic Pantograph Differential Equation |
| title_fullStr | Improve Stock Price Model-Based Stochastic Pantograph Differential Equation |
| title_full_unstemmed | Improve Stock Price Model-Based Stochastic Pantograph Differential Equation |
| title_short | Improve Stock Price Model-Based Stochastic Pantograph Differential Equation |
| title_sort | improve stock price model based stochastic pantograph differential equation |
| topic | stochastic pantograph differential equations stock price modeling numerical techniques positivity prediction |
| url | https://www.mdpi.com/2073-8994/14/7/1358 |
| work_keys_str_mv | AT mahmoudaeissa improvestockpricemodelbasedstochasticpantographdifferentialequation AT melsayed improvestockpricemodelbasedstochasticpantographdifferentialequation |