Convergence, non-negativity and stability of a new Lobatto IIIC-Milstein method for a pricing option approach based on stochastic volatility model

Eissa, Mahmoud A.; Ye, Qiang

doi:10.1007/s13160-020-00443-x

Cited by 2 publications

(1 citation statement)

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“…Although Kahl [11] shows the different ways to avert the numerical negativity, the balanced implicit method (BIM) method and the Milstein method have proven that the numerical method based on the Euler scheme is a finite time for all SDE (i.e., the numerical methods do not preserve positivity of the solution of SDEs), recently published research still considers numerical methods based on the Euler scheme in order to approximate the paths of stochastic models with respect to delay dependence in financial mathematics [5,12]. Based on Kahl's work, there are few works in the literature discussing this issue; for example, the fundamental analysis of Milstein-type methods with respect to non-negativity has been discussed for a family of financial models [13][14][15][16][17][18][19]. Moreover, classes of the BIM method were provided in [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

Eissa

Elsayed

2022

Symmetry

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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.

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Section: Introductionmentioning

confidence: 99%

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

Eissa

Elsayed

2022

Symmetry

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Stochastic Epidemic Model for COVID-19 Transmission under Intervention Strategies in China

2022

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In this paper, we discuss an EIQJR model with stochastic perturbation. First, a globally positive solution of the proposed model has been discussed. In addition, the global asymptotic stability and exponential mean-square stability of the disease-free equilibrium have been proven under suitable conditions for our model. This means that the disease will die over time. We investigate the asymptotic behavior around the endemic equilibrium of the deterministic model to show when the disease will prevail. Constructing a suitable Lyapunov functional method is crucial to our investigation. Parameter estimations and numerical simulations are performed to depict the transmission process of COVID-19 pandemic in China and to support analytical results.

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Convergence, non-negativity and stability of a new Lobatto IIIC-Milstein method for a pricing option approach based on stochastic volatility model

Cited by 2 publications

References 33 publications

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

Improve Stock Price Model-Based Stochastic Pantograph Differential Equation

Stochastic Epidemic Model for COVID-19 Transmission under Intervention Strategies in China

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