Article
Mathematics, Applied
Jiling Cao, Biyuan Wang, Wenjun Zhang
Summary: The famous Black-Scholes model, known for its elegant pricing formula for European options, is not perfect due to its idealized assumptions. Leland introduced a modified replicating strategy to account for transaction costs, addressing a gap in the model.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Shoude Huang, Xunxiang Guo
Summary: This study investigates the pricing of European-style vulnerable option when the price process of the underlying asset follows nonaffine stochastic volatility and double exponential jump. An approximate expression for the joint characteristic function of the log-price of the underlying asset and the log-value of the counterparty asset is derived. An analytical approximate price of the European-style vulnerable option is obtained using the Fourier-cosine method. Numerical experiments confirm the accuracy and efficiency of the proposed method compared with Monte Carlo simulation, and sensitivity analysis is conducted to further explain the theoretical results.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics
Chen Mao, Guanqi Liu, Yuwen Wang
Summary: This paper presents a simplified approach to price log-return variance swaps under the CIR-Heston hybrid model and obtains a closed-form solution. The closed-form solution offers accurate pricing and eliminates the need to adjust parameters using numerical methods. Additionally, this paper analyzes the impact of sampling frequency on the pricing formula and proposes an approximate formula. Numerical simulations demonstrate that the approximate formula is simple and reliable.
Article
Mathematics, Applied
Chun-Sung Huang, John G. O'Hara, Sure Mataramvura
Summary: The paper introduces a highly efficient and accurate valuation method for exotic-style options using the novel Shannon wavelet inverse Fourier technique, successfully deriving a more realistic pricing method for power options. Numerical experiments demonstrate that the SWIFT method is not only more efficient, but also robust across different market conditions.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Yurong Xie, Guohe Deng
Summary: This paper investigates the pricing of European-style vulnerable options under the Heston stochastic volatility and stochastic interest rate model, with mean-reversion levels modulated by a continuous-time Markov process. It derives an analytical pricing formula using the Esscher transform, joint characteristic function, and multivariate Fourier transform technique, and provides an efficient approximation using the FFT method.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Economics
John Crosby, Carme Frau
Summary: In this paper, we present a new term-structure model for commodity futures prices based on Trolle and Schwartz (2009) and extend it by incorporating multiple jump processes. Our model allows for valuation of plain vanilla options on futures prices with stochastic volatility and time-dampening jumps. We obtain an analytical representation of the futures prices and pricing of plain vanilla options using the fast Fourier transform methodology. Our model achieves higher accuracy and significant savings in computing time compared to earlier models.
Article
Statistics & Probability
Jianping Lyu, Yong Ma, Wei Sun
Summary: A general option pricing framework is proposed, incorporating double Heston stochastic volatility, stochastic interest rate, jumps, and Markov regime switching. Analytical pricing formulas for European options are derived using Fourier transform technique. Numerical examples demonstrate significant variations in option prices and implied volatility curves under different regimes, with regime-switching and jumps having differing effects on option prices.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2022)
Article
Business, Finance
Christian-Oliver Ewald, Yuexiang Wu, Aihua Zhang
Summary: We price Asian options on commodity futures contracts with stochastic convenience yield, stochastic interest rates, and jumps in the commodity spot price. Without jumps, we obtain a closed-form solution for a geometric average Asian option, which can be used as a control variate when pricing the corresponding arithmetic average Asian option. We also discuss further applications and comparative statics. To cover the case with jumps, we condition on the jump times first and then average over the sequences of jump times.
QUANTITATIVE FINANCE
(2023)
Article
Computer Science, Information Systems
Tian Chen, Guangchen Wang, Zhen Wu
Summary: In this paper, we investigate a linear-quadratic optimal control problem for partially observed forward-backward stochastic systems with random jumps. By applying a backward separation approach, we overcome the problem of cyclic dependence of control and observation and derive the necessary and sufficient conditions for optimal control.
SCIENCE CHINA-INFORMATION SCIENCES
(2022)
Article
Business, Finance
Kenji Nagami
Summary: This paper applies the smart expansion method based on the Malliavin calculus to price options in the Heston-Hull-White model, obtaining a second-order expansion formula and conducting numerical studies. The results indicate that this method has good accuracy in high volatility scenarios.
JOURNAL OF COMPUTATIONAL FINANCE
(2021)
Article
Mathematics, Interdisciplinary Applications
Guangjie Li, Qigui Yang
Summary: This paper investigates the exponential stability of the theta-method for neutral stochastic functional differential equations with Markovian switching and jumps. It is shown that the trivial solution is almost surely and mean-square exponentially stable, and the same conclusion holds for the theta-method. Numerical examples are provided to illustrate the obtained results.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Statistics & Probability
Yong Ma, Li Chen, Jianping Lyu
Summary: In this paper, a double exponential jump-diffusion option pricing model with stochastic interest rates, stochastic volatility, and stochastic jump intensity is presented. Markov regime-switching is also introduced to modulate the mean-reverting level of the squared volatility. Analytical pricing formulae for European options under this model are obtained. Numerical examples are used to explore the effects of regime-switching, stochastic jump intensity, and the distribution of jump size on the option price or implied volatility.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Computer Science, Information Systems
Xiaowu Mu, Zenghui Hu
Summary: The study focuses on almost surely exponential stability of semi-Markovian switched stochastic systems with randomly impulsive jumps. It examines cases where switches and impulses occur synchronously and asynchronously, deriving sufficient conditions for exponential stability based on the ergodic property of semi-Markovian process. The proposed theoretical results are validated through a numerical example.
SCIENCE CHINA-INFORMATION SCIENCES
(2021)
Article
Automation & Control Systems
Zhi Li, Liping Xu, Litan Yan
Summary: This paper presents a novel approach to studying the global attracting sets of mild solutions for stochastic functional partial differential equations driven by Levy noise, establishing new sufficient conditions and obtaining new criteria for exponential stability. By employing a weak convergence method, stability conditions in distribution of the segment processes of mild solutions are investigated for stochastic delay partial differential equations with jumps, improving some known results. Several examples are explored to illustrate the theory.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2021)
Article
Statistics & Probability
Farshid Mehrdoust, Somayeh Fallah, Oldouz Samimi
Summary: This paper studies the Heston-CIR model with double exponential jumps, verifying the existence and uniqueness of solutions related to the price process, calibrating option prices to observed index options, and using LSM algorithm to numerically examine multi-asset American style put options under the model.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2021)
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Dohee Jung, Changbum Chun
Summary: The paper presents a general approach to enhance the Pade iterations for computing the matrix sign function by selecting an arbitrary three-point family of methods based on weight functions. The approach leads to a multi-parameter family of iterations and allows for the discovery of new methods. Convergence and stability analysis as well as numerical experiments confirm the improved performance of the new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Abhishek Yadav, Amit Setia, M. Thamban Nair
Summary: In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fernando Chacon-Gomez, M. Eugenia Cornejo, Jesus Medina, Eloisa Ramirez-Poussa
Summary: The use of decision rules allows for reliable extraction of information and inference of conclusions from relational databases, but the concepts of decision algorithms need to be extended in fuzzy environments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper considers the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay. To solve this problem numerically, a higher-order difference method is constructed and the error estimate for its solution is obtained. Based on the method of energy estimates, the fully discrete scheme is shown to be convergent of order four in space and of order two in time. The given numerical results illustrate the convergence and effectiveness of the numerical method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tong-tong Shang, Guo-ji Tang, Wen-sheng Jia
Summary: The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound and upper bound of the solutions in the sense of the infinity norm of the TLCP are obtained when the problem has a solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fabio Difonzo, Pawel Przybylowicz, Yue Wu
Summary: This paper focuses on the existence, uniqueness, and approximation of solutions of delay differential equations (DDEs) with Caratheodory type right-hand side functions. It presents the construction of the randomized Euler scheme for DDEs and investigates its error. Furthermore, the paper reports the results of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Priyanka Roy, Geetanjali Panda, Dong Qiu
Summary: In this article, a gradient based descent line search scheme is proposed for solving interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational perspectives. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhongqian Wang, Changqing Ye, Eric T. Chung
Summary: In this paper, the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions for elasticity equations in high contrast media is developed. The method offers advantages such as independence of target region's contrast from precision and significant impact of oversampling domain sizes on numerical accuracy. Furthermore, this is the first proof of convergence of CEM-GMsFEM with mixed boundary conditions for elasticity equations. Numerical experiments demonstrate the method's performance.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Samaneh Soradi-Zeid, Maryam Alipour
Summary: The Laguerre polynomials are a new set of basic functions used to solve a specific class of optimal control problems specified by integro-differential equations, namely IOCP. The corresponding operational matrices of derivatives are calculated to extend the solution of the problem in terms of Laguerre polynomials. By considering the basis functions and using the collocation method, the IOCP is simplified into solving a system of nonlinear algebraic equations. The proposed method has been proven to have an error bound and convergence analysis for the approximate optimal value of the performance index. Finally, examples are provided to demonstrate the validity and applicability of this technique.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
Summary: A generalization of the KP equation involving higher-order dispersion is studied. The Lie point symmetries and conservation laws of the equation are obtained using Noether's theorem and the introduction of a potential. Sech-type line wave solutions are found and their features, including dark solitary waves on varying backgrounds, are discussed.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Susanne Saminger-Platz, Anna Kolesarova, Adam Seliga, Radko Mesiar, Erich Peter Klement
Summary: In this article, we study real functions defined on the unit square satisfying basic properties and explore the conditions for generating bivariate copulas using parameterized transformations and other constructions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lulu Tian, Nattaporn Chuenjarern, Hui Guo, Yang Yang
Summary: In this paper, a new local discontinuous Galerkin (LDG) algorithm is proposed to solve the incompressible Euler equation in two dimensions on overlapping meshes. The algorithm solves the vorticity, velocity field, and potential function on different meshes. The method employs overlapping meshes to ensure continuity of velocity along the interfaces of the primitive meshes, allowing for the application of upwind fluxes. The article introduces two sufficient conditions to maintain the maximum principle of vorticity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Cheng Wang, Jilu Wang, Steven M. Wise, Zeyu Xia, Liwei Xu
Summary: In this paper, a temporally second-order accurate numerical scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations is proposed and analyzed. The scheme utilizes a modified Crank-Nicolson-type approximation for time discretization and a mixed finite element method for spatial discretization. The modified Crank-Nicolson approximation allows for mass conservation and energy stability analysis. Error estimates are derived for the phase field, velocity, and magnetic fields, and numerical examples are presented to validate the proposed scheme's theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)