Article
Mathematics
Martha Carpinteyro, Francisco Venegas-Martinez, Ali Aali-Bujari
Summary: This paper develops a stochastic volatility model to explain the dynamics of gold, silver, and platinum returns from 1994 to 2019. The study reveals differences in volatility and jump characteristics among the three precious metals, providing substantial recommendations for investors.
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
Computer Science, Artificial Intelligence
Sha Lin, Xin-Jiang He
Summary: This paper proposes a new model with a two-factor stochastic equilibrium volatility level for pricing variance and volatility swaps with nonlinear payoff. The model uses the CIR process as the volatility process and incorporates regime switching mechanics to better describe the underlying price. Numerical experiments are conducted to compare the results with and without regime switching in order to understand its impact on swap prices.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
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
Mathematics, Applied
Chen Mao, Guanqi Liu
Summary: This paper studies the pricing problem of log-return variance swaps under the double mean reversion model. By introducing a square-root process and a stochastic approach, analytical and approximate solutions are obtained. Numerical examples show a good fit between the exact solution and MC simulation. The parameter of the long-term mean has an important impact on the solution, implying the necessity of a multi-factor model.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
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
Operations Research & Management Science
Yanlin Shi
Summary: This paper investigates the confusion between long memory and regime switching in the second moment using the stochastic volatility methodology. It proposes an MRS-LMSV model to effectively distinguish between different processes and estimate the long-memory parameter. An empirical study demonstrates the superiority of the model and highlights its important financial implications for risk management operations in practice.
ANNALS OF OPERATIONS RESEARCH
(2023)
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
Business, Finance
Yu-Min Lian, Jun-Home Chen
Summary: This study examines the valuation of foreign exchange (FX) options using a two-factor Markov-modulated stochastic volatility model with double exponential jumps. The model is able to capture both long- and short-term stochastic volatility as well as asymmetrical jumps in the underlying spot FX rate. A Markov-modulated Heath-Jarrow-Morton model is employed for the dynamics of domestic/foreign instantaneous forward interest rates. The study employs the dynamic measure change technique to determine a pricing kernel for deriving the FX option pricing formula and provides numerical illustrations and analysis.
FINANCE RESEARCH LETTERS
(2022)
Article
Automation & Control Systems
Siyu Lv, Jie Xiong
Summary: This paper investigates a two-player nonzero-sum stochastic differential game, where both players utilize impulse controls and the state process evolves as a regime switching diffusion. A verification theorem is established based on a system of variational inequalities, serving as a sufficient criterion for optimality. Nash equilibrium strategies for the two players, indicating the optimal timing and method of intervention, are presented in terms of the obstacle parts of the variational inequalities.
Article
Mathematics
Laura Arenas, Ana Maria Gil-Lafuente
Summary: Idiosyncratic volatility is important in high-tech ETF pricing, with the relationship between idiosyncratic risk and return being driven by different volatility regimes and changing across them.
Article
Computer Science, Artificial Intelligence
Ji-Su Yu, Jeong-Hoon Kim
Summary: The variance swap is a popular volatility derivative used for risk management of financial instruments. We propose a hybrid model for evaluating the fair strike prices, and validate the theoretical formula through Monte Carlo simulation.
Article
Business, Finance
Alexandre R. Scarcioffolo, Xiaoli L. Etienne
Summary: This study reveals different volatility patterns for oil and natural gas prices. Through quantile regression analysis, it is found that economic policy uncertainty increases the probability of turbulent market conditions for both commodities, although this effect has weakened in the post-shale period.
INTERNATIONAL REVIEW OF ECONOMICS & FINANCE
(2021)
Article
Automation & Control Systems
Kairong Liu, Zhikun She
Summary: This paper focuses on the upper bound of failure probability for a class of nonautonomous stochastic hybrid systems, called Regime-Switching Jump Diffusions (RSJDs). By utilizing multiple vectorial barrier certificates and a generalized c-martingale condition, an asymptotically decreasing bound of failure probability with respect to time is established. The problem is transformed into semi-definite programming problems and solved using sum of squares programming.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2023)
Article
Business, Finance
Xing Jin, Yi Hong
Summary: This paper examines tractable jump-diffusion models, particularly stochastic volatility models, for stock returns and variance processes. The study applies the Markov chain Monte Carlo (MCMC) method for model estimation and evaluates the models' ability to capture the term structure of variance swap rates and fit the dynamics of stock returns. The findings suggest that stochastic volatility models with self-exciting and linearly-dependent jumps in variance are consistent in estimating models, explaining stylized facts in variance swaps, and improving pricing performance. Empirical results indicate that infrequent self-exciting jumps in spot variance contribute to term structure modeling for variance swaps, while small-sized jumps in central-tendency variance signal substantial regime changes in the long run, particularly during market turmoils from 2008 to 2021.
INTERNATIONAL REVIEW OF FINANCIAL ANALYSIS
(2023)
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)