A high-order RBF-FD method for option pricing under regime-switching stochastic volatility models with jumps

Tour, Geraldine; Thakoor, Nawdha; Tangman, Désiré Yannick; Bhuruth, Muddun

doi:10.1016/j.jocs.2019.05.007

Cited by 14 publications

(3 citation statements)

References 21 publications

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“…Numerical experiments confirm the efficiency, robustness and usefulness of the proposed methods; MSOR method is superior to the classical PSOR method in computational efficiency. An interesting topic for future research will be to extend the FVM combined with the MSOR method for pricing American options under the two-asset Merton jump-diffusion model and the regime-switching stochastic volatility model with jumps, which were recently studied by the authors in [4,50].…”

Section: Discussionmentioning

confidence: 99%

Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

Gan

Chen

2022

Taiwanese J. Math.

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In this paper we introduce a new numerical method for the linear complementarity problems (LCPs) arising from two-asset Black-Scholes and Heston's stochastic volatility American options pricing. Based on barycenter dual mesh, a class of finite volume method (FVM) is proposed for the spatial discretization, coupled with the backward Euler and Crank-Nicolson schemes are employed for time stepping of the partial differential equations (PDEs). Then, for the resulting time-dependent LCPs are solved by using an efficient modulus-based successive overrelaxation (MSOR) iteration method. Numerical experiments are carried out to verify the efficiency and usefulness of the proposed method.

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Section: Discussionmentioning

confidence: 99%

Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

Gan

Chen

2022

Taiwanese J. Math.

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“…The RBF methodology was rst introduced in 1971 and have been variously studied [8][9][10]. Recently, these functions have also been used in the numerical solution of stochastic equations, Also, they used in solving equation arisen in nancial mathematics [11][12][13][14]. This method has been applied for solving different kinds of equations, problems and models such as PDEs, IEs and ODEs arisen in physics, biology and neural network etc.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of stochastic biochemical oxygen demand equations via RBF method

Shekarabi

2022

International Journal of Environmental Studies

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In this paper, it is proposed a new approach to numerical simulations of stochastic biochemical oxygen demand equations. The analysis of biochemical oxygen demand is necessary in evaluating the effects of water pollution. Here, we consider radial basis functions. This approximation process can also be interpreted as a simple kind of neural network. Illustrative example is included to demonstrate the validity and applicability of the approach. The numerical experiments show that method perform well.

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“…As a result, m o systems of partial differential equations (PDEs) are required to solve on a fixed rectangular domain. Tour et al [23] developed a high‐order RBF‐FD method for option pricing under regime‐switching stochastic volatility models with jumps. Moreover Tour et al [22] also proposed a spectral element method for pricing different type of options under regime‐switching with jumps.…”

Section: Introductionmentioning

confidence: 99%

Partial differential integral equation model for pricing American option under multi state regime switching with jumps

Yousuf

2021

Numerical Methods Partial

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In this paper, we consider a two dimensional partial differential integral equation (PDIE) model for pricing American option. A nonlinear rationality parameter function for two asset problems is introduced to deal with the free boundary. The rationality parameter function is added in the PDIEs used for pricing American option problems under multi-state regime switching with jumps. The resulting two dimensional nonlinear system of PDIE is then numerically solved. Based on real poles rational approximation, a strongly stable highly efficient and reliable method is developed to solve such complicated systems of PIDEs. The method is build in a predictor corrector style which makes it linearly implicit, therefore, avoids solving nonlinear systems of equations at each time step in all regimes. The method is seen to maintain the stability and convergence for large jump sizes and high volatility in each regime. The impact of regime switching on option prices corresponding to different values interest rate, volatility, and rationality parameter is computed, illustrated by graphs and given in the tables. Convergence results in each regime are presented and time evolution graphs are given to show the effectiveness and reliability of the method.

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A high-order RBF-FD method for option pricing under regime-switching stochastic volatility models with jumps

Cited by 14 publications

References 21 publications

Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

Numerical simulations of stochastic biochemical oxygen demand equations via RBF method

Partial differential integral equation model for pricing American option under multi state regime switching with jumps

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