A Spectral Element Method for Option Pricing Under Regime-Switching with Jumps

Tour, Geraldine; Thakoor, Nawdha; Ma, Jingtang; Tangman, Désiré Yannick

doi:10.1007/s10915-020-01252-7

Cited by 9 publications

(4 citation statements)

References 55 publications

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“…The core assumption for building the classical BS model is that the risk-free interest rate and underlying asset volatility are constants. However, actual evidence from the real market suggests these assumptions are unreasonable [26,28]. Constant parameters fail to take into account the influences of short-term economic and political.…”

Section: Introductionmentioning

confidence: 99%

“…Driven by actual demands, various discretization methods and iterative algorithms have been developed and used to handle regime-switching option pricing problems [8,10,19,26,29,31]. Notably, Khaliq and Liu [20] transformed the original pricing model into a nonlinear parabolic problem by the penalty method, and proposed a semi-implicit scheme to approximate option values.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Gan and Yin [10] proposed a Crank-Nicolson fitted finite volume method for pricing regime-switching options. Also, Tour et al [26] proposed a spectral element method for the valuation of regime-switching options with jumps, which substantially increased the convergence rate. Zhu et al [33] used integral equations to price American options under regime-switching models, and Liu et al [22] proposed a high order compact finite difference method for solving regime-switching American put options.…”

Section: Introductionmentioning

confidence: 99%

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Primal‐dual active set algorithm for valuating American options under regime switching

Song,

Xu,

Yang

et al. 2024

Numerical Methods Partial

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This paper focuses on numerical algorithms to value American options under regime switching. The prices of such options satisfy a set of complementary parabolic problems on an unbounded domain. Based on our previous experience, the pricing model could be truncated into a linear complementarity problem (LCP) over a bounded domain. In addition, we transform the resulting LCP into an equivalent variational problem (VP), and discretize the VP by an Euler‐finite element method. Since the variational matrix in the discretized system is P‐matrix, a primal‐dual active set (PDAS) algorithm is proposed to evaluate the option prices efficiently. As a specialty of PDAS, the optimal exercise boundaries in all regimes are obtained without further computation cost. Finally, numerical simulations are carried out to test the performance of our proposed algorithm and compare it to existing methods.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Primal‐dual active set algorithm for valuating American options under regime switching

Song,

Xu,

Yang

et al. 2024

Numerical Methods Partial

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“…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. Godin et al [8] developed novel approached for pricing options under regime‐switching models.…”

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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An Efficient Numerical Scheme to Approach the Time Fractional Black–Scholes Model Using Orthogonal Gegenbauer Polynomials

Aghdam,

Mesgarani,

Amin

et al. 2023

Comput Econ

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A Spectral Element Method for Option Pricing Under Regime-Switching with Jumps

Cited by 9 publications

References 55 publications

Primal‐dual active set algorithm for valuating American options under regime switching

Primal‐dual active set algorithm for valuating American options under regime switching

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

An Efficient Numerical Scheme to Approach the Time Fractional Black–Scholes Model Using Orthogonal Gegenbauer Polynomials

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