Pricing American bond options using a cubic spline collocation method

hajaji, Abdelmajid El; Hilal, Khalid; Serghini, A.; Mermri, El Bekkaye

doi:10.5269/bspm.v32i2.21354

Cited by 6 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ì ÓÖ Ñ 2.1 (see [11,18])º Problem (6) is second order convergent for θ = 1 2 and first order convergent for θ ∈ 1 2 , 1 , i.e., there exists a constant Cte such that…”

Section: The Time Semidiscretization and Description Of The θ-Methodsmentioning

confidence: 99%

A Quintic Spline Collocation Method for Solving Time-Dependent Convection-Diffusion Problems

hajaji

Serghini

Melliani

et al. 2021

Tatra Mountains Mathematical Publications

Self Cite

View full text Add to dashboard Cite

In this paper, we develop a new numerical algorithm for solving a time dependent convection-diffusion equation with Dirichlet’s type boundary conditions. The method comprises the horizontal method of lines for time integration and (θ-method, θ ∈ [1/2, 1] (θ = 1 corresponds to the backward Euler method and θ = 1/2 corresponds to the Crank-Nicolson method) to discretize in temporal direction and the quintic spline collocation method. The convergence analysis of proposed method is discussed in detail, and it justified that the approximate solution converges to the exact solution of orders O(Δt + h 3) for the backward Euler method and O(Δt 2 + h 3) for the Crank-Nicolson method, where Δt and h are mesh sizes in the time and space directions, respectively. It is also shown that the proposed method is unconditionally stable. This scheme is applied on some test examples, the numerical results illustrate the efficiency of the method and confirm the theoretical behaviour of the rates of convergence. Results shown by this method are in good agreement with the known exact solutions. The produced results are also more accurate than some available results given in the literature.

show abstract

“…Ì ÓÖ Ñ 2.1 (see [11,18])º Problem (6) is second order convergent for θ = 1 2 and first order convergent for θ ∈ 1 2 , 1 , i.e., there exists a constant Cte such that…”

Section: The Time Semidiscretization and Description Of The θ-Methodsmentioning

confidence: 99%

A Quintic Spline Collocation Method for Solving Time-Dependent Convection-Diffusion Problems

hajaji

Serghini

Melliani

et al. 2021

Tatra Mountains Mathematical Publications

Self Cite

View full text Add to dashboard Cite

show abstract

“…To further verify the efficiency of the proposed model, the convergence trend of the method is calculated by adopting the double mesh principle [43,44]. Table 3 gives the GRE with different time steps for q = 0.01 and σ = 0.1.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Lattice Boltzmann method for the linear complementarity problem arising from American option pricing

Wu,

Zhang,

Wang

et al. 2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this paper, a lattice Boltzmann method is proposed for solving the linear complementarity problem (LCP) arising in single and multi-asset American put option pricing. The LCP for American option is a variable coefficient parabolic model defined on an unbounded domain. Initially, using the far field estimate method and the penalty method respectively, the LCP could be reformulated into a nonlinear parabolic partial differential equation on a bounded domain. To construct a unified lattice Boltzmann model for the option pricing problems, the above transformation equations are rewritten into an equivalent divergence form. Then, through the incorporation of an amending function into the evolution equation, which assists in recovering the source term and eliminating the error term, the lattice Boltzmann model with spatial second-order accuracy is constructed. Finally, the present model is validated using numerical simulations, and the numerical results agree well with the option values obtained by existing methods, which indicates that the present lattice Boltzmann model is efficient for solving the American put option pricing problem.

show abstract

“…In the past two decades, many scholars have conducted in-depth research on numerical methods for pricing bond options, such as the lattice method, finite difference method, finite element method, and so on for the valuation of American bond options, for instance, [18][19][20][21][22][23]. In 2004, Yang [20] used the finite element method coupled with the Crank-Nicolson method to price American zero-coupon bond options, and presented the existence and uniqueness of these solutions.…”

Section: Introductionmentioning

confidence: 99%

“…In 2012, Zhang et al [21] proposed the fitted finite volume method for pricing discounted American bond options and proved the convergence of the method. Later, Hilal et al [22] transformed the pricing problem of bond options into a parabolic partial differential complementarity problem and proposed the cubic spline interpolation and generalized Newton's method to solve it. In 2021, Gan et al [23] used the modular matrix splitting iterative method to price zero-coupon bond options.…”

Section: Introductionmentioning

confidence: 99%

Projection and Contraction Method for Pricing American Bond Options

Zhang,

Wang,

Zuo

et al. 2023

Mathematics

View full text Add to dashboard Cite

In this paper, an effective numerical method is proposed for a linear complementarity problem (LCP) arising in the valuation of American bond options under the Cox–Ingersoll–Ross (CIR) model. Firstly, a variable substitution is used to simplify the linear complementary model. Secondly, the finite difference method is adopted to discretize the simplified model, and an equivalent variational form is obtained. Based on the positive definiteness of the discretized matrix, a projection and contraction method (PCM) is adopted for the resulting discretized variational problem. Finally, numerical experiments highlight the effectiveness and performance of the proposed algorithm.

show abstract

Pricing American bond options using a cubic spline collocation method

Cited by 6 publications

References 19 publications

A Quintic Spline Collocation Method for Solving Time-Dependent Convection-Diffusion Problems

A Quintic Spline Collocation Method for Solving Time-Dependent Convection-Diffusion Problems

Lattice Boltzmann method for the linear complementarity problem arising from American option pricing

Projection and Contraction Method for Pricing American Bond Options

Contact Info

Product

Resources

About