TR-BDF2 for fast stable American option pricing

Floc'h, Fabien Le

doi:10.21314/jcf.2014.289

Cited by 11 publications

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“…Also Oosterlee [26] applied BDF2 in the context of the American option problem, in combination with a multigrid approach (see also Oosterlee et al [27]). Le Floc'h [22] applied the trapezoidal rule combined with BDF2 as a one-step method (TR-BDF2) to the American option problem.…”

Section: Introductionmentioning

confidence: 99%

Backward differentiation formula finite difference schemes for diffusion equations with an obstacle term

Bokanowski

Debrabant

2020

IMA Journal of Numerical Analysis

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Abstract Finite difference schemes, using backward differentiation formula (BDF), are studied for the approximation of one-dimensional diffusion equations with an obstacle term of the form $$\begin{equation*}\min(v_t - a(t,x) v_{xx} + b(t,x) v_x + r(t,x) v, v- \varphi(t,x))= f(t,x).\end{equation*}$$For the scheme building on the second-order BDF formula, we discuss unconditional stability, prove an $L^2$-error estimate and show numerically second-order convergence, in both space and time, unconditionally on the ratio of the mesh steps. In the analysis an equivalence of the obstacle equation with a Hamilton–Jacobi–Bellman equation is mentioned, and a Crank–Nicolson scheme is tested in this context. Two academic problems for parabolic equations with an obstacle term with explicit solutions and the American option problem in mathematical finance are used for numerical tests.

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Section: Introductionmentioning

confidence: 99%

Backward differentiation formula finite difference schemes for diffusion equations with an obstacle term

Bokanowski

Debrabant

2020

IMA Journal of Numerical Analysis

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“…In addition, the futures payoff functions are differentiable unlike the option payoffs. For some alternative numerical methods and for a discussion on the arising differences we refer to [19]. Let us mention in addition the integral approach of [17] applied to American option pricing.…”

Section: Introductionmentioning

confidence: 99%

On the American style futures contracts

Zaevski

2024

Croat. oper. res. rev. (Online)

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There is a large number of sources devoted to the American style options. On the other hand, the American futures contracts are understudied in the scientific literature. This motivated us to examine these instruments in comparison to the relevant options. Their optimal boundaries are obtained and a finite difference scheme is applied to the pricing problem. We consider separately the long and short positions.

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“…Also Oosterlee [25] applied BDF2 in the context of the American option problem, in combination with a multigrid approach (see also K. Oosterlee et al [26]). Le Floc'h [21] applied the trapezoidal rule combined with BDF2 as a one-step method (TR-BDF2) to the American option problem.…”

Section: Introductionmentioning

confidence: 99%

Backward Differentiation Formula finite difference schemes for diffusion equations with an obstacle term

Bokanowski,

Debrabant

2018

Preprint

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Finite difference schemes, using Backward Differentiation Formula (BDF), are studied for the approximation of one-dimensional diffusion equations with an obstacle term, of the formFor the scheme building on BDF2, we discuss unconditional stability, prove an L 2 -error estimate and show numerically second order convergence, in both space and time, unconditionally on the ratio of the mesh steps. In the analysis, an equivalence of the obstacle equation with a Hamilton-Jacobi-Bellman equation is mentioned, and a Crank-Nicolson scheme is tested in this context. Two academic problems for parabolic equations with an obstacle term with explicit solutions and the American option problem in mathematical finance are used for numerical tests.

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TR-BDF2 for fast stable American option pricing

Cited by 11 publications

References 0 publications

Backward differentiation formula finite difference schemes for diffusion equations with an obstacle term

Backward differentiation formula finite difference schemes for diffusion equations with an obstacle term

On the American style futures contracts

Backward Differentiation Formula finite difference schemes for diffusion equations with an obstacle term

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