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- Fang Fang, Cornelis W. Oosterlee
- SIAM J. Scientific Computing
- 2008

Abstract. Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The key insight is in the close relation of the characteristic function with the series coefficients of the Fourier-cosine expansion of the density function. In most cases, the convergence rate of the COS method is… (More)

- Yogi A. Erlangga, Cornelis W. Oosterlee, Cornelis Vuik
- SIAM J. Scientific Computing
- 2006

- Fang Fang, Cornelis W. Oosterlee
- Numerische Mathematik
- 2009

We present a pricing method based on Fourier-cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth (C[a, b] ∈ R) transitional probability density functions. The computational complexity is… (More)

We discuss a nonlinear multigrid method for a linear complementarity problem. The convergence is improved by a recombination of iterants. The problem under consideration deals with option pricing from mathematical finance. Linear complementarity problems arise from so-called American-style options. A 2D convectiondiffusion type operator is discretized with… (More)

In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation,… (More)

A jump-diffusion model for a single-asset market is considered. Under this assumption the value of a European contingency claim satisfies a general partial integro-differential equation (PIDE). The equation is localized and discretized in space using finite differences and finite elements and in time by the second order backward differentiation formula… (More)

- Lech A. Grzelak, Cornelis W. Oosterlee
- SIAM J. Financial Math.
- 2011

We discuss the Heston [Heston-1993] model with stochastic interest rates driven by Hull-White [Hull,White-1996] (HW) or Cox-Ingersoll-Ross [Cox, et al.-1985] (CIR) processes. Two projection techniques to derive affine approximations of the original hybrid models are presented. In these approximations we can prescibe a non-zero correlation structure between… (More)

- R. Lord, Fang Fang, F. Bervoets, Cornelis W. Oosterlee
- SIAM J. Scientific Computing
- 2008

- Ariel Almendral, Cornelis W. Oosterlee
- SIAM J. Scientific Computing
- 2007

A finite-difference method for integro-differential equations arising from Lévy driven asset processes in finance is discussed. The equations are discretized in space by the collocation method and in time by an explicit backward differentiation formula. The discretization is shown to be second-order accurate independently of the degree of the singularity in… (More)

Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The convergence rate of the COS method is exponential and the computational complexity is linear. It has a wide range of applicability for different underlying dynamics, including Lévy processes and Heston’s stochastic volatility… (More)