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van der Have, Z. (author), Oosterlee, C.W. (author)In this paper, we consider the COS method for pricing European and Bermudan options under the stochastic alpha beta rho (SABR) model. In the COS pricing method, we make use of the characteristic function of the discrete forward process. We observe second-order convergence by using a second-order Taylor scheme in the discretization, or by...journal article 2018
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Grzelak, L.A. (author), Witteveen, J.A.S. (author), Oosterlee, C.W. (author), Suárez-Taboada, M. (author)In this article, we propose an efficient approach for inverting computationally expensive cumulative distribution functions. A collocation method, called the Stochastic Collocation Monte Carlo sampler (SCMC sampler), within a polynomial chaos expansion framework, allows us the generation of any number of Monte Carlo samples based on only a...journal article 2018
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Suárez-Taboada, María (author), Witteveen, Jeroen A.S. (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)In this paper, we study the impact of the parameters involved in Heston model by means of Uncertainty Quantification. The Stochastic Collocation Method already used for example in computational fluid dynamics, has been applied throughout this work in order to compute the propagation of the uncertainty from the parameters of the model to the...journal article 2018
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Chau, K.W. (author), Oosterlee, C.W. (author)We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate...journal article 2018
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von Sydow, Lina (author), Milovanović, Slobodan (author), Larsson, Elisabeth (author), In 't Hout, Karel (author), Wiktorsson, Magnus (author), Oosterlee, C.W. (author), Shcherbakov, Victor (author), Wyns, Maarten (author), Leitao Rodriguez, A. (author), Jain, S. (author), Haentjens, Tinne (author), Waldén, Johan (author)In the recent project BENCHOP–the BENCHmarking project in Option Pricing we found that Stochastic and Local Volatility problems were particularly challenging. Here we continue the effort by introducing a set of benchmark problems for this type of problems. Eight different methods targeted for the Stochastic Differential Equation (SDE)...journal article 2018
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van der Stoep, A.W. (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)We present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994, 7, 18–20], [Int. J. Theor. Appl. Finance, 1998, 1, 61–110] models. In particular, we consider the stochastic local volatility model—see e.g. Lipton et al. [Quant. Finance, 2014, 14, 1899–1922], Piterbarg [Risk, 2007,...journal article 2017
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Leitao Rodriguez, A. (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European...journal article 2017
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Cong, F. (author), Oosterlee, C.W. (author)This paper enhances a well-known dynamic portfolio management algorithm, the BGSS algorithm, proposed by Brandt et al. (Review of Financial Studies, 18(3):831–873, 2005). We equip this algorithm with the components from a recently developed method, the Stochastic Grid Bundling Method (SGBM), for calculating conditional expectations. When solving...journal article 2016
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Cong, F. (author), Oosterlee, C.W. (author)This paper enhances a well-known dynamic portfolio management algorithm, the BGSS algorithm, proposed by Brandt et al. (Review of Financial Studies, 18(3):831–873, 2005). We equip this algorithm with the components from a recently developed method, the Stochastic Grid Bundling Method (SGBM), for calculating conditional expectations. When...journal article 2016
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Ortiz-Gracia, Luis (author), Oosterlee, C.W. (author)In the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error bounds. The nature of the local Shannon wavelets...journal article 2016
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Zhao, J. (author), Vollebregt, E.A.H. (author), Oosterlee, C.W. (author)The boundary element method (BEM) is widely used in fast numerical solvers for concentrated elastic contact problems arising from the wheel-rail contact in the railway industry. In this paper we extend the range of applicability of BEM by computing the influence coefficients (ICs) numerically. These ICs represent the Green's function of the...journal article 2016
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Zhao, J. (author), Vollebregt, E.A.H. (author), Oosterlee, C.W. (author)In this paper we extend the range of applicability of the boundary element method (BEM) for concentrated elastic contact problems by computing the influence coefficients (ICs) numerically. These ICs represent the Green's function of the problem, i.e. the surface deformation due to unit loads. For the half-space they are analytically available....report 2015
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Knibbe, H. (author), Vuik, C. (author), Oosterlee, C.W. (author)In geophysical applications, the interest in least-squares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of high-performance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The...journal article 2015
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Knibbe, H.P. (author), Vuik, Cornelis (author), Oosterlee, C.W. (author)In geophysical applications, the interest in least-squares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of high-performance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The...journal article 2015
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Zhao, J. (author), Vollebregt, E.A.H. (author), Oosterlee, C.W. (author)In this paper we extend the range of applicability of the boundary element method (BEM) for concentrated elastic contact problems by computing the influence coefficients (ICs) numerically. These ICs represent the Green's function of the problem, i.e. the surface deformation due to unit loads. For the half-space they are analytically available....report 2015
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Ruijter, M.J. (author), Oosterlee, C.W. (author)We develop a Fourier method to solve backward stochastic differential equations (BSDEs). A general theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier cosine series expansions, relying on the availability of a characteristic function. The method is...journal article 2015
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Luo, P. (author), Rodrigo, C (author), Gaspar, F. J. (author), Oosterlee, C.W. (author)In this study, a nonlinear multigrid method is applied for solving the system of incompressible poroelasticity equations considering nonlinear hydraulic conductivity. For the unsteady problem, an additional artificial term is utilized to stabilize the solutions when the equations are discretized on collocated grids. We employ two nonlinear...journal article 2015
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Zhao, J. (author), Vollebregt, E.A.H. (author), Oosterlee, C.W. (author)This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from a 3D frictional contact problem. It incorporates an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, and use azimuth angles as...report 2014
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Knibbe, H.P. (author), Mulder, W.A. (author), Oosterlee, C.W. (author), Vuik, C. (author)Three-dimensional reverse-time migration with the constant-density acoustic wave equation requires an efficient numerical scheme for the computation of wavefields. An explicit finite-difference scheme in the time domain is a common choice. However, it requires a significant amount of disk space for the imaging condition. The frequency-domain...journal article 2014
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Ortiz-Gracia, L. (author), Oosterlee, C.W. (author)We present a novel method for pricing European options based on the wavelet approximation method and the characteristic function. We focus on the discounted expected payoff pricing formula and compute it by means of wavelets. We approximate the density function associated to the underlying asset price process by a finite combination of jth order...journal article 2013