- document
-
Salvador, Beatriz (author), Oosterlee, C.W. (author), van der Meer, R. (author)Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). The classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied here. Instead of using numerical techniques based on finite element or difference methods, we...journal article 2021
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
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
- document
-
Zhang, B. (author), Oosterlee, C.W. (author)Swing options give contract holders the right to modify amounts of future delivery of certain commodities, such as electricity or gas. We assume that these options can be exercised at any time before the end of the contract, and more than once. However, a recovery time between any two consecutive exercise dates is incorporated as a constraint to...journal article 2013
- document
-
Zhang, B. (author), Oosterlee, C.W. (author)We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European style and American-style Asian options and for discretely and continuously monitored versions. In the present paper...journal article 2013
- document
-
Ruijter, M.J. (author), Oosterlee, C.W. (author)The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826--848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27--62]. In this paper, we extend the method to higher dimensions, with a multidimensional asset price...journal article 2012
- document
-
Zhang, B. (author), Van der Weide, J.A.M. (author), Oosterlee, C.W. (author)In this article, we propose an efficient pricing method for Asian options with early–exercise features. It is based on a two–dimensional integration and a backward recursion of the Fourier coefficients, in which several numerical techniques, like Fourier cosine expansions, Clenshaw–Curtis quadrature and the Fast Fourier transform (FFT) are...report 2012
- document
-
Zhang, B. (author), Oosterlee, C.W. (author)We propose an efficient pricing method for arithmetic, and geometric, Asian options under Levy processes, based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European–style and American–style Asian options, and for discretely and continuously monitored versions. In the present paper we...report 2011
- document
-
Huang, X. (author), Oosterlee, C.W. (author)We derive two types of saddlepoint approximations for expectations in the form of E[(X - K)+], where X is the sum of n independent random variables and K is a known constant. We establish error convergence rates for both types of approximations in the independently and identically distributed case. The approximations are further extended to...journal article 2011
- document
-
Fang, F. (author), Oosterlee, C.W. (author)We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier cosine series expansion, as in [F. Fang and C.W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826–848...journal article 2011
- document
-
Van der Pijl, S.P. (author), Oosterlee, C.W. (author)This work aims to model the optimal control of dike heights. The control problem leads to so-called Hamilton-Jacobi-Bellman (HJB) variational inequalities, where the dike-increase and reinforcement times act as input quantities to the control problem. The HJB equations are solved numerically with an Essentially Non-Oscillatory (ENO) method. The...journal article 2011
- document
-
Van der Pijl, S.P. (author), Oosterlee, C.W. (author)This work aims to model the optimal control of dike heights. The control problem leads to so-called Hamilton-Jacobi-Bellman (HJB) variational inequalities, where the dike-increase and reinforcement times act as input quantities to the control problem. The HJB equations are solved numerically with an Essentially Non-Oscillatory (ENO) method. The...journal article 2011
- document
-
Rodrigo, C. (author), Gaspar, F.J. (author), Oosterlee, C.W. (author), Yavneh, I. (author)The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted ElFMG, which compares the total error of the l-level FMG solution against the inherent discretization error. This measure can be used for...journal article 2010
- document
-
Grzelak, L.A. (author), Oosterlee, C.W. (author)We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull-White [HW96]. We then extend the framework by...report 2010