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van Rhijn, J. (author), Oosterlee, C.W. (author), Grzelak, L.A. (author), Liu, S. (author)Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ito ^ stochastic differential equations (SDEs). We propose a scheme that approximates the path-wise conditional...journal article 2022
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Liu, S. (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By employing an artificial neural network to learn these...journal article 2022
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den Haan, T.R.B. (author), Chau, K. W. (author), van der Schans, M. (author), Oosterlee, C.W. (author)In this work, we consider rule-based investment strategies for managing a defined contribution pension savings scheme, under the Dutch pension fund testing model. We find that dynamic, rule-based investment strategies can outperform traditional static strategies, by which we mean that the investor may achieve the target retirement income with...journal article 2022
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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
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Andersson, K.H. (author), Oosterlee, C.W. (author)In this paper, we propose a neural network-based method for CVA computations of a portfolio of derivatives. In particular, we focus on portfolios consisting of a combination of derivatives, with and without true optionality, e.g., a portfolio of a mix of European- and Bermudan-type derivatives. CVA is computed, with and without netting, for...journal article 2021
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Chau, K.W. (author), Tang, Jok (author), Oosterlee, C.W. (author)In this work, we developed a Python demonstrator for pricing total valuation adjustment (XVA) based on the stochastic grid bundling method (SGBM). XVA is an advanced risk management concept which became relevant after the recent financial crisis. This work is a follow-up work on Chau and Oosterlee in (Int J Comput Math 96(11):2272–2301, 2019)...journal article 2020
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van der Stoep, A.W. (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) framework, introduced in [L. A. Grzelak (2019) The CLV framework-A fresh look at efficient pricing with smile, International Journal of Computer Mathematics 96 (11), 2209-2228]. The CV framework consists of two elements, a ...journal article 2020
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Fontanari, A. (author), Cirillo, Pasquale (author), Oosterlee, C.W. (author)A novel generating mechanism for non-strict bivariate Archimedean copulas via the Lorenz curve of a non-negative random variable is proposed. Lorenz curves have been extensively studied in economics and statistics to characterize wealth inequality and tail risk. In this paper, these curves are seen as integral transforms generating increasing...journal article 2020
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Kumar, P. (author), Rodrigo, Carmen (author), Gaspar, Francisco J. (author), Oosterlee, C.W. (author)We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that is modeled using the Richards equation. We propose a stochastic extension for the empirical models that are typically employed to close the Richards equations. This is achieved by treating the soil parameters in...journal article 2019
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Le Floch, F.L.Y. (author), Oosterlee, C.W. (author)This paper explains how to calibrate a stochastic collocation polynomial against market option prices directly. The method is first applied to the interpolation of short-maturity equity option prices in a fully arbitrage-free manner and then to the joint calibration of the constant maturity swap convexity adjustments with the interest rate...journal article 2019
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Liu, S. (author), Borovykh, Anastasia (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training hidden neurons within a machine learning framework, based on available financial option prices. The...journal article 2019
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Le Floch, F.L.Y. (author), Oosterlee, C.W. (author)This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different representations against market option prices, detail how to...journal article 2019
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Liu, S. (author), Oosterlee, C.W. (author), Bohte, Sander M. (author)This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a...journal article 2019
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Kumar, P. (author), Luo, P. (author), Gaspar, Francisco J. (author), Oosterlee, C.W. (author)A multilevel Monte Carlo (MLMC) method for Uncertainty Quantification (UQ) of advection-dominated contaminant transport in a coupled Darcy–Stokes flow system is described. In particular, we focus on high-dimensional epistemic uncertainty due to an unknown permeability field in the Darcy domain that is modelled as a lognormal random field....journal article 2018
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Feng, Q. (author), Oosterlee, C.W. (author)We study the impact of wrong way risk (WWR) on credit valuation adjustment (CVA) for Bermudan options. WWR is modeled by a dependency between the underlying asset and the intensity of the counterparty's default. Two WWR models are proposed, based on a deterministic function and a CIR-jump (CIRJ) model, respectively. We present a nonnested...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 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