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Extending the BEM for elastic contact problems beyond the half-space approach

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

Extending the BEM for elastic contact problems beyond the half-space approach

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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A fast nonlinear conjugate gradient based method for 3D frictional contact problems

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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Efficient pricing of Asian options under Lévy processes based on Fourier cosine expansions. Part II. Early-exercise features and GPU implementation

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

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Efficient pricing of Asian options under Lévy processes based on Fourier cosine expansions Part I: European-style products

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

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On cross-currency models with stochastic volatility and correlated interest rates

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

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Efficient pricing of commodity options with early-exercise under the Ornstein–Uhlenbeck process

Zhang, B. (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)

We analyze the efficiency properties of a numerical pricing method based on Fourier-cosine expansions for early-exercise options. We focus on variants of Schwartz’ model [20] based on a mean reverting Ornstein-Uhlenbeck process [23], which is commonly used for modeling commodity prices. This process however does not possess favorable properties...

report 2010

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An efficient pricing algorithm for swing options based on fourier cosine expansions

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. In this paper, 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...

report 2010

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Acceleration of option pricing technique on graphics processing units

Zhang, B. (author), Oosterlee, C.W. (author)

The acceleration of an option pricing technique based on Fourier cosine expansions on the Graphics Processing Unit (GPU) is reported. European options, in particular with multiple strikes, and Bermudan options will be discussed. The influence of the number of terms in the Fourier cosine series expansion, the number of strikes, as well as the...

report 2010

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An equity-interest rate hybrid model with stochastic volatility and the interest rate smile

Grzelak, L.A. (author), Oosterlee, C.W. (author)

We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main processes. By an appropriate change of measure the...

report 2010

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Efficient option pricing with multi-factor equity-interest rate hybrid models

Grzelak, L.A. (author), Oosterlee, C.W. (author), Van Weeren, S. (author)

report 2009

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Saddlepoint approximations for expectations

Huang, X. (author), Oosterlee, C.W. (author)

report 2009

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On the Heston Model with stochastic interest rates

Grzelak, L.A. (author), Oosterlee, C.W. (author)