Cornelis W. Oosterlee

A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions

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 exponential and the computational complexity is linear. Its range of application covers underlying asset processes for which the characteristic function is known and various types of option contracts. We will present the method and its applications in two separate parts. The first one is this paper, where we deal with European options in particular. In a follow-up paper we will present its application to options with early-exercise features.

A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wavenumber Helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner.

A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options under Lévy Processes

A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by recognizing that it is a convolution. The resulting convolution is dealt with numerically by using the fast Fourier transform. This novel pricing method, which we dub the convolution method, is applicable to a wide variety of payoffs and requires only the knowledge of the characteristic function of the model. As such, the method is applicable within many regular affine models, among which is the class of exponential Levy models. For an

Pricing early-exercise and discrete barrier options by fourier-cosine series expansions

M

Geometric multigrid with applications to computational fluid dynamics

-times exercisable Bermudan option, the overall complexity is

A Fourier-Based Valuation Method for Bermudan and Barrier Options under Heston's Model

O(MN\log_2(N))

A new iterative solver for the time-harmonic wave equation

, with

Accurate Evaluation of European and American Options Under the CGMY Process

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On Three-Grid Fourier Analysis for Multigrid

grid points used to discretize the price of the underlying asset. American options are priced efficiently by applying Richardson extrapolation to the prices of Bermudan options.

On American Options Under the Variance Gamma Process

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 (