Wavelet Galerkin pricing of American options on Lévy driven assets

Matache, Ana-Maria; Nitsche, Pál-Andrej; Schwab, Christoph

doi:10.1080/14697680500244478

Cited by 97 publications

(72 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Table 6: The input parameters for evaluating European put options under CGMY when Y > 1. When Y = 1.4, the parameters are taken from [16], whereas the parameters for Y = 1.8 are selected to stress our numerical algorithm.…”

Section: European Optionsmentioning

confidence: 99%

“…Compared with [16], our approach can be easily implemented in existing option pricing software. We use only finite difference discretization methods and standard sparse matrix solvers.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Lévy process models have become popular in the financial literature [1,2,3,4,5,6,7]. Option pricing, under exponential Lévy process with finite activity [5,8,9,10,11,12] and infinite activity [13,14,15,16,17] has been extensively studied. In these papers, various numerical methods were proposed for solving the option pricing Partial IntegroDifferential Equation (PIDE).…”

Section: Introductionmentioning

confidence: 99%

“…In [16], a Wavelet-Galerkin finite element approach is used to price options under an infinite activity process. Compared with [16], our approach can be easily implemented in existing option pricing software.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust numerical valuation of European and American options under the CGMY process

Wang¹,

Wan²,

Forsyth³

2007

JCF

View full text Add to dashboard Cite

We develop an implicit discretization method for pricing European and American options when the underlying asset is driven by an infinite activity Lévy process. For processes of finite variation, quadratic convergence is obtained as the mesh and time step are refined. For infinite variation processes, better than first order accuracy is achieved. The jump component in the neighborhood of log jump size zero is specially treated by using a Taylor expansion approximation and the drift term is dealt with using a semi-Lagrangian scheme. The resulting Partial Integro-Differential Equation (PIDE) is then solved using a preconditioned BiCGSTAB method coupled with a fast Fourier transform. Proofs of fully implicit timestepping stability and monotonicity are provided. The convergence properties of the BiCGSTAB scheme are discussed and compared with a fixed point iteration. Numerical tests showing the convergence and performance of this method for European and American options under processes of finite and infinite variation are presented.

show abstract

Section: European Optionsmentioning

confidence: 99%

“…Compared with [16], our approach can be easily implemented in existing option pricing software. We use only finite difference discretization methods and standard sparse matrix solvers.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust numerical valuation of European and American options under the CGMY process

Wang¹,

Wan²,

Forsyth³

2007

JCF

View full text Add to dashboard Cite

show abstract

“…Valuing American options in such models is however far from trivial, due to the weakly singular kernels of the integral terms appearing in the PIDE, as reported in, e.g., [2,6,10,11].…”

Section: Introductionmentioning

confidence: 99%

A Fast Method for Pricing Early-Exercise Options with the FFT

Lord¹,

Fang

Bervoets³

et al. 2007

Computational Science – ICCS 2007

View full text Add to dashboard Cite

Abstract.A fast and accurate method for pricing early exercise options in computational finance is presented in this paper. The main idea is to reformulate the well-known risk-neutral valuation formula by recognizing that it is a convolution. This novel pricing method, which we name the 'CONV' method for short, is applicable to a wide variety of payoffs and only requires the knowledge of the characteristic function of the model. As such the method is applicable within exponentially Lévy models, including the exponentially affine jump-diffusion models. For an M -times exercisable Bermudan option, the overall complexity is O (MN log(N )) with N grid points used to discretize the price of the underlying asset. It is also shown that American options can be very efficiently computed by combining Richardson extrapolation to the CONV method.

show abstract

Finite Difference Methods for Early Exercise Options

Toivanen

2010

Encyclopedia of Quantitative Finance

View full text Add to dashboard Cite

Usually, options with early exercise possibility like American and Bermudan options have to be priced numerically. In this article, approaches based on partial differential operators and their finite difference discretization are considered. The early exercise possibility leads to an inequality constraint for the price of the option. Linear complementarity problem (LCP) and other formulations incorporating this constraint are discussed. Fairly standard finite difference discretizations can be used for the underlying partial differential operator. Several solution and approximation methods including the projected successive over relaxation (PSOR) method and penalty methods are described. As an example, an American put option is priced using different methods under the Black–Scholes model.

show abstract

Wavelet Galerkin pricing of American options on Lévy driven assets

Cited by 97 publications

References 34 publications

Robust numerical valuation of European and American options under the CGMY process

Robust numerical valuation of European and American options under the CGMY process

A Fast Method for Pricing Early-Exercise Options with the FFT

Finite Difference Methods for Early Exercise Options

Contact Info

Product

Resources

About