Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform

Larsson, Elisabeth; hlander, Krister; Hall, Andreas

doi:10.1016/j.cam.2007.10.039

Cited by 41 publications

(25 citation statements)

References 25 publications

(39 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fausshauer et al, 2004a;Hon and Mao, 1999;Larsson et al, 2008;Pettersson et al, 2008) In these cases, L is a second order elliptic differential operator, and the computation of (LΦ) X is straightforward. For jump-diffusions, which are finite activity, this algorithm (and its companion version for American options below) has been implemented and studied in (Chan, 2010; with different choices of basis functions (inverse multi-quadric and cubic spline, respectively).…”

Section: Determine the Rbf-interpolantmentioning

confidence: 99%

See 1 more Smart Citation

A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models

Brummelhuis

Chan

2013

Applied Mathematical Finance

View full text Add to dashboard Cite

We use Radial Basis Function (RBF) interpolation to price options in exponential Lévy models by numerically solving the fundamental pricing PIDE. Our RBF scheme can handle arbitrary singularities of the Lévy measure in 0 without introducing further approximations, making it simpler to implement than competing methods. In numerical experiments using processes from the CGMY-KoBoL class, the scheme is found to be second order convergent in the number of interpolation points, including for processes of unbounded variation.

show abstract

Section: Determine the Rbf-interpolantmentioning

confidence: 99%

“…(e.g. Fausshauer et al, 2004a;Hon and Mao, 1999;Larsson et al, 2008;Pettersson et al, 2008). (Chan, 2010) and (Chan, 2011) extended these studies to jump-diffusion models, which are finite activity.…”

Section: Introductionmentioning

confidence: 99%

A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models

Brummelhuis

Chan

2013

Applied Mathematical Finance

View full text Add to dashboard Cite

show abstract

“…Therefore two different matrices need to be factorised. In order to avoid this we use the BDF-2 scheme as described in [11].…”

Section: The Penalty Methodsmentioning

confidence: 99%

“…, N t . In [11] it is shown how the time steps can be chosen in such a way that β n 0 ≡ β 0 . Then the coefficient matrix is the same in all time steps and only one matrix factorisation is needed.…”

Section: The Penalty Methodsmentioning

confidence: 99%

Radial basis function partition of unity operator splitting method for pricing multi-asset American options

Shcherbakov

2016

Bit Numer Math

View full text Add to dashboard Cite

PostprintThis is the accepted version of a paper published in BIT Numerical Mathematics. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination. AbstractThe operator splitting method in combination with finite differences has been shown to be an efficient approach for pricing American options numerically. Here, the operator splitting formulation is extended to the radial basis function partition of unity method. An approach that has previously often been used together with radial basis function methods to deal with the free boundary arising in American option pricing is to solve a penalised version of the Black-Scholes equation. It is shown that the operator splitting technique outperforms the penalty approach when used with the radial basis function partition of unity method. Numerical experiments are performed for one, two and three underlying assets. The advantage of the operator splitting technique grows with the number of dimensions.

show abstract

“…, N t . In [38] it is shown how the time steps can be chosen in such a way that β n 0 ≡ β 0 . Then the coefficient matrix is the same in all time steps and only one matrix factorization is needed.…”

Section: The Bdf-2 Time Stepping Schemementioning

confidence: 99%

Radial basis function partition of unity methods for pricing vanilla basket options

Shcherbakov

Larsson

2016

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

PostprintThis is the accepted version of a paper published in Computers and Mathematics with Applications. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.Citation for the original published paper (version of record):Shcherbakov, V., Larsson, E. (2016) Radial basis function partition of unity methods for pricing vanilla basket options. Abstract Mesh-free methods based on radial basis function (RBF) approximation are becoming widely used for solving PDE problems. They are flexible with respect to the problem geometry and highly accurate. A disadvantage of these methods is that the linear system to be solved becomes dense for globally supported RBFs. A remedy is to introduce localisation techniques such as partition of unity. RBF partition of unity methods (RBF-PUM) allow for a significant sparsification of the linear system and lower the computational effort. In this work we apply a global RBF method as well as RBF-PUM to problems in option pricing. We consider one-and two-dimensional vanilla options. In order to price American options we employ a penalty approach. A penalty term, suitable for American multi-asset call options, has been designed. RBF-PUM is shown to be competitive compared with a finite difference method and a global RBF method. It is as accurate as the global RBF method, but significantly faster. The results for RBF-PUM look promising for extension to higher-dimensional problems. Computers and Mathematics with

show abstract

Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform

Cited by 41 publications

References 25 publications

A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models

A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models

Radial basis function partition of unity operator splitting method for pricing multi-asset American options

Radial basis function partition of unity methods for pricing vanilla basket options

Contact Info

Product

Resources

About