Using meshfree approximation for multi‐asset American options

Fasshauer, Gregory E.; Khaliq, Abdul; Voss, D.A.

doi:10.1080/02533839.2004.9670904

Cited by 88 publications

(55 citation statements)

References 13 publications

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“…The penalty approach has been implemented in three versions: implicit, implicit-explicit and explicit. Previously the implicit-explicit formulation has been commonly used with radial basis functions [3,17,18], because it allowed to avoid solving a non-linear problem, while enforcing a "rather mild" constraint on the time step size, which still led to unnecessary extra calculations in the time integration. This work shows that, if the partition of unity technique is employed, the implicit version should be preferred.…”

Section: Resultsmentioning

confidence: 99%

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

Shcherbakov

2016

Bit Numer Math

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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.

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Section: Resultsmentioning

confidence: 99%

“…We use the type of penalty function for American put options that was introduced by Nielsen et al [13] and has been used later by several authors together with finite differences [14] as well as radial basis functions [3,17,18]. The penalty function is given by…”

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

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“…Hence, the approach deals with high-dimensional data with relative ease and its numerical results o er an e cient, highly accurate and versatile spatial approximation to the true solution (Du y (2006)). In addition, the technique works easily with correlation terms without requiring special development (Fasshauer et al (2004)). This feature is of crucial importance in the growing market of multi-asset derivative products.…”

Section: The Meshfree Methods and The Radial Basis Function Interpolamentioning

confidence: 99%

“…They are widely used in engineering in providing numerical solutions to PDEs (see Liu (2003) and Fasshauer (2007)). In nance, the applications are concentrated in the solution of time-dependent PDEs for pricing options (Fasshauer et al (2004), Pettersson et al (2008) and Mei and Cheng (2008)) and credit derivatives (Guarin et al (2011)). …”

Section: The Meshfree Methods and The Radial Basis Function Interpolamentioning

confidence: 99%

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Recovering default risk from CDS spreads with a nonlinear filter

Guarin¹,

Liu²,

Ng³

2014

Journal of Economic Dynamics and Control

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We propose a nonlinear lter to estimate the time-varying instantaneous default risk from the term structure of credit default swap (CDS) spreads. Based on the numerical solution of the Fokker-Planck equation (FPE) using a meshfree interpolation method, the lter performs a joint estimation of default intensities and CIR model parameters. As the FPE can account for nonlinear functions and nonGaussian errors, the proposed framework provides more exibility and accuracy.We test the nonlinear lter on simulated CDS spreads and apply it to daily CDS spreads of the Dow Jones Industrial Average component companies from 2005 to 2010 with supportive results.

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A greedy algorithm for partition of unity collocation method in pricing American options

Fadaei

Khan

Akgül

2019

Math Methods in App Sciences

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A greedy algorithm in combination with radial basis functions partition of unity collocation (GRBF‐PUC) scheme is used as a locally meshless method for American option pricing. The radial basis function partition of unity method (RBF‐PUM) is a localization technique. Because of having interpolation matrices with large condition numbers, global approximants and some local ones suffer from instability. To overcome this, a greedy algorithm is added to RBF‐PUM. The greedy algorithm furnishes a subset of best nodes among the points X. Such nodes are then used as points of trial in a locally supported RBF approximant for each partition. Using of greedy selected points leads to decreasing the condition number of interpolation matrices and reducing the burdensome in pricing American options.

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Using meshfree approximation for multi‐asset American options

Cited by 88 publications

References 13 publications

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

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

Recovering default risk from CDS spreads with a nonlinear filter

A greedy algorithm for partition of unity collocation method in pricing American options

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