Balanced Milstein Methods for Ordinary SDEs

Kahl, Christian; Schurz, Henri

doi:10.1163/156939606777488842

Cited by 15 publications

(14 citation statements)

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“…There are schemes based on implicit time-stepping integrators, see for example Alfonsi [3], Kahl and Schurz [44] and Dereich, Neuenkirch and Szpruch [19]. Other time-discretization approaches involve splitting the drift and diffusion vector fields and evaluating their separate flows (sometimes exactly) before they are recomposed together, typically using the Strang ansatz.…”

Section: Introductionmentioning

confidence: 99%

Chi-Square Simulation of the Cir Process and the Heston Model

Malham

Wiese

2013

Int. J. Theor. Appl. Finan.

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The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First, we establish a new representation for the central chi-square density based on sums of powers of generalized Gaussian random variables. Second, we show that Marsaglia's polar method extends to this distribution, providing a simple, exact, robust and efficient acceptance-rejection method for generalized Gaussian sampling and thus central chi-square sampling. Third, we derive a simple, high-accuracy, robust and efficient direct inversion method for generalized Gaussian sampling based on the Beasley-Springer-Moro method. Indeed the accuracy of the approximation to the inverse cumulative distribution function is to the tenth decimal place. We then apply our methods to non-central chi-square variance sampling in the Heston model. We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. Using the additivity property of the chi-square distribution, our methods apply in all parameter regimes.

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Section: Introductionmentioning

confidence: 99%

Chi-Square Simulation of the Cir Process and the Heston Model

Malham

Wiese

2013

Int. J. Theor. Appl. Finan.

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“…Discretization schemes with strong rates (which is important for the multilevel method presented later) given the Feller condition (or even stronger conditions) have been shown in [1,3,7,19] and [39]. Recently, Hutzenthaler et al [37] have proven a strong rate under the condition that 0.5σ 2 < 2κθ .…”

Section: Discretization Schemes For Sdesmentioning

confidence: 97%

FPGA Based Accelerators for Financial Applications

Schryver¹

2015

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“…we can not use a semi discrete method. If we want to produce a boundary preserving numerical scheme then these sdes (that we should fully discretize) can be approximated by balanced Milstein methods (see [14], [15], [16] and [2]).…”

Section: Summary and Commentsmentioning

confidence: 99%