High-order ADI schemes for diffusion equations with mixed derivatives in the combination technique

Hendricks, Christian; Ehrhardt, Matthias; Günther, Michael

doi:10.1016/j.apnum.2015.11.003

Cited by 23 publications

(15 citation statements)

References 17 publications

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“…These have motivated our approaches. In this paper, we are particularly interested in computations based on a Heston put option model [4,5,8,10,12,22].…”

Section: Introductionmentioning

confidence: 99%

An Exploration of a Balanced Up-downwind Scheme for Solving Heston Volatility Model Equations on Variable Grids

Sun¹,

Sheng²

2018

Preprint

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This paper studies an effective finite difference scheme for solving two-dimensional Heston stochastic volatility option pricing model problems. A dynamically balanced up-downwind strategy for approximating the cross-derivative is implemented and analyzed. Semi-discretized and spatially nonuniform platforms are utilized. The numerical method comprised is simple, straightforward with reliable first order overall approximations. The spectral norm is used throughout the investigation and numerical stability is proven. Simulation experiments are given to illustrate our results.

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“…These have motivated our approaches. In this paper, we are particularly interested in computations based on a Heston put option model [4,5,8,10,12,22].…”

Section: Introductionmentioning

confidence: 99%

An Exploration of a Balanced Up-downwind Scheme for Solving Heston Volatility Model Equations on Variable Grids

Sun¹,

Sheng²

2018

Preprint

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“…In this chapter we combine the approaches from [21] and [16], to obtain a sparse grid high-order ADI scheme for option pricing in stochastic volatility models. In the next section we recall stochastic volatility models for option pricing and the related convection-diffusion partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Sparse Grid High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models

2016

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“…Equation (19) defines a fourth-order compact approximation for (19). In other words, we have a system of equations which defines a fourth-order accurate approximation for (19) at any point on the inner grid of the spatial domain (all points of the spatial domain except those that lie on the x and y boundaries).…”

Section: High-order Compact Scheme For Implicit Stepsmentioning

confidence: 99%

“…In other words, we have a system of equations which defines a fourth-order accurate approximation for (19) at any point on the inner grid of the spatial domain (all points of the spatial domain except those that lie on the x and y boundaries). To approximate (19) at points along the x boundaries of the inner grid of the spatial domain, we will require a contribution from the Dirichlet values at the x-boundaries of the spatial domain. We collect these separately in a vector d. Details on the boundary conditions are given in Section 7.…”

Section: High-order Compact Scheme For Implicit Stepsmentioning

confidence: 99%

“…In [13] this approach was combined with different high-order discretisations in space, using highorder compact schemes for two-dimensional convection-diffusion problems with mixed derivatives and constant coefficients. In [19] this approach was combined with sparse grids and applied to a multi-dimensional Black-Scholes equation, again with constant coefficients.…”

Section: Introductionmentioning

confidence: 99%

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High-order ADI scheme for option pricing in stochastic volatility models

Düring

Miles

2017

Journal of Computational and Applied Mathematics

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We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer's ADI time-stepping method, to obtain an efficient method which is fourth-order accurate in space and second-order accurate in time. Numerical experiments for the European put option pricing problem using Heston's stochastic volatility model confirm the high-order convergence.

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High-order ADI schemes for diffusion equations with mixed derivatives in the combination technique

Cited by 23 publications

References 17 publications

An Exploration of a Balanced Up-downwind Scheme for Solving Heston Volatility Model Equations on Variable Grids

An Exploration of a Balanced Up-downwind Scheme for Solving Heston Volatility Model Equations on Variable Grids

Sparse Grid High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models

High-order ADI scheme for option pricing in stochastic volatility models

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