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

Düring, Bertram; Hendricks, Christian; Miles, James A.

doi:10.1007/978-3-319-61282-9_16

Cited by 1 publication

(2 citation statements)

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“…A straightforward extension of this paper is the introduction of the so-called SVCJ model which allows for jumps in both returns and volatility. As a second extension, one can combine the method presented in this paper with high-order alternating direction implicit methods [18] and with sparse grids methods [21,16]. We leave these extensions for future research.…”

Section: Discussionmentioning

confidence: 99%

“…[25] where different efficient methods for solving the American option pricing problem for the Heston model are proposed. Other approaches include finite element-finite volume [37], multigrid [8], sparse wavelet [24], FFT-based [30], spectral [36], hybrid tree-finite difference [5] methods and operator splitting techniques [23,15,18,21,16].…”

Section: Introductionmentioning

confidence: 99%

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High-order compact finite difference scheme for option pricing in stochastic volatility jump models

Düring

Pitkin

2019

Journal of Computational and Applied Mathematics

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We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential equation. The scheme is fourth order accurate in space and second order accurate in time. Numerical experiments for the European option pricing problem are presented. We validate the stability of the scheme numerically and compare its performance to standard finite difference and finite element methods. The new scheme outperforms a standard discretisation based on a second-order central finite difference approximation in all our experiments. At the same time, it is very efficient, requiring only one initial LU -factorisation of a sparse matrix to perform the option price valuation. Compared to finite element approaches, it is very parsimonious in terms of memory requirements and computational effort, since it achieves high-order convergence without requiring additional unknowns, unlike finite element methods with higher polynomial order basis functions. The new high-order compact scheme can also be useful to upgrade existing implementations based on standard finite differences in a straightforward manner to obtain a highly efficient option pricing code.

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Section: Discussionmentioning

confidence: 99%