On American options under the variance gamma process

Ariel Almendral; Cornelis W. Oosterlee

doi:10.1080/13504860600724885

On American options under the variance gamma process

Ariel Almendral^*
, Cornelis W. Oosterlee

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

American options are considered in a market where the underlying asset follows a Variance Gamma process. A sufficient condition is given for the failure of the smooth fit principle for finite horizon call options. A second-order accurate finite-difference method is proposed to find the American option price and the exercise boundary. The problem is formulated as a Linear Complementarity Problem and solved numerically by a convenient splitting. Computations have been accelerated with the help of the Fast Fourier Transform. A stability analysis shows that the scheme is conditionally stable, with a mild stability condition of the form k=O(|log(h)|-1). The theoretical results are verified numerically throughout a series of numerical experiments.

Original language	English
Pages (from-to)	131-152
Number of pages	22
Journal	Applied Mathematical Finance
Volume	14
Issue number	2
DOIs	https://doi.org/10.1080/13504860600724885
Publication status	Published - May 2007
Externally published	Yes

Bibliographical note

Funding Information:
This research was supported by the Dutch government through the national program BSIK: knowledge and research capacity, in the ICT project BRICKS (http://www.bsik-bricks.nl), theme MSV1. We would like to thank the referees for valuable comments.

Funding

This research was supported by the Dutch government through the national program BSIK: knowledge and research capacity, in the ICT project BRICKS (http://www.bsik-bricks.nl), theme MSV1. We would like to thank the referees for valuable comments.

Keywords

FFT
Finite differences
Integro-differential equations
Variance gamma

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10.1080/13504860600724885

Cite this

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title = "On American options under the variance gamma process",

abstract = "American options are considered in a market where the underlying asset follows a Variance Gamma process. A sufficient condition is given for the failure of the smooth fit principle for finite horizon call options. A second-order accurate finite-difference method is proposed to find the American option price and the exercise boundary. The problem is formulated as a Linear Complementarity Problem and solved numerically by a convenient splitting. Computations have been accelerated with the help of the Fast Fourier Transform. A stability analysis shows that the scheme is conditionally stable, with a mild stability condition of the form k=O(|log(h)|-1). The theoretical results are verified numerically throughout a series of numerical experiments.",

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AB - American options are considered in a market where the underlying asset follows a Variance Gamma process. A sufficient condition is given for the failure of the smooth fit principle for finite horizon call options. A second-order accurate finite-difference method is proposed to find the American option price and the exercise boundary. The problem is formulated as a Linear Complementarity Problem and solved numerically by a convenient splitting. Computations have been accelerated with the help of the Fast Fourier Transform. A stability analysis shows that the scheme is conditionally stable, with a mild stability condition of the form k=O(|log(h)|-1). The theoretical results are verified numerically throughout a series of numerical experiments.

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On American options under the variance gamma process

Abstract

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