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High-order compact finite difference schemes for a nonlinear Black-Scholes equation

journal contribution
posted on 2023-06-08, 08:38 authored by Bertram Duering, Michel Fournié, Ansgar Jüngel
A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

History

Publication status

  • Published

Journal

International Journal of Theoretical and Applied Finance

ISSN

0219-0249

Publisher

World Scientific Publishing

Issue

7

Volume

6

Page range

767-789

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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