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

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2001
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Düring, Bertram
Fournié, Michel
Jüngel, Ansgar
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CoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie
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Zusammenfassung

A nonlinear Black-Scholes equation which models transaction costs arising in the heding of portfolios is discretized semi-implicitly using high order compact finite difference schemes. In particular, the compact schemes of Rigal are generalized. 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.

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Fachgebiet (DDC)
510 Mathematik
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option pricing, transaction costs, parabolic equations, compact finite difference discretizations
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ISO 690DÜRING, Bertram, Michel FOURNIÉ, Ansgar JÜNGEL, 2001. High order compact finite difference schemes for a nonlinear Black-Scholes equation
BibTex
@techreport{During2001order-617,
  year={2001},
  series={CoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie},
  title={High order compact finite difference schemes for a nonlinear Black-Scholes equation},
  number={2001/07},
  author={Düring, Bertram and Fournié, Michel and Jüngel, Ansgar}
}
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