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Z -Transform and preconditioning techniques for option pricing


  • Gianluca Fusai
  • Daniele Marazzina
  • Marina Marena
  • Michael Ng


In the present paper, we convert the usual n -step backward recursion that arises in option pricing into a set of independent integral equations by using a z -transform approach. In order to solve these equations, we consider different quadrature procedures that transform the integral equation into a linear system that we solve by iterative algorithms and we study the benefits of suitable preconditioning techniques. We show the relevance of our procedure in pricing options (such as plain vanilla, lookback, single and double barrier options) when the underlying evolves according to an exponential Lévy process.

Suggested Citation

  • Gianluca Fusai & Daniele Marazzina & Marina Marena & Michael Ng, 2012. "Z -Transform and preconditioning techniques for option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1381-1394, November.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:9:p:1381-1394 DOI: 10.1080/14697688.2010.538074

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    References listed on IDEAS

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    4. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    5. Enrico De Giorgi, "undated". "A Note on Portfolio Selection under Various Risk Measures," IEW - Working Papers 122, Institute for Empirical Research in Economics - University of Zurich.
    6. Solange M. Berstein & Rómulo A. Chumacero, 2006. "Quantifying the costs of investment limits for Chilean pension funds," Fiscal Studies, Institute for Fiscal Studies, vol. 27(1), pages 99-123, March.
    7. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, February.
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    Cited by:

    1. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," LSE Research Online Documents on Economics 67564, London School of Economics and Political Science, LSE Library.

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