Z-Transform and preconditioning techniques for option pricing

Gianluca Fusai, Daniele Marazzina*, Marina Marena, Kwok Po NG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1381-1394
Number of pages14
JournalQuantitative Finance
Issue number9
Publication statusPublished - Sept 2012

Scopus Subject Areas

  • Finance
  • Economics, Econometrics and Finance(all)

User-Defined Keywords

  • Exotic options
  • Linear systems
  • Numerical methods for option pricing
  • Preconditioners
  • Toeplitz matrices


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