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Z -Transform and preconditioning techniques for option pricing

Author

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

Abstract

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 L�vy 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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    Cited by:

    1. S. Corsaro & D. Marazzina & Z. Marino, 2015. "A parallel wavelet-based pricing procedure for Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 15(1), pages 101-113, January.
    2. Fusai, Gianluca & Germano, Guido & Marazzina, Daniele, 2016. "Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options," European Journal of Operational Research, Elsevier, vol. 251(1), pages 124-134.
    3. Sesana, Debora & Marazzina, Daniele & Fusai, Gianluca, 2014. "Pricing exotic derivatives exploiting structure," European Journal of Operational Research, Elsevier, vol. 236(1), pages 369-381.

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