Methodology and Computing in Applied Probability

, Volume 11, Issue 3, pp 359–383 | Cite as

Fourier Inversion Formulas in Option Pricing and Insurance

  • Daniel DufresneEmail author
  • Jose Garrido
  • Manuel Morales


Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max (SK, 0) also arises in excess-of-loss or stop-loss insurance, and we show that Fourier methods may be used to compute them. In this paper, we take the idea of using Parseval’s theorem further: (1) formulas requiring weaker assumptions; (2) relationship with classical inversion theorems for probability distributions; (3) formulas for payoffs which occur in insurance. Numerical examples are provided.


Fourier inversion Option pricing Stop-loss premiums Risk theory 

AMS 2000 Subject Classification

42A61 91B30 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Daniel Dufresne
    • 1
    • 2
    Email author
  • Jose Garrido
    • 3
  • Manuel Morales
    • 4
  1. 1.EconomicsUniversity of MelbourneMelbourneAustralia
  2. 2.Centre for Actuarial StudiesUniversity of MelbourneMelbourneAustralia
  3. 3.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada
  4. 4.Department of Mathematics and StatisticsUniversité de MontréalMontrealCanada

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