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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
Article

Abstract

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.

Keywords

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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