Methodology and Computing in Applied Probability

, Volume 11, Issue 3, pp 359–383

# Fourier Inversion Formulas in Option Pricing and Insurance

• Daniel Dufresne
• 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

42A61 91B30

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## 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