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Fourier Inversion Formulas in Option Pricing and Insurance

Author

Listed:
  • Daniel Dufresne

    (University of Melbourne
    University of Melbourne)

  • Jose Garrido

    (Concordia University)

  • Manuel Morales

    (Université de Montréal)

Abstract

Several authors have used Fourier inversion to compute prices of puts and calls, some using Parseval’s theorem. The expected value of max (S – K, 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.

Suggested Citation

  • Daniel Dufresne & Jose Garrido & Manuel Morales, 2009. "Fourier Inversion Formulas in Option Pricing and Insurance," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 359-383, September.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:3:d:10.1007_s11009-007-9049-z
    DOI: 10.1007/s11009-007-9049-z
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
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    Citations

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    Cited by:

    1. Adam W. Kolkiewicz & Fangyuan Sally Lin, 2017. "Pricing Surrender Risk in Ratchet Equity-Index Annuities under Regime-Switching Lévy Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 433-457, July.
    2. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
    3. Ackerer Damien & Vatter Thibault, 2017. "Dependent defaults and losses with factor copula models," Dependence Modeling, De Gruyter, vol. 5(1), pages 375-399, December.
    4. Alessandro Ramponi, 2016. "On a Transform Method for the Efficient Computation of Conditional V@R (and V@R) with Application to Loss Models with Jumps and Stochastic Volatility," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 575-596, June.
    5. Feunou Bruno & Tafolong Ernest, 2015. "Fourier inversion formulas for multiple-asset option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 531-559, December.
    6. Alessandro Ramponi, 2012. "Fourier Transform Methods For Regime-Switching Jump-Diffusions And The Pricing Of Forward Starting Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1-26.
    7. D. J. Manuge & P. T. Kim, 2014. "A fast Fourier transform method for Mellin-type option pricing," Papers 1403.3756, arXiv.org, revised Mar 2014.
    8. A. Cassagnes & Y. Chen & H. Ohashi, 2014. "Heterogeneous Computation Of Rainbow Option Prices Using Fourier Cosine Series Expansion Under A Mixed Cpu–Gpu Computation Framework," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 21(2), pages 91-104, April.

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