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On the Distribution of Cash Flows Using Esscher Transforms

Author

Listed:
  • D. Vyncke
  • M. J. Goovaerts
  • A. De Schepper
  • R. Kaas
  • J. Dhaene

Abstract

In their seminal paper, Gerber and Shiu (1994) introduced the concept of the Esscher transform for option pricing. As examples they considered the shifted Poisson process, the random walk, a shifted gamma process, and a shifted inverse Gaussian process to describe the logarithm of the stock price. In the present article it is shown how upper and lower bounds in convex order can be obtained when we use these types of models to describe the stochastic accumulation factors for a given cash flow.

Suggested Citation

  • D. Vyncke & M. J. Goovaerts & A. De Schepper & R. Kaas & J. Dhaene, 2003. "On the Distribution of Cash Flows Using Esscher Transforms," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(3), pages 563-575, September.
    • Handle: RePEc:bla:jrinsu:v:70:y:2003:i:3:p:563-575
    DOI: 10.1111/1539-6975.t01-1-00065
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    Cited by:

    1. Brenda López Cabrera & Martin Odening & Matthias Ritter, 2013. "Pricing Rainfall Derivatives at the CME," SFB 649 Discussion Papers SFB649DP2013-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Haruyoshi Ito & Jing Ai & Akihiko Ozawa, 2016. "Managing Weather Risks: The Case of J. League Soccer Teams in Japan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 877-912, December.
    3. López Cabrera, Brenda & Odening, Martin & Ritter, Matthias, 2013. "Pricing rainfall futures at the CME," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4286-4298.
    4. Gzyl, Henryk & Mayoral, Silvia, 2010. "A method for determining risk aversion functions from uncertain market prices of risk," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 84-89, August.

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