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On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisited

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  • Peter Carr
  • Michael Schroder

Abstract

The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding the financial relevance of its results. First, we show that the Geman and Yor Laplace transform is not that of an Asian option price, as reported in Geman and Yor and other papers. We nonetheless show how the Geman and Yor Laplace transform can be used to obtain the price of an Asian option. Second, we find that following Geman and Yor these Laplace transfoms are available only if the risk-neutral drift is not less than half the squared volatility. Using complex analytic techniques, we lift this restriction, thus extending the financial applicability of the Laplace transform approach.

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  • Peter Carr & Michael Schroder, 2001. "On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisited," Papers math/0102080, arXiv.org.
    • Handle: RePEc:arx:papers:math/0102080
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    Cited by:

    1. Rupak Chatterjee & Zhenyu Cui & Jiacheng Fan & Mingzhe Liu, 2018. "An efficient and stable method for short maturity Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(12), pages 1470-1486, December.
    2. Frank J. Fabozzi & Arturo Leccadito & Radu S. Tunaru, 2012. "A new method for generating approximation algorithms for financial mathematics applications," Quantitative Finance, Taylor & Francis Journals, vol. 12(10), pages 1571-1583, October.
    3. Cruz Báez, Domingo Israel & González Rodríguez, José Manuel, 2008. "Valoración de opciones. Un enfoque diferente," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 26, pages 341-362, Abril.

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