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Australian Asian options

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  • Manuel Moreno
  • Javier F. Navas

Abstract

We study European options on the ratio of the stock price to its average and viceversa. Some of these options are traded in the Australian Stock Exchange since 1992, thus we call them Australian Asian options. For geometric averages, we obtain closed-form expressions for option prices. For arithmetic means, we use dierent approximations that produce very similar results.

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Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 680.

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Date of creation: Feb 2003
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Handle: RePEc:upf:upfgen:680

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Web page: http://www.econ.upf.edu/

Related research

Keywords: Asian options; arithmetic average; geometric average; edgeworth expansion; lognormal distribution; gamma distribution;

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  1. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(4), pages 407-428.
  2. Peter Ritchken & L. Sankarasubramanian & Anand M. Vijh, 1993. "The Valuation of Path Dependent Contracts on the Average," Management Science, INFORMS, INFORMS, vol. 39(10), pages 1202-1213, October.
  3. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, INFORMS, vol. 46(8), pages 1116-1136, August.
  4. De Schepper, A. & Teunen, M. & Goovaerts, M., 1994. "An analytical inversion of a Laplace transform related to annuities certain," Insurance: Mathematics and Economics, Elsevier, vol. 14(1), pages 33-37, April.
  5. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
  6. Alziary, Benedicte & Decamps, Jean-Paul & Koehl, Pierre-Francois, 1997. "A P.D.E. approach to Asian options: analytical and numerical evidence," Journal of Banking & Finance, Elsevier, vol. 21(5), pages 613-640, May.
  7. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 10(3), pages 347-369, November.
  8. Klaus Sandmann & J. Aase Nielsen, 2002. "Pricing of Asian exchange rate options under stochastic interest rates as a sum of options," Finance and Stochastics, Springer, vol. 6(3), pages 355-370.
  9. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
  10. Merton, Robert C, 1975. "An Asymptotic Theory of Growth under Uncertainty," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 42(3), pages 375-93, July.
  11. Nielsen, J.A. & Sandmann, K., 1998. "Asian Exchange Rate Options under Stochastic Interest Rates: Pricing as a Sum of Delayed Payment Options," Discussion Paper Serie B 431, University of Bonn, Germany.
  12. Milevsky, Moshe Arye & Posner, Steven E., 1998. "Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 409-422, September.
  13. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, INFORMS, vol. 40(12), pages 1705-1711, December.
  14. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 449-473, June.
  15. Nielsen, J. A. & K. Sandmann, 1995. "The Pricing of Asian Options under Stochastic Interest Rates," Discussion Paper Serie B 323, University of Bonn, Germany, revised Dec 1995.
  16. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, Elsevier, vol. 11(5), pages 474-491, October.
  17. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
  18. Yor, Marc, 1993. "From planar Brownian windings to Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 13(1), pages 23-34, September.
  19. Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, INFORMS, vol. 42(6), pages 926-938, June.
  20. Bouaziz, Laurent & Briys, Eric & Crouhy, Michel, 1994. "The pricing of forward-starting asian options," Journal of Banking & Finance, Elsevier, vol. 18(5), pages 823-839, October.
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